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LRFD design of double composite box girder bridges

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Title:
LRFD design of double composite box girder bridges
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Book
Language:
English
Creator:
Patel, Purvik
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
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Subjects / Keywords:
Composite behavior
Innovative design
Steel bridges
Fatigue
Concrete
Dissertations, Academic -- Civil Engineering -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: Conventional continuous steel bridges only exhibit composite behavior in the positive moment region. Similar composite action may also be achieved in the negative moment region by casting a bottom concrete slab between the points of inflection. Such a section is referred to as "double composite" since it is composite in both the positive and negative moment regions. Savings in double composite bridges arise because expensive steel is replaced by inexpensive concrete to carry compressive loads. Although double composite bridges have been designed and constructed since at least 1978 there has been limited research. Thus, current designs rely on existing provisions for designing conventional 'single' composite bridges. This fails to fully exploit the advantages or recognize the weaknesses, if any, of double composite action. This thesis presents findings from a cooperative research project involving USF/URS/FDOT in which full-scale tests and theoretical analyses were carried to develop appropriate limit state rules for designing double composite bridges. A 4 ft. deep, 48 ft. long, 16 ft. wide box girder bridge representing the entire negative moment section at a support of a continuous full-size box girder bridge was fabricated and tested at FDOT's Structural Research Center, Tallahassee under fatigue, service and ultimate loading. Based on the findings from these tests and non-linear finite element analyses conducted by USF, URS proposed new design rules. This thesis focuses on the applications of these rules to develop a model design example for use by bridge engineers. The example was specifically selected from AISI so that a cost comparison with conventional design could be made. For completeness, an overview of the experimental results is also included in the thesis.
Thesis:
Thesis (M.S.C.E.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Purvik Patel.
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Title from PDF of title page.
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Document formatted into pages; contains 112 pages.

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aleph - 002069360
oclc - 608290302
usfldc doi - E14-SFE0003218
usfldc handle - e14.3218
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ABSTRACT: Conventional continuous steel bridges only exhibit composite behavior in the positive moment region. Similar composite action may also be achieved in the negative moment region by casting a bottom concrete slab between the points of inflection. Such a section is referred to as "double composite" since it is composite in both the positive and negative moment regions. Savings in double composite bridges arise because expensive steel is replaced by inexpensive concrete to carry compressive loads. Although double composite bridges have been designed and constructed since at least 1978 there has been limited research. Thus, current designs rely on existing provisions for designing conventional 'single' composite bridges. This fails to fully exploit the advantages or recognize the weaknesses, if any, of double composite action. This thesis presents findings from a cooperative research project involving USF/URS/FDOT in which full-scale tests and theoretical analyses were carried to develop appropriate limit state rules for designing double composite bridges. A 4 ft. deep, 48 ft. long, 16 ft. wide box girder bridge representing the entire negative moment section at a support of a continuous full-size box girder bridge was fabricated and tested at FDOT's Structural Research Center, Tallahassee under fatigue, service and ultimate loading. Based on the findings from these tests and non-linear finite element analyses conducted by USF, URS proposed new design rules. This thesis focuses on the applications of these rules to develop a model design example for use by bridge engineers. The example was specifically selected from AISI so that a cost comparison with conventional design could be made. For completeness, an overview of the experimental results is also included in the thesis.
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LRFD Design of Double Composite Box Girder Bridges by Purvik Patel A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Department of Civil and Environmental Engineering College of Engineering University of South Florida Major Professor: Rajan Sen, Ph.D. A.G. Mullins, Ph.D. William Carpenter, Ph.D. Date of Approval: July 2, 2009 Keywords: composite behavior, innovative d esign, steel bridges, fatigue, concrete Copyright 2009 Purvik Patel

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ACKNOWLEDGEMENTS Firstly, I would like to sincerely thank Dr. Rajan Sen for his support and guidance during my M.S. program at University of South Florida. This project could not be completed without his knowledge and insight. Dr. Rajan Sen was the s ource of inspiration and motivation throughout the project. I acknowledge Dr. Niranjan Pai for hi s assistance and support throughout the project. I would like to thank Florida Department of Transportation (FDOT) for supporting for supporting me in this project. This project could not be co mpleted without the help of Marc Ansley, P.E., Will Potter and Steven Eudy of Florida Depa rtment of Transportation. I would like to acknowledge the valuable input from Steven Stroh, P.E., and Dennis Golabek, P.E., and of URS Corporations. This project would not be possible without th e help of my colleagues and fellow students at USF. I would like to thank Julio Aguilar, Lori Elkins and Vladimir Simonovsky. I would like to thank Dr. William Carpenter and Dr. Austin Gray Mullins for serving on my committee. Finally I would like to thank my parents and my family members. They have always supported me in pursuing my education.

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i TABLE OF CONTENTS LIST OF TABLES ................................................................................................................ ....... iv LIST OF FIGURES ............................................................................................................... ....... v ABSTRACT ...................................................................................................................... ........... vi 1. INTRODUCTION ........................................................................................................... ..... 1 1.1 Overview ................................................................................................ ............... 1 1.2 Scope of Study .......................................................................................... ............ 2 1.3 Organization of Thesis ................................................................................. ........ 4 2. LITERATURE REVIEW ..................................................................................................... 5 2.1 Introduction ............................................................................................ ............... 5 2.2 Applications ............................................................................................ .............. 5 2.3 Experimental Research ................................................................................... ...... 7 2.4 Code Provisions ......................................................................................... ........... 8 3. OVERVIEW OF EXPERIMENTAL STUDY ................................................................... 10 3.1 Introduction ............................................................................................ ............. 10 3.2 Fatigue Test ............................................................................................ ............. 12 3.2.1 Test Parameters .......................................................................... ......... 13 3.2.2 Test Procedure ........................................................................... .......... 13 3.3 Service Test ............................................................................................ ............. 14 3.4 Fatigue Test Results .................................................................................... ........ 15 3.4.1 Deflection Under Fatigue Load ........................................................... 15 3.4.2 Slip ..................................................................................... ................. 17 3. 4.3 Strain in Concrete Under Fatigue Load .............................................. 17 3.4.4 Summary of Fatigue Test Results ....................................................... 19 3.5 Service I Test Results .................................................................................. ........ 20 3.5.1 Deflection Under Service I Load ........................................................ 2 0 3.5.2 Top Rebar Strain ......................................................................... ........ 22 3.5.3 Summary of Service I Test Results ..................................................... 23 3.6 Service II Test Results ................................................................................. ....... 23 3.6.1 Deflection Under Service II Load ....................................................... 2 4 3.6.2 Strain in Steel Under Service II Load ................................................. 25 3.6.3 Summary of Se rvice II Test Results.................................................... 28 3.7 Ultimate Test Results ................................................................................... ....... 28 3.7.1 Failure Mode ............................................................................. .......... 29 3.7.2 Deflection Under Ultimate Load ......................................................... 3 0 3.7.3 Strain in Concrete Under Ultimate Load ............................................ 31 3.7.4 Strain in Steel Under Ultimate Load ................................................... 32 3.7.5 Summary of Ultimate Load Test Results ............................................ 34

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ii 4. DESIGN RULES FOR DOUBLE COMPOSITE BRIDGES ............................................ 35 4.1 Introduction ............................................................................................ ............. 35 4.2 Single Composite Bridges ................................................................................ ... 36 4.3 Double Composite Bridges ................................................................................ 37 4.3.1 Contraflexure Points ..................................................................... ...... 37 4.4 Design Provisions for Double Co mposite Bridges ............................................. 39 4.4.1 Construction Sequence .................................................................... .... 40 4.4.2 Design Provisions ........................................................................ ....... 40 5. MODEL DESIGN OF A DOUBLE COMPOSITE BRIDGE ............................................ 43 5.1 Introduction ............................................................................................ ............. 43 5.2 Design Overview ......................................................................................... ....... 43 5.2.1 Design Steps ............................................................................. ........... 44 5.3 General Information and Geometry .................................................................... 45 5.4 Materials ............................................................................................... .............. 47 5.4.1 Concrete ................................................................................. ............. 48 5.4.2 Structural Steel ......................................................................... ........... 48 5.4.3 Steel Reinforcement ...................................................................... ...... 48 5.4.4 Shear Connectors ......................................................................... ....... 49 5.4.5 Miscellaneous............................................................................. ......... 49 5.5 Design Loads ............................................................................................ .......... 49 5.5.1 Dead Load ................................................................................ ........... 49 5.5.2 Live Load ................................................................................ ............ 51 5.5.3 Fatigue Load ............................................................................. .......... 51 5.6 Load Factors and Load Modification Factors ..................................................... 51 5.6.1 Load Factors ............................................................................. ........... 51 5.6.2 Load Modification Factors ................................................................ .. 52 5.7 Distribution Factors .................................................................................... ........ 52 5.8 Load Combinations ....................................................................................... ...... 53 5.8.1 Location of Inflection Points ............................................................ ... 54 5.9 Section Properties ...................................................................................... ......... 55 5.10 Plastic Neutral Axis ..................................................................................... ....... 56 5.11 Strength I Limit State ................................................................................... ....... 58 5.11. 1 Web Slenderness ........................................................................... ...... 58 5.11.2 Slab Ductility Requirement for Bottom Slab ..................................... 59 5.11.3 Compressive Stress in Concrete Slab ................................................. 60 5.11.4 Flexural Resistance of Steel Flanges .................................................. 60 5.12 Shear Design ............................................................................................. .......... 61 5.12.1 Nominal Shear Resistance of Unstiffened Webs .............................. 62 5.13 Shear Connectors ......................................................................................... ....... 63 5.14 Temporary Bracing of Bottom Flange ................................................................ 64 5.15 Material Cost Comparison ................................................................................. 65 5.16 Summary .................................................................................................. ........... 67 6. CONCLUSIONS AND RECOMMENDATIONS ............................................................. 68 6.1 Introduction ............................................................................................ ............. 68 6.2 Conclusions ............................................................................................. ............ 68 6.3 Future Work ............................................................................................. ........... 69 REFERENCES .................................................................................................................... ....... 70

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iii APPENDICES .................................................................................................................... ........ 72 Appendix A: Design of a Double Composite Box Girder Bridge................................ 73

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iv LIST OF TABLES Table 3.1 Test Program ..................................................................................................... ....... 11 Table 3.2 Fatigue Test Parameters .......................................................................................... 13 Table 4.1 Design Rules for Single Composite Bridges............................................................ 37 Table 4.2 Contraflexure Points for Different Load Cases ........................................................ 39 Table 4.3 Contraflexure Points for Different Span Ratios ....................................................... 39 Table 4.4 Design Rules for Double Composite Bridges .......................................................... 42 Table 5.1 General Information .............................................................................................. ... 46 Table 5.2 Geometry of Box Girder Section ............................................................................. 47 Table 5.3 Material Properties .............................................................................................. ..... 47 Table 5.4 Design Parameters ................................................................................................ ... 48 Table 5.5 Non-composite Dead Loads Per Box Girder ........................................................... 50 Table 5.6 Composite Dead Loads Per Box Girder ................................................................... 50 Table 5.7 Superimposed Dead Loads Per Box Girder ............................................................. 50 Table 5.8 Load Factors for Strength I and Fatigue .................................................................. 52 Table 5.9 Maximum Unfactored and Factor ed Moments at Interior Pier Section ................... 54 Table 5.10 Maximum Unfactored and Factored Shear at Interior Pier Section ......................... 54 Table 5.11 Section Properties of Non-co mposite and Composite Sections ............................... 56 Table 5.12 Forces in the Cross-section ...................................................................................... 57 Table 5.13 Cost Analysis of Materials Used in Negative Flexure Region for Single Composite Section .......................................................................................... ......... 65 Table 5.14 Cost Analysis of Materials Used in Negative Flexure Region for Double Composite Section .......................................................................................... ......... 66 Table 5.15 Cost Comparison of Double Composite Sections .................................................... 66 Table A.1 Unfactored and Distributed Moments for Single Box Girder .................................. 81 Table A.2 Factored Moments for Single Box Girder ................................................................ 82 Table A.3 Unfactored Shear for Negative Section in Kips ..................................................... 101 Table A.4 Factored and Distributed Shear for Negative Section in Kips ............................... 102

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v LIST OF FIGURES Figure 1.1 Typical Crosssection of Test Specimen .................................................................. 3 Figure 2.1 Typical Cross-section of Double Composite Bridge ................................................ 5 Figure 2.2 First Double Compos ite Bridge, Ciervana Bridge. ................................................... 6 Figure 2.3 Cross-section of St. John River Bridge, New Brunswick, Canada ........................... 7 Figure 2.4 Test Set-up and Slab Cracking in Double Composite Girder Test. .......................... 8 Figure 3.1 Test Set-up ..................................................................................................... ......... 11 Figure 3.2 Service Test Set-up ................................................................................................. 12 Figure 3.3 Deflection at Actuator End LVDT # 7 ................................................................... 16 Figure 3.4 Deflection at Actuator End LVDT # 8 ................................................................... 17 Figure 3.5 Strain in Bottom Concrete Slab on Hold Down Side SG 111 ................................ 18 Figure 3.6 Placement of Bottom Concrete Slab ....................................................................... 19 Figure 3.7 Deflection at Cantilevered End ............................................................................... 21 Figure 3.8 Longitudinal Deflection of Double Composite Box Girder ................................... 21 Figure 3.9 Strain in Top Slab Reinforcement on Actuator Side-I ............................................ 22 Figure 3.10 Strain in Top Slab Re inforcement on Actuator Side-II .......................................... 23 Figure 3.11 Deflection at Cantilevered End for Service II Load Test ....................................... 24 Figure 3.12 Longitudinal Deflection of Double Composite Box Girder for Service II ............. 25 Figure 3.13 Strain in Top Fl ange at Center Support .................................................................. 26 Figure 3.14 Strain in Bottom Flange on Hold Down Side ......................................................... 27 Figure 3.15 Comparison of Steel Strain of Fatigue and Service Test ........................................ 27 Figure 3.16 Failed Bottom Flange on Hold Down Side ............................................................ 29 Figure 3.17 Failed Bottom Concrete Slab on Hold Down Side ................................................. 30 Figure 3.18 Deflection at Cantilevere d End for Ultimate Load Test ......................................... 30 Figure 3.19 Longitudinal Deflection of Doubl e Composite Box Beam for Ultimate ................ 31 Figure 3.20 Strain in Conc rete in Failure Region ...................................................................... 32 Figure 3.21 Strain in Top Flange at Ce nter Support for Ultimate Load Test ............................ 33 Figure 3.22 Strain in Bottom Flange on Ho ld Down Side for Ultimate Load Test ................... 33 Figure 5.1 Typical Cross-section of Double Composite Bridge .............................................. 45 Figure 5.2 Typical Cross-section of Double Composite Box Girder ....................................... 46 Figure 5.3 Forces in the Cross-section ..................................................................................... 56 Figure A.1 Typical Cross-section of Bridge ............................................................................. 76 Figure A.2 Typical Cross-section of Box Girder ...................................................................... 76

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vi LRFD Design of Double Composite Box Girder Bridges Purvik Patel ABSTRACT Conventional continuous steel bridges only e xhibit composite behavior in the positive moment region. Similar composite action may also be achieved in the negative moment region by casting a bottom concrete slab between the points of inflection. Such a section is referred to as “double composite” since it is composite in both the positive and negative moment regions. Savings in double composite bridges arise because expensive steel is replaced by inexpensive concrete to carry compressive load s. Although double composite bridges have been designed and constructed since at least 1978 there has been limited research. Thus, current designs rely on existing provisions for designing co nventional ‘single’ composite bridges. This fails to fully exploit the advantages or recogni ze the weaknesses, if any, of double composite action. This thesis presents findings from a cooperative research project involving USF/URS/FDOT in which full-scale tests and th eoretical analyses were carried to develop appropriate limit state rules for designing double composite bridges. A 4 ft. deep, 48 ft. long, 16 ft. wide box girder bridge representing the entire negative moment section at a support of a continuous full-si ze box girder bridge was fabricated and tested at FDOT’s Structural Research Center, Tallaha ssee under fatigue, service and ultimate loading. Based on the findings from these tests and non-linear finite element analyses conducted by USF, URS proposed new design rules. This thesis focuses on the applications of th ese rules to develop a model design example for use by bridge engineers. The example was specifically selected from AISI so that a cost

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vii comparison with conventional design could be made. For completeness, an overview of the experimental results is also included in the thesis.

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1 1. INTRODUCTION 1.1 Overview Conventional steel bridges are designed to ta ke advantage of composite action between concrete and steel in the positive moment regi on. This idea can also be extended to “double composite” action by casting a bottom concrete slab in the negative moment region in continuous structures. Since concrete is continuously bonded to the steel, the need for bracing is eliminated thereby bringing about substantial cost savings. Moreover, since the weight of the bottom slab lowers the neutral axis, the depth of the web in compression is reduced and thinner web sections can be designed as compact with attendant benefits since the full plastic moment capacity can be realized. These advantages have the potential to make double composite girder bridges competitive in the 200-400 ft. span range. Though several double composite bridges have been designed and built in Europe, in particular Spain and Germany, there has been no similar interest in the United States in part due to a lack of design guidelines and uncertainty regarding the behavior of double composite steel bridges. In 2004, the Florida and US Department of Transportation initiated a 2-year cooperative research program study involving USF/URS/FDOT to develop appropriate design rules for double composite bridges on the basis of full-scale testing and non-linear analysis. This 2-year study became a 5-year study because of delays in fabricating the test specimen, updating Tallahassee’s testing facilities to accommodate the enormous load s needed to initiate failure (predicted as 1200 kips), getting forms for the top slab, scheduling the test and providing sufficiently strong sections to serve as an intermediate support.

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2 The design of the test specimen was carried out by URS. The instrumentation and test program was developed by USF with appropriate input from URS and FDOT. Data from the tests was electronically sent to USF for analysis. Following completion of USF’s analysis of the test results and Finite Element Analysis (FEA) results, URS proposed design rules for double composite sections. A non-linear Finite Element Analysis (FEA) was conducted to validate the experimental data. The analysis has taken l onger because the test data was anomalous; for example the top slab unexpectedly cracked under fairly low loads. This thesis focuses on the application of the LRFD design rules developed by URS. The model example selected is taken from the AISI manual since it allows designers to immediately recognize the changes in design and the bene fits of double composite construction. 1.2 Scope of Study The primary objectives of the research project was to evaluate the response of a double composite steel box bridge under fatigue, service an d ultimate loading, to develop LRFD design rules and a model design example to illustrate their application. Full-scale testing was intended to evaluate the applicability of existing LRFD provisions for the design of double composite sections and those parameters not addressed by the code. For example, loads on the bottom concrete slab are qu ite different from those on the top slab since they are not subjected to any lo calized wheel loads. Moreover, th e bottom slab is restrained by steel webs at its ends compared to the top slab where there is no similar restraint. The connection of the bottom slab to the stee l plate is through shear connectors over the entire width. This contrasts with the top slab which is attached to the steel flanges over a much narrower width. Whether the concrete strength and reinforc ement in the bottom slab should be the same as that for the top slab is not known. Since cost savings depend on the thickness of the bottom steel plate, construction issues relating to how it can support the weight of the wet concrete become important. Also, since the section is comp act, it can reach full plastic capacity; whether

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3 the steel reinforcement provided in the top slab wa s sufficient to resist the combined effect of shear from localized wheel loads when the top deck was completely cracked at full plastic capacity was a concern. The test section had to satisfy constraints im posed by the testing facilities. In particular, this dictated the maximum dimensions, the maximum load and the maximum number of parameters that could be instrumented. Based on these considerations, the entire negative section over a continuous support in a double composite box girder was designed. The overall length of the section was 48 feet, its depth of 4 ft. 10 in. and its width 16 feet. The top slab was 8 in. thick and the 6 feet wide bottom slab was 7 in. thic k bottom. High performance steel (HPS) was used for the fabrication of the steel box girder. The top steel flange was 1 in. thick whereas the bottom flange was only in. thick. The webs were each in thick (Fig. 1.1). The steel box was fabricated by Tampa Steel and shipped to Tallahassee where the top and bottom slabs were cast separately. Figure 1.1 Typical Cross-Section of Test Specimen Load, strain, deflection and slip data were recorded and analyzed to determine the behavior of the double composite box girder test specimen. The analysis of all the results was carried out at USF. Since the test results led to the formulation of the design rules, a brief Shear Studs Top flange Long. pitch = 16 Bottom flange Long. pitch = 23 Drawing not to scale 72 7” 16 1 74” 192 8 49

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4 overview of the results is presented in this thesis. The focus of this thesis is on the application of the newly developed design rules developed by URS. 1.3 Organization of Thesis A brief literature review on the state-of-the art on double composite box girder bridges is presented in Chapter 2. An overview of the results from the experimental study is summarized in Chapter 3. The design recommendations and critical issues pertaining to design are discussed in Chapter 4 and their application illustrated in Chapter 5. Conclusions and recommendations for future research are summarized in Chapter 6.

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5 2. LITERATURE REVIEW 2.1 Introduction Double composite steel bridges were built in Europe using prevailing design codes. However, information regarding their design is fairly limited. This chapter provides details on existing double composite steel br idges and on previous research. 2.2 Applications The term “double composite” refers to steel sections with concrete slabs in both the positive and negative moment regions as shown in Fig. 2.1. The addition of a concrete slab to the bottom flange raises construction issues and imposes additional load on the foundation. Nonetheless, costs can be lower making steel more competitive. Figure 2.1 Typical Cross-section of Double Composite Bridge Top slab reinforcement Top Slab Web Plate Top Flange Bottom Flange Bottom Slab

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6 Figure 2.2 First Double Composite Bridge, Ciervana Bridge. ( Courtesy J.M. Calzon ) The Ciervana Bridge (Fig. 2.2) is the first example of a double composite bridge [1]. The three span continuous bridge with spans of 40-50-40m was built in Spain in 1978. The crosssection consisted of rectangular or trapezoidal box sections fabricated using high strength steel. The concrete bottom slab was reinforced for resis ting torsion and its own weight in the transverse direction. It is not clear whether any longitudinal steel was provided to resist negative moments over the supports. Other examples of double compos ite bridges built in Spain include a bridge over A-7 highway [2], over Tremor river [3] and at Majadahonda [4]. In all these cases the cross section consisted of a single trapezoidal box section. Examples of the double composite bridges ma y also be found in Germany and Venezuela [2] and [3]. A five span bridge with a main span of 213.8 m and a total length of 478.8 m was constructed across the Caroni rive r at Ciudad at the Guyana/Venezuela border. The superstructure of the combined highway-railway bridge consiste d of a two cell box girder for the main span and the long spans whereas an I-girder with 3 webs w as used for the side span s. The thickness of the bottom slab varied from 85 cm at main pier to 20 cm at the intermediate pier. The thickness of top slab was 24 cm which was heavily reinforced (4.8 %). The design was based on the assumption that the bottom slab over the piers was cast first. Thus, the bottom slab acts compositely to resist the stresses due to weight of the steel structure, the top concrete slab and the applied loads [2].

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7 There are other examples of double composite bridges built in Germany [3-5]. These are largely descriptive and do not contain any details on their design. This is also the case for two double composite box bridges recently complete d over St. John and Jemseg Bridges on the Fredericton-Moncton Highway in Canada in 2001 [6 7]. Fig 2.3 shows the cross section of the Frederiction-Moncton Highway Bridge at mid span and at center support. Figure 2.3 Cross-section of St. John River Bridge, New Brunswick, Canada 2.3 Experimental Research A fatigue test was conducted in Germany to evaluate the fatigue performance of a high speed railway bridge. In the test, two 6.8 m long and 1.1 m deep girders were tested under negative moment. The girders were attached to a 120 cm 30 cm slab reinforced longitudinally with a reinforcement ratio of 2.5%. The slab cracked after 2.0 million cycles with the cracks evenly distributed at 15 cm. The maximum crack width did not exceed 7.8 mils (0.0078 inch). The tensile stresses in the reinforcement and the girder were smaller than the predicted values.

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8 Figure 2.4 Test Set-up and Slab Cracking in Double Composite Girder Test. [3] An ultimate load test was carried out that showed that the full plastic capacity of the girder was reached. “Perfobond” shear connectors were used to connect the slab to the girders. Fig. 2.4 shows the experimental test set-up used in Germany and the cracking observed in the top slab. This set up was used in our study. 2.4 Code Provisions The limited information available indicates that there are concerns relating to the reinforcement that is to be provided in the top slab in double composite applications. The bridge built in Venezuela used 4.8% steel whereas the German railway bridge used 2.5%. The prevailing LRFD provisions in AASHTO require a reinforcement ratio of 1% with two-thirds of the rebars placed in the top layer and the remaining one-third in the bottom layer. The Spanish code [8] incorporate provisions for designing double composite slabs. For the design of reinforced slabs supported on tr ansverse members, this states: “When the deck slab is supported on steel, c oncrete or composite transverse members, it is necessary to analyze, in the area of negative be nding, the combined effect of shear stress in the slab caused by external loading and tensile stress due to the general bending of the slab. In thin

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9 slab and where there is no shear reinforcement this effect may be decisive; and it will be necessary to guarantee the slab strength by testing, as at present the standards do not include realistic values of resistance to shear stre ss for high qualities of longitudinal reinforcement. In order to control cracking, a minimum qua ntity of 1 % should be allowed, limiting the characteristic width of cracking to 0.2 mm under normal conditions.”

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10 3. OVERVIEW OF EXPERIMENTAL STUDY 3.1 Introduction A brief review of the publis hed literature showed that a number of double composite bridges have been built primarily in Europe us ing prevailing codes. However, it was not known whether their provisions were valid or whether they took full advantage of the benefits offered by this type of design. In view of this, full-scale tests were conducted to evaluate the response of a double composite box girder section under different loadings and also to validate and develop LRFD provisions of the AASHTO specifications for the design of double composite bridges. A full-scale box girder test specimen 48 ft. long, 16 ft. wide, 4 ft 10 in. deep representing a section of a bridge between infl ection points was tested under fatigue, service and ultimate loads. The specimen was designed to be supported at the middle; however, this was not possible. As a result, it was asymmetrically suppor ted with spans of 23 ft. and 25 ft. The load was applied at the free end of the longer span while a hold down frame prevented movement at the other end. Thus, the entire section was subjected to negative moments, see Fig 3.1 and 3.2. Table 3.1 summarizes the test program. As noted earlier, the fabricated steel box was shipped to Tallahassee where the top and bottom slabs were cast separately. The 16 feet wide top slab was 8 inches thick while the 6 feet wide bottom slab was 7 inch thick. Composite action was ensured through shear connectors welded to the top and bottom flanges of the box.

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11 Table 3.1 Test Program Description Load (kips) Criteria Critical Fatigue 5-105 5.65 million cycles Slip, changes in stiffness Service I 421 0.6 Fy stress in rebar Crack width, stresses in rebar, steel and concrete, and deflections Service II 638 0.95 Fy in top steel flange based on Grade 50 steel Crack width, stresses in rebar, steel and concrete, and deflections Service III 894 0.95Fy in top steel flange based on HPS (F y = 70 ksi) Crack width, stresses in rebar steel and concrete and deflections Ultimate 1200 AASHTO Failure Mode, Ductility Figure 3.1 Test Set-up Load cells, LVDTs and strain gages were u sed to monitor the response of the test specimen. A total of 162 channels were used initia lly of which 140 were set aside for the fatigue test. In essence, two cross-sections distant h (the full depth of the section including the slab is 4 ft. 10 in.) were fully instrumented to allow determinat ion of the strain variation in the cross-section and the position of the neutral axis. Additionally, 32 rebars in the top slab 1 ft away from the center support on either span were instrumented. Slip was monitored in the top and bottom slabs at both the hold and actuator ends with deflections measured along the entire length of the member at the supports, quarter point and the loaded end. 23' 0 25' 0 Hold Down Frame Actuator Top Slab Bottom Slab Bearing Center Support

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12 Figure 3.2 Service Test Set-up However, the first application of the fatigue load that varied from 5 to 105 kips resulted in unexpected cracking of the top slab. This dest royed all 17 strain gages that were bonded to the top concrete surface. As a result, 123 channels were monitored for the fatigue test and 145 channels for the service and ultimate tests. 3.2 Fatigue Test The fatigue test was conducted as there was no prior experimental data available on the performance of double composite bridges under fati gue loading. This was particularly the case because of the thin ( in.) bottom steel flange used. The we lding of shear studs to such a thin bottom plate can induce deformation and localized stresses that may be unfavorable under fatigue loading. The intent of the test was to verify the AASHTO LRFD provisions for the design of shear connectors and to document the performance of stud shear connectors in the negative flexure region. Hold Down Frame End Hold Down Frame Actuators Actuator End Center Support West East

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13 3.2.1 Test Parameters The key parameters in the fatigue testing were the load range, the frequency and the number of fatigue cycles. The load range was decided by the capacity of the fatigue testing system (110 kips). For this reason, the load range was limited to 100 kips and varied from 5 kips to 105 kips. The fatigue load was applied at the free end as shown in the test set-up. The predicted fatigue cycles were calculated based on this load ra nge in accordance with the Article 6.10.10.2-2 of AASHTO LRFD specifications as 5.65 million cycles. The calculations were adjusted to take into account the asymmetric test set-up and the actual strength of the concrete measured just prior to the testing (Table 3.2). Table 3.2 Fatigue Test Parameters Parameter Fatigue Test Load Range 5-105 kips Frequency 1.16 Hz Number of Cycles 5.65 million Concrete strength Top slab Actuator span 9905 psi Hold down span 7590 psi Bottom slab 8178 psi The frequency was selected to be 1.16Hz. This meant that 100,000 fatigue cycles were completed over 24 hours of continuous testing. 3.2.2 Test Procedure The fatigue test was carried out after comple tion of two static tests to provide baseline measurements. In these tests, the specimen was load ed to 105 kip at the rate of 1 kip/sec and all measurements recorded. Following completion of these tests, the inst rumentation was zeroed out and the load range set from 5 to 105 kips. The fatigue test was then initiated at a frequency of 1.16 Hz by the

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14 means of the hydraulic load actuator under electroni c feedback control operating in a load control mode. The fatigue loading was interrupted periodi cally and a static cycle applied between the minimum and maximum load to monitor response. Ten measurements were taken at approximate 0.5 million intervals with the last one at the end of the test. Since results overlapped, not all 11 static cycles are plotted; only selected cycles ar e presented in the results of the fatigue test. 3.3 Service Test The top concrete slab was designed based on LRFD provision of AASHTO specifications with the longitudinal reinforcement ratio set at 1% It may be noted from the previous chapter that a very large reinforcement ratio (in one case as hi gh as 4.8 %) was used in the top concrete deck in a previously built double composite railway bridge [3]. It was not known whether a higher limit was necessary although compact double compos ite sections can support higher loads than conventional composite bridges. Tests were therefore conducted to evaluate three AASHTO specified service loads, referred to as Service I, Service II and Service III (Table 3.1). Critical parameters in these tests were the stresses in the rebar, stresses in the concrete and steel, and the maximum crack width (Table 3.1). Under Service I, the stresses in the rebar were targeted to 0.6fy. Service II loads were targeted to 0.95Fy in the top steel flange, with Fy taken as 50 ksi. This was intended to represent performance of normal grade structural steel. The final service load test, Service III targeted the stress in the top steel flange at 0.95Fy with Fy taken as 70 ksi to represent the high performance steel (HPS) used for the specimen. The loads co rresponding to these three service conditions were respectively 421 kips, 638 kips and 894 kips. In each series, the loads were planned to be applied and released a total of five times. A final ultimate load test corresponding to a 1200 kip load was planned following the conclusion of the service tests. However the ultim ate load test was not conducted because of failure in the bottom steel flange that occurred in the first cycle of the service III load case. For

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15 this reason, this test is referred to as the ultimate load test in this thesi s. It was evident from the buckling failure that there was reduction in stiffn ess of the test-specimen during fatigue test. 3.4 Fatigue Test Results As stated earlier, the fatigue test was in tended to evaluate the performance of shear connectors that ensured composite action for the bottom slab. Loss of composite action could be detected from slip measurements of both the top and bottom slabs. The results from the test that are significant are (1) deflection at the cantilevered end and (2) slip at the respective actuator and hold dow n ends. However, since the bottom steel plate failed prematurely in buckling in ultimate test, the strain profile in the concrete and steel close to the center support became important as well. Of these 11 cycles, the fatigue results are presented only for the 1st static cycle, 0.5 million, 1.5 million, 3.0 million, 4.9 million and 5. 65 million cycles. The location of the relevant sensors is indicated in all the plots. 3.4.1 Deflection Under Fatigue Load The deflection at free end is the most critical deflection since it is the largest and was used for evaluating the effects of the fatigue loading. Fig. 3.3 and 3.4 shows the deflection at the cantilevered end measured by LVDTs # 7 and # 8. The results for 0.5 million and 3 million cycles in Fig. 3.3 are anomalous since they are not reproduced in Fig. 3.4. This is proba bly due to instrumentation problems. The deflection profile in Fig. 3.3 indicates that the maximum deflection was 0.65 in. after the 1st static test (the predicted deflection from si mple cracked beam analysis was 0.56 in.) and progressively increased to 0.78 in. after completion of 5.65 million cycles. Thus, there is approximately a 17 % reduction in stiffness of the section. The progressive increase in deflection

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16 suggests an overall stiffness reduction caused by additional cracking of the top and bottom slabs. This is confirmed by the st rain data shown later. Figure 3.3 Deflection at Actuator End LVDT # 7

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17 Figure 3.4 Deflection at Actuator End LVDT # 8 3.4.2 Slip The relative horizontal movement between the c oncrete and the steel interface at both the loaded and the hold down ends were monitored throughout the testing. No slip was recorded at either ends for both the top and bottom slabs. 3.4.3 Strain in Concrete Under Fatigue Load The strain in concrete in the bottom slab was monitored at the section located 4 ft. 10 in. from the center support on either side. Although the applied load was we ll within the elastic limit, the strain variation observed in the c oncrete was non-linear. The non-linearity in the concrete strain can be caused by secondary effects ot her than loading e.g. restraint at its ends by the steel webs, differential shrinkage, temperature difference etc.

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18 The concrete strain variation in Fig. 3.5 indicates a change in the response after 1.5 million cycles. There is a marked reduction in th e stiffness at low loads (upto 30 kips) followed by increased stiffness in the range from 30-50 kips after which the stiffness remains constant. This kind of behavior of concrete was not expected. The placement of concrete blocks (6 in 6 in 6 in.) at 4 ft on centers during the casting of the bottom slab may be the possible reason for such behavior in the concrete (Fig. 3.6). Sim ilar profile of strain was not observed on the corresponding actuator side and corresponding st rain gage located on the symmetric flange location (not presented in this thesis). Figure 3.5 Strain in Bottom Concrete Slab on Hold Down Side SG 111

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19 Figure 3.6 Placement of Bottom Concrete Slab 3.4.4 Summary of Fatigue Test Results 1) The fatigue test was conducted over a load ra nge of 100 kips which is significantly lower than the cracking load of 154 kips; still the top slab cracked. This could be possibly due to the weaker concrete mix on the hold dow n side. The maximum crack width recorded on the top concrete slab was of 7 mils. 2) It can be concluded from the deflection data that there was a 17 % reduction in stiffness of the test-specimen. 3) Strain data in the concrete suggest a reduc tion in stiffness at low loads. This may be because of possible debonding of the botto m flange and bottom slab and secondary effects like restraint by the webs, shrinkage and presence of concrete blocks (Fig 3.6). 4) The strain in the top slab reinforcement 1 ft away from the center support in either span increased by 25% increase signifying that ther e was additional cracking in the concrete. 5) The strain variation in the web of the cross-section indicated a lowering of the neutral axis after completion of the fatigue test. This again indicated cracking in the top slab so that a larger area was required to support the same force.

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20 3.5 Service I Test Results The stress in the top slab rebars was limited to 0.6fy for Service I load test. The maximum load required to develop this stress was 421 kips The load was applied and removed for 5 times and the loading rate was 1 kip/sec. The most important results for this test were the deflection and strain developed in the rebars. The analysis of the slip data indicated that there was no slip recorded at the either end of the test specimen. 3.5.1 Deflection Under Service I Load Deflections were recorded at the cantilevered end, close to center support (2 ft. in.) on either side and along the length of the beam. Th e deflections close to the center support on hold down side are critically important because of the buckling failure that occurred in the ultimate load test. Fig. 3.7 shows the plot of the deflection r ecorded at the cantilevered end. The average maximum deflection of 3.1 in. was recorded with the load of 421 kips. This is significantly (39%) greater than the prediction of 2.25 in. obtaine d from a simplified cracked beam analysis. The increase in deflection suggests additional cracking in the concrete. Fig 3.8 shows the longitudinal deflection profile at 100 kip intervals recorded along the length of the beam. The portion of the profile highl ighted with circle indicates the out of plane bending of the bottom flange. The profile indicates temporary out of plane bending of the bottom flange close to center support on hold down si de. This was probably due to debonding of the concrete and steel (Fig. 3.6).

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21 Figure 3.7 Deflection at Cantilevered End Figure 3.8 Longitudinal Deflection of Double Composite Box Girder

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22 3.5.2 Top Rebar Strain Strain in the rebars was monitored at 1 ft from center support in either span. The strain was recorded in 16 rebars on either side of the center support. Since all the 16 gages could not be included in single plots, the results for the eight ga ges are presented in Fig. 3.9 and Fig. 3.10. The applied moment on the actuator side was higher because of the asymmetric test set-up. Static moment on the actuator side was 10,104 kip-ft. and on the hold down side, 10067 kip-ft. Therefore, the results presented are fo r rebars located in the actuator span. In this test, the stress in top slab rebars was limited to 0.6fy. Fig. 3.9 and Fig. 3.10 show the straight line corresponding to maximum strain of 1241 which corresponds to the limit of 0.6fy in the rebars. The highest strain was reco rded in the rebars placed over the web exceeded the stipulated limit of 1241 This was the case because of shear lag effects. However the average stress in rebars in either hold down span and actuator span was found to be 36 ksi and 33 ksi respectively. Figure 3.9 Strain in Top Slab Reinforcement on Actuator Side-I

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23 Figure 3.10 Strain in Top Slab Reinforcement on Actuator Side-II 3.5.3 Summary of Service I Test Results 1) The maximum deflection recorded at the cantilevered end was 39 % higher than the theoretically calculated value. 2) The deflection close to center support suggest localized distortion in steel plate(Fig. 3.6). 3) The strain data validates the AASHTO’s provision of 1 % steel for top concrete slab. The average stress recorded in the rebars was 36 ksi and 30 ksi in actuator and hold down span respectively. 3.6 Service II Test Results The only change made in the service II load test was the maximum load was increased from 421 kips to 638 kips, rest all the test parame ters and instrumentation were kept same. This load corresponded to the condition where the st ress in the flange was limited to 0.95Fy with Fy

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24 taken as 50 ksi, that is 47.5 ksi. The results re ported for the Service II load case are deflection and strain variation in steel top flange and bottom flange. 3.6.1 Deflection Under Service II Load The maximum deflection recorded at the can tilevered end was 4.72 inch. Fig 3.11 plots the variation of deflection with load for the senso rs located at the free end. The overlapping of deflection profile indicates the absence of any torsio n effects. The actual recorded deflection is 38 % higher than the predicted deflection of 3.4 in. Fig. 3.12 shows the variation in the aver age deflection of the box specimen along its length for loads ranging 100 to 638 kips. A discontinuity close to the support (2 ft. in.) is observed in the hold-down span suggesting localized distress. Figure 3.11 Deflection at Cantilevered End for Service II Load Test

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25 Figure 3.12 Longitudinal Deflection of Double Composite Box Girder for Service II 3.6.2 Strain in Steel Under Service II Load The stress in steel top flange was limited to 0.95Fy in this test. For this reason, the results for the top flange steel strain at the center support are plotted (gages 73, 74) in Fig. 3.13. The strain variation with the applied load is linear. The maximum recorded strain was 1603 which corresponds to a calculated stress of 0.93Fy for Grade 50 steel, close to the targeted 0.95Fy stress.

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26 Figure 3.13 Strain in Top Flange at Center Support The strain was also recorded in the bottom flange on the hold down side and actuator side at 4 ft. 10 in. from the center support. The strain recorded on the hold down side (gage 122 – 125) is presented herein because of the unusual r esponse of the steel bottom flange. Fig. 3.14 shows the variation of strain recorded with th e applied load in the bottom flange on hold down side. The gage positioned in the center (gage 124) shows the unusual response compared to the gages located at the same location. The strain reverses from compression to tension after 150 kips of load. This trend is not repeated for the tw o gages located over the web (123, 125). For these gages, the response is non linear but similar. Ho wever the calculated stress on the hold down side exceeded the nominal yield value of 50 ksi as th e maximum recorded strain in gage 125 was 1754 which exceeds the yield strain of 1638

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27 Figure 3.14 Strain in Bottom Flange on Hold Down Side Figure 3.15 Comparison of Steel Strain of Fatigue and Service Test

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28 The strain recorded in the service II load test was compared with the fatigue test, service I and 1st cycle of service II load case. Fig 3.15 compares the strain variation in gage 125 on hold down side for the fatigue and for 1st and 5th cycle of Service I and II. Again, this suggests that there was some degradation of the specimen unde r service II loading. The repetitive loading of same magnitude is causing dama ge to the test-specimen. 3.6.3 Summary of Service II Test Results 1) The maximum recorded deflection was 38 % hi gher than the estimated deflection. The longitudinal deflection profile inidcates the localized distortion in bottom flange close to center support (2 ft. in.) on hold down side (see Fig 3.12). 2) The strain recorded in the top flange is within the 0.95Fy (47.5 ksi) limit (see Fig 3.13). Strain recorded for the bottom flange was nonlinear and exceeded the targeted value (see Fig. 3.14). 3) Comparison of strain with fatigue and service I load test reveals that there is reduction in stiffness of specimen due to increased strain in bottom plate on hold down side. Fig. 3.15 also indicated that repetitive loading is responsible for loss in stiffness. 3.7 Ultimate Test Results The last service test was designed to evalua te the response when the applied load (894 kips) corresponded to the stress of 0.95Fy (66.5 ksi) in Grade 70 steel. The test was to be conducted in the same manner as the previous two service test and instrumentation would remain unchanged. The intent of this test was to determine ser vice response when the stress in the steel flanges reached 0.95Fy or 66.5 ksi. Results are presented for deflection, concrete/steel strains at critical locations.

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29 3.7.1 Failure Mode The specimen failed in compression mode due to buckling of the bottom flange close to center support on hold down side. The specimen fail ure occurred when the lo ad was sustained at 894 kips for the inspection of cracking on top sl ab. Immediately following the failure the load dropped to 394 kips. Since buckling is not possible if the flange were continuously bonded to the concrete bottom slab, failure was inevitably initia ted due to debonding of the concrete. Also the confining of the bottom concrete slab was responsible for the endured failure. Fig 3.16 shows the buckled bottom flange close to center support in the hold down span. The buckled flange extended transversely over al most its 6 ft width and between the first and second shear connectors lines (11 in. and 34 in. from the center support) in the longitudinal direction. Fig 3.17 shows more picture of the failed bottom slab. Figure 3.16 Failed Bottom Flange on Hold Down Side Failed Bottom Flan g e

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30 Figure 3.17 Failed Bottom Concrete Slab on Hold Down Side 3.7.2 Deflection Under Ultimate Load The maximum deflection was measured at the cantilevered end. The maximum recorded deflection at the cantilevered end was 7.75 in. whic h is 38 % higher than the estimated value of 4.78 in. Fig. 3.18 shows the variation of deflect ion with load at the cantilevered end. The deflection profile is almost linear. Figure 3.18 Deflection at Cantilevered End for Ultimate Load Test Exposed Rebar Near Center Support Failure Region on Hold Down Side

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31 Fig. 3.19 shows the variation in the deflec tion along its length with increasing load. The deflection profile indicates the damage to botto m flange close to center support on hold down side. This is partly due to reduction in stiffness because of fatigue loading, shrinkage cracking, localized distortion and other factors. The failure load of the specimen was 894 kips Structure response clearly indicates that loads were still transferred despite the serious dist ress in the thin bottom flange. In this sense, the resistance mechanism in the double composite sec tion follows the well known tension field action in which webs are able to support shear even after they have buckled [8]. Figure 3.19 Longitudinal Deflection of Doubl e Composite Box Beam for Ultimate 3.7.3 Strain in Concrete Under Ultimate Load Strain in the bottom concrete slab was mon itored on either side of center support (4 ft. 10 in.). Unfortunately there was no strain gage pr ovided in the failure region. Fig. 3.20 shows the variation in strain with load in the two gag es (#109, 111) closest to the failure location on the hold down side. The variation is initially non-lin ear but is largely linear subsequently. The concrete underwent stress rever sal from tension to compression at low loads in gage 109. The

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32 maximum stress of 0.6f'c was recorded in gage 111. This cl early indicates that the failure mode was complex. Figure 3.20 Strain in Concrete in Failure Region 3.7.4 Strain in Steel Under Ultimate Load The most critical section is located 4 ft 10 in. from center support on the hold down side. Unfortunately there was only one transverse st rain gage located in the failure region. Fig. 3.21 plots the variation in strain developed in the top flange at the location of the maximum moment at the center support. The top flange began to yield at 680 kips and the maximum recorded strain was 3500 The behavior of the bottom flange is more complex. No transverse strains were recoded by gage 122. The variation of stra in with load for the three gages (123-125) located at the exterior surface of the bottom flange 4 ft 10 in. from the center support in the hold down span is shown in Fig. 3.22. The maximum compressive strain occu rs at the web/flange intersection measured by

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33 gages 123 (2292 ) and 125 (2414 ). The response of these gages is somewhat non-linear with a discontinuity at a load of 638 kips. Figure 3.21 Strain in Top Flange at Center Support for Ultimate Load Test Figure 3.22 Strain in Bottom Flange on Hold Down Side for Ultimate Load Test

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34 A similar discontinuity was recorded by gage 124. The strain in this gage started as compressive but changed to tensile at around 150 kips. Subsequently, it continued as tensile reaching a maximum value of around 600 This reversal signifies localized bending stresses caused by separation of the concrete surface from the bottom plate. 3.7.5 Summary of Ultimate Load Test Results 1) The specimen failed in the very first minute under the sustained loading close to center support on hold down side (Fig. 3.16-3.17). The failure was compression failure. 2) The bottom concrete slab crushed in the fa ilure region following buckling of the bottom flange. Deflection data suggested localized di stress of bottom flange in the failure zone. 3) The stress in top slab rebars exceeded th e yield point in 27 of the 32 rebars. 4) Strain data recorded for concrete and steel was non linear. The top flange yielded at a load of 680 kips. 5) The maximum strain in the bottom flange at maximum load was 0.95Fy. The strain in the bottom flange exceeded the yield point after th e failure of the bottom concrete slab. Since there was only one strain gage (in the transverse direction) in the critical region, there was no strain data available for the failed region. Other gages attached to the bottom flange did not provide conclusive evidence.

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35 4. DESIGN RULES FOR DOUBLE COMPOSITE BRIDGES 4.1 Introduction Prior to testing, there were concerns about the reinforcement that had to be provided in the top slab. There was also a belief that sections at the support would be compact and reach full plastic moment capacity at ultimate. The test results indicated that the concerns regarding the top slab steel reinforcement ratio were unfounded. On the other hand, the expectation that the composite bottom slab would reach full plastic cap acity was proven to be incorrect because the shear connectors designed to current AASHTO specif ications were ineffective at higher loading. The evidence from the testing was overwhelmi ng and indicated localized separation of the concrete from the steel at relatively low loads. In the light of these findings, URS proposed changes to current provisions to allow the design of double composite sections. In their propo sed rules, the stresses in the bottom slab are limited to 0.6fy at ultimate. Additionally, there is a du ctility requirement in terms of limits on the location of the neutral axis. There is no criterion for selecting the minimum thickness of bottom flange. However the bottom flange shoul d be checked for the buckling failure. Aside from these provisions, the design of doubly composite sections is very similar to that of conventional single composite sections This chapter summarize s the design rules for double composite bridges based on the experimental results.

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36 4.2 Single Composite Bridges A ‘single’ composite bridge refers to steel bridges with concrete slab decks in which composite action is limited to the positive mome nt region. Composite action is ensured by welding stud shear connectors to the steel flange that minimizes slip between the slab and the steel beam under loads. Unshored construction is typically used. This means that the steel beam alone supports the dead load of the slab while superimposed dead and live load are supported by composite action. The composite section comprises the steel section and an effective width of the concrete slab. Stress analysis utilizes transformed section based on modular ratios that are adjusted to account for stresses due to sustained loads. Ultim ate load analysis, however, is based on the nominal material properties of concrete and steel. Composite bridges are designed in accordance with Article 6.10.1.1 and 6.11.7.1 of the LRFD guidelines of the AASHTO specifications. Shear connectors conform to Article 6.10.10 and 6.11.10 of the LRFD guidelines. Table 4.1 summa rizes these rules for designing single composite box girder and I-sections.

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37 Table 4.1 Design Rules for Single Composite Bridges No. Design Rules for Single Co mposite Section LRFD Articles 1. General Dimensioning and Detailing of Bridge Section Straight I – Sections Straight Box Sections 6.7 6.7.4.2 6.7.4.3 2. Design Load and Load Combination Dead Loads Live Load Fatigue Load Load Factors and Load Combination 3.5 3.6 3.6.1.4 3.4 3. Structural Analysis and Evaluation of Bridge Superstructures Live Load Lateral Distribution Factors 4.6 4.6.2.2 4 Cross-Section proportions for I – Section and Box Section 6.10.2 and 6.11.2 5. Non-Composite and Composite Section Properties Article 6.10.1.1 6. Plastic Moment Capacity Article D6.1 7. Limit States Service Limit State Fatigue Limit State Strength Limit State 6.10.4 and 6.11.4 6.10.5 and 6.11.5 6.10.6 and 6.11.6 8. Flexure Resistance Composite Section in Positive Flexure Non-composite and Composite Section in Negative Flexure 6.10.7 and 6.11.7 6.10.8 and 6.11.8 9. Shear Resistance 6.10.9 and 6.11.9 10. Shear Connectors 6.10.10 and 6.11.10 4.3 Double Composite Bridges In continuous bridges, the concrete deck slab is cracked in the negative moment region over the support and therefore any composite action is limited to the contribution of the reinforcing steel. Since concrete can support comp ressive loads more effi ciently than steel, the structure can be made composite in the negative moment region by casting a bottom concrete slab between the points of contraflexure. 4.3.1 Contraflexure Points The point of contraflexure refers to the zero moment location in continuous structures. Its location in a structure is not fixed since it depends on many factors such as the type of deck, span geometry, relative stiffness of the spans and loading. The maximum contraflexure length is

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38 relevant in design since this is the length wh ere the steel compression flange needs to be continuously braced so that the cross-section is compact. Design moments in bridge structures are controlled by loading consisting of a combination of truck and lane loads. The location of the point of contraflexure for such loading can only be accurately determined from appropriate numerical analysis. However, for continuous beams with the same stiffness and the same lengt h, information on the contraflexure location may be readily found, e.g. AISC handbook. Table 4.2 summarizes information from th e AISC handbook for 3-span and 4-span structures of the same span and stiffness under pa ttern loading [10]. Inspection of this table indicates that the largest distance corresponds to lo ading of adjacent spans (0.23L, 0.24L) and the smallest where alternate spans are loaded (0.10L 0.10L). In design, the higher value, that is 0.24L will be used. In general, contraflexure le ngths will be greater under distributed load than concentrated loaded. Because moments are highest at the first support, it is customary for the end spans to be made shorter so that moments are equalized. The optimal ratio between the interior to the end span falls in the range 1.2 to 1.4. Table 4.3 su mmarizes information on the location of the point of contraflexure for this case. Information summarized in Table 4.3 is from the web resource [11]. Based on Table 4.2 the length of the distance of contraflexure point from interior support can be generalized to 0.30L, considering the optimum span ratio is in the range of 1.2 to 1.4.

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39 Table 4.2 Contraflexure Points for Different Load Cases Load Pattern Number of Spans Contraflexure point from Interior Support Maximum Negative Moment (adjacent spans loaded) 3 0.23L Maximum Positive Moment (alternate spans loaded) 3 0.10L Dead Load (all Span Loaded) 3 0.20L Maximum Negative Moment (adjacent spans loaded) 4 0.24L Maximum Positive Moment (alternate spans loaded) 4 0.10L Uniformly Distributed Load (All span Loaded) 4 0.21L Note: L denotes the length of the span. Table 4.3 Contraflexure Points for Different Span Ratios Number of Spans End Span Main Span Ratio of Main span to End Span Location of Contraflexure Point from Interior Pier 3 50 50 1.0 0.20L 3 50 55 1.1 0.22L 3 50 60 1.2 0.243L 3 50 65 1.3 0.271L 3 50 70 1.4 0.302L 3 50 75 1.5 0.336L 3 50 80 1.6 0.375L 3 50 85 1.7 0.41L Note: L denotes the length of the end span. 4.4 Design Provisions for Double Composite Bridges One of the main attractions for using double co mposite construction is that it is designed using the same provisions as single composite girders. The double composite sections should also be checked for the same fatigue, service and strength limit state criteria as the single composite bridges. As with the design of the single compos ite structure, the steel beam supports the dead load of the slab in unshored construction. In this case, however, there are two slabs one at the bottom over the supports and the deck slab; since it is possible to cast either slab first, the design steps will depend on how the bridge is constructed. Ho wever, as a practical matter of access, it is more convenient to cast the bottom slab first and af ter it has cured, the top deck slab can be cast.

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40 4.4.1 Construction Sequence The construction of double composite bridges is s lightly different compared to that of the single composite bridges. Several additional step s are necessary for the construction of steel box girders in the field. The construction sequence fo r the double composite bridges is listed below. 1) The box section and I–section should be fabricated in the shop as single composite section. The shear connectors on the bottom flange should be installed during the fabrication. Temporary bottom flange bracing should also be bolted during the fabrication of steel section. Temporary bracing is requi red to support bottom concrete slab. Also install guide rails for screeding the bottom conc rete slab using the bolted and/or welded connections. 2) Once the structural steel is received on the fi eld, the erection of structural steel is dependent on the placement of the bottom concrete slab. 3) The reinforcement for the bottom concrete slab should be first. Once the reinforcement is in place, bottom concrete slab can be placed and screeded to the designed thickness. 4) Remove the temporary bracing after the bottom slab cures. 5) Top slab shall be casted after the bottom slab h as hardened. The self weight of top slab is supported by the composite bottom flange in th e negative flexure region. Continue with the normal bridge construction. 4.4.2 Design Provisions The design provisions for the double composite box girder section are summarized in this section. These are based on experimental resu lts and non-linear FEM analysis. These rules presented only pertain to the desi gn of negative flexure section; the design of the positive section is same as that for single composite bridges. As noted already, the same design provisions of the LRFD guidelines for the design of single composite section should be followed fo r the design of double composite sections. The

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41 detailed rules in the design of double composite sect ions are listed in Tabl e 4.4. However, some additional rules are necessary because of the additi on of the bottom concrete slab in the negative flexure region. These are listed below. 1) Determination of “point of contraflexure” for the placement of bottom slab. The points of contraflexure should be determined by using appropriate numerical analysis. In general, based on the ratio of interior span to exterior span, the distance from the interior pier to inflection point can be maximized to 0.3L for optimum span ratio of 1.2–1.4, where L is the length of the end span. 2) The maximum longitudinal compressive stress in the bottom slab at the strength limit state, determined as specified in AASHTO Article 6.10.1.1.1d, should not exceed 0.6f c. 3) Reinforcement ratio of 1% is with two-thir ds placed in the top layer as per prevailing LRFD provisions is adequate for the top slab reinforcement. It may be noted from the literature review that in some cases, the rein forcement ratio considered for the top slab was as high as 4.8%. However, from the experi mental results it is concluded that the AASHTO specified provision for design of top concrete slab is sufficient. 4) To prevent the premature crushing of concrete in the bottom slab the ductility requirement shall be satisfied as follows: Dp<0.42Dt where: Dp = distance from the bottom of the botto m slab to the neutral axis of the composite section at the plastic moment (in.) Dt = depth of the composite section measured from the top layer of reinforcing to the bottom of the concrete bottom slab (in.) 5) Shear connectors installed in the bottom flange shall be designed as per LRFD provisions of Article 6.10.10 and 6.11.10. 6) Lateral bracing requirements of the compression flange is eliminated as the entire section is fully braced with the concrete.

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42 7) Designers must consider temporary bracing of bottom flange to support dead weight of concrete till it hardens. The deflection of the bo ttom flange at all times shall be less than L/360 and stress should be limited to 20 ksi for through thickness bending. Table 4.4 Design Rules for Double Composite Bridges No. Design Rules for Double Comp osite Section LRFD Articles 1. General Dimensioning and Detailing of Bridge Section Straight I – Sections Straight Box Sections 6.7 6.7.4.2 6.7.4.3 2. Points of Contraflexure Points of contraflexure shall be determined based on the appropriate numerical and structur al analysis. Analysis should consider AASHTO provisions fo r geometry and structural analysis. Example: Live load lateral distribution factors 3. Design Load and Load Combination Dead Loads Live Load Fatigue Load Load Factors and Load Combination 3.5 3.6 3.6.1.4 3.4 4. Structural Analysis and Evaluation of Bridge Superstructures Live Load Lateral Distribution Factors 4.6 4.6.2.2 5. Cross-Section proportions for I – Section and Box Section 6.10.2 and 6.11.2 6. Non-Composite and Composite Section Properties Article 6.10.1.1 7. Plastic Neutral Axis Article D6.1 8. Limit States Service Limit State Fatigue Limit State Strength Limit State 6.10.4 and 6.11.4 6.10.5 and 6.11.5 6.10.6 and 6.11.6 9. Flexure Resistance Composite Section in Positive Flexure Non-composite and Composite Section in Negative Flexure 6.10.7 and 6.11.7 6.10.8 and 6.11.8 10. Bottom Slab The maximum longitudinal Compressive stress in bottom slab at strength limit state shall be less than 0.6f'c. To prevent the premature crushing of the bottom slab the slab ductility requirement shall be satisfied. 6.10.1.1.1d 11. Shear Resistance 6.10.9 and 6.11.9 12. Shear Connectors 6.10.10 and 6.11.10 13. Temporary Bracing of Bottom Flange Bottom Flange at all time shall satisfy the deflection criteria of L/360 and thru thickness bending limited to less than 20 ksi.

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43 5. MODEL DESIGN OF A DOUBLE COMPOSITE BRIDGE 5.1 Introduction A model design of a double composite box girder bridge is presented in this chapter. Normal grade 50 steel is used The design is based on the AASHTO LRFD Bridge Design Specifications, 3rd Edition, 2004 [12] the FDOT Structures Design Guidelines (FSDG), January 2005 [13] and design recommendations presented in th e previous chapter based on the results of the testing. A three span continuous twin box girder bri dge consisting of two 190 ft end spans and a 236 ft main span s is designed. This configurati on was selected because it is identical to an AISI design example for a composite box girder bridge [14]. The design illustrates the application of the design provisions for flexure and shear at an interior pier section where the moments are negative. In the design it was assumed that the bo ttom slab was cast first, with the top slab cast after the bottom slab had hardened. As a result, the weight of the top slab is resisted by the composite bottom flange. Design moments were determined using QConBridge a software program developed by the Washington State Department of Transportation (WSDOT) All detailed calculations were carried out using MathCAD v14.0 as shown in Appendix A. 5.2 Design Overview The design of double composite bridges involves designing two composite sections corresponding to both the positive and negative mome nt regions in the continuous element. The basis of design for both sections is similar; differences arise because th e load for which the

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44 section acts compositely is not identical and depends on the sequence in which the slabs are cast. Since efficient design requires the bottom steel flange to be as thin as possible, limits are set on its minimum thickness based on buckling consider ations. Additional requirements have been proposed in this thesis that limits the maximum st ress in the bottom concrete slab as outlined in the previous chapter. 5.2.1 Design Steps The steps involved in the desi gn example are summarized in this section. Only a design for the negative moment section is presented here. The steps listed below are consistent with those followed in the design example included in the AISI reference. 1) General information and bridge geometry (Section 5.3). 2) Material properties in accordance with AASHTO and ASTM specifications (Section 5.4). 3) Calculation of loads in accordance with AASHTO LRFD provisions (Section 5.5) 4) Calculation of load factors and load combina tions for Strength I and Fatigue limit states in accordance with Article 3.4 of LRFD guidelines (Section 5.6 and Section 5.8). 5) Structural analysis for the load distribution in accordance with Article 4.6.2.2 of LRFD provisions (Section 5.7). 6) Calculation of section properties for non-com posite, short-term com posite and long-term composite sections (Section 5.9) 7) Determination of the plastic neutral axis location in accordance with Article D6.1. 8) Checking section for Strength I limit state and flexural requirements. Specifically the section should be checked for web slenderness, nominal flexural capacity and flexural resistance of box flanges, stresses in the concrete bottom slab, and shear (Section 5.11 and 5.13). 9) Check that bottom slab satisfi es slab ductility requirement to avoid premature crushing of concrete slab (Section 5.11).

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45 10) Detail shear connectors in bottom flange per prevailing LRFD provisions for fatigue and ultimate limit states (Section 5.14). 11) Consider provisions for temporary bracing of bottom flange to support the bottom concrete slab until it hardens (Section 5.15). 5.3 General Information and Geometry This section presents general information on the bridge and its geometry. Figure 5.1 shows the entire cross-section of the double composite bridge with two box girders. Figure 5.2 shows the typical cross-section of the box girder section considered for the design of negative flexure section. General information is summarized in Table 5.1. Information on the bridge geometry including its cross sectional dimensions are summarized in Table 5.2. Figure 5.1 Typical Cross-section of Double Composite Bridge

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46 Figure 5.2 Typical Cross-section of Double Composite Box Girder Table 5.1 General Information General Information Notation Parameter Number of box girders Ng 2 Number of spans Nsp 3 Number of design lanes NL 3 Length of middle span L2 236 ft. Length of side span (equal length) L1 190 ft. Girder spacing GS 11.375 ft. Roadway width Rw 40 ft. Concrete deck thickness (structural) tts 9 in Concrete bottom slab thickness tbs 13 in. Concrete deck overhang (width) OHc 4.5 ft. Side walks None Haunch thickness th 3 in. Reinforcement ratio Rr 0.01

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47 Table 5.2 Geometry of Box Girder Section Girder Dimensions Notation Parameter Web Depth (plumb) Dw 70 in. Inclination to vertical is 14.03 deg 14.036 Web Depth (inclined) D 72.15 in. Web plate thickness tw 0.75 in. Top flange thickness ttf 2.65 in. Top flange width btf 25 in. Bottom flange thickness tbf 1.00 in. Bottom flange width bbf 100 in. Height of girder HG 73.65 in. Top slab width bts 507 in. Top slab thickness tts 9 in. Bottom slab width bbs 99.25 in. Bottom slab thickness tbs 13 in. Area of web plate Aw = 2Dtw 108.23 in.2 Area of top flanges Atf = 2btfttf 132.5 in.2 Area of bottom flange Abf = bbftbf 100 in.2 Area of Steel Section As = Aw + Atf +Abf 340.73 in.2 Area of top slab Ats = btstts 4563 in.2 Area of bottom slab Abs = bbstbs 1290.25 in.2 5.4 Materials Table 5.3 summarizes information on the compressive strength of the concrete, the yield strength of the steel and the unit weight of th e stay-in-place form and future wearing surface assumed in the design. Table 5.3 Material Properties Material Notation Unit Weight Notation Design Value (ksi) Concrete c 145 pcf f'c 6.5 Structural steel s 490 pcf Fy 50 Reinforcing steel fyr 60 Shear connectors fys 60 Stay in place form sip 20 psf Future wearing surface ws 21 psf

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48 5.4.1 Concrete The compressive strength of the concrete is assumed to be 6500 psi. The concrete used in the bridge must conform to AASHTO Specificati ons. Normal weight conc rete is used with a unit weight of 145 pcf. Table 5.4 summarizes de sign parameters assumed in the design. Table 5.4 Design Parameters Design Parameters Notations Design Value (ksi) Design concrete strength fc 6.5 Modulus of concrete Ec 4181 Yield strength of steel Fy 50 Modulus of steel Es 29000 Shear modulus of steel Gs 12000 The modulus of concrete in Table 5.4 was calculated in accordance with FSDG for limestone aggregates as: 4181ksi 6.5 0.145 33000 0.9 c f' 33000 0.9 c E5 1 5 1 cw 5.4.2 Structural Steel Grade 50 structural steel conforming to ASTM A709 specifications was used for the box girder plates. Nominal yield strength is 50 ksi and unit weight is 490 pcf. 5.4.3 Steel Reinforcement Grade 60 steel bars conforming to ASTM 615 specifications are used for reinforcing both the top and bottom slabs. Nominal yield strength is 60 ksi.

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49 5.4.4 Shear Connectors Shear connectors used are in accordance with AASHTO M 169 and ASTM A108 specifications. The in. diameter shear connect ors used in the top and bottom concrete slab have a nominal yield strength of 60 ksi. 5.4.5 Miscellaneous Stay-in-place forms are used for the placement of the top concrete slab. Unit weight is 20 psf. The unit weight of the future wearing surface is taken as 21 psf. The unit weight of the 1.5 ft wide concrete barrier is taken as 581 plf. 5.5 Design Loads This section provides information for the de sign dead, live and fatigue loads which were calculated in accordance with AASHTO LRFD pr ovisions. The loads presented here were calculated for the negative moment section at an inte rior pier. Since the model bridge is straight and has uniform deck and overhang widths, the de sign loads are equally shared between the two box girders. 5.5.1 Dead Load Dead loads used in the design were grouped into four separate load cases to account for the various stages of construction and differi ng load factors specified in AASHTO LRFD. Permanent loads which generated moments resisted by the steel girder only (i.e., non-composite section) were grouped into load case DC1 as show n in Table 5.5. This included the self-weight of the steel girder, an additional 10% allowan ce for steel detailing elements (e.g., shear studs, stiffeners, etc.) and the reinforced c oncrete bottom slab prior to curing.

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50 Table 5.5 Non-composite Dead Loads Per Box Girder Dead Loads Load Case Unit Weight Cross-sectional Area (in2) Load (klf) Steel Section DC1 490 pcf 340.73 1.16 Steel Details DC1 490 pcf 31.82 0.116 Bottom Slab DC1 150 pcf 1287 1.34 Total 2.62 Permanent loads which resulted in negative moments carried by the composite section, comprised of the structural steel and the bottom slab, were grouped into load case DC2 as shown in Table 5.6. This included the weight of the stay-in-place forms and the reinforced concrete top slab, including haunches. Table 5.6 Composite Dead Loads Per Box Girder Dead Loads Load Case Unit Weight Cross-sectional Area (in2) Load (klf) SIPs DC2 20 psf n/a 0.27 Haunches DC2 150 pcf 132 0.156 Top Slab DC2 150 pcf 2281.5 2.377 Total 2.803 The superimposed loads resulting from the placeme nt of the concrete traffic barriers and future wearing surface were classified as separate load cases (i.e., DC3 and DW) in order to account for the differing load factors specified in AASHTO LRFD. The weight of the barrier and the weight allowance for the wearing surface, as s hown in Table 5.7, were selected to match the values used in the AISI example in order to maintain a consistent loading condition. Moments generated by the superimposed dead loads are resisted by the fully composite box girder, including the structural steel webs and flanges, the bottom slab concrete and the longitudinal reinforcing steel located in the top slab. Table 5.7 Superimposed Dead Loads Per Box Girder Dead Loads Load Case Unit Weight Length (ft) Load (klf) Concrete barrier DC3 n/a n/a 0.581 Wearing Surface DW 21 psf 20 0.420

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51 5.5.2 Live Load Vehicular live load considered for the de sign was based on the AASHTO HL-93 model, whereby live load is a combination of a design truck or a design tandem and design lane loads (see AASHTO 3.6.1.2 ). The design truck used was the HS 20 truck. Since the calculation of live load moments fo r multi-span continuous bridges is tedious, QConBridge a free software program from the Washington State Department of Transportation, was used to calculate the design live load moment s, as well as the dead load moments. The calculated live load moments are resisted in full by the short-term composite section, D, as defined in section 5.9. 5.5.3 Fatigue Load The fatigue loading used in the design of th e bottom slab shear connectors was calculated in accordance with AASHTO Article 3.6.1.4 An HS 20 design truck was used to calculate the maximum fatigue related moments using the QConBridge software. 5.6 Load Factors and Load Modification Factors This section provides information on the load factors for the Strength I and Fatigue limit states and the load modification factors used in the design. 5.6.1 Load Factors The load factors for dead load, live load a nd fatigue load for the Strength I and Fatigue limit states are specified in Table 5.8. These factors are in accordance with Article 3.4 of LRFD guidelines.

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52 Table 5.8 Load Factors for Strength I and Fatigue Limit State Dead Load DC Wearing Surface DW Live Load LL Strength I 1.25 1.50 1.75 Fatigue 0.75 5.6.2 Load Modification Factors Load modification factors are multipliers a ssociated with duct ility, redundancy and operational importance as described in Articles 1.3.2, 1.3.3 and 1.3.4 of the AASHTO LRFD specifications. Once determined, the individual modification factors are multiplied together to obtain a single number. They can also vary in relation to the limit state under consideration. However, in this design example, the load modi fier for each of the limit states considered, Strength I and Fatigue, is simply one. Therefore, the final design moments are unaffected by the load modification factors. 5.7 Distribution Factors Distribution factors are used to distribute th e live load moments and shears in the lateral direction. The distribution factors used in th is design were determined using the approximate method for beam-slab bridges in accordance with Article 4.6.2.2 of the LRFD guidelines. The following conditions must be satisfied to use the approximate method: 1) Width of the deck is constant. 2) Number of beams is not less than four unless otherwise specified. 3) Beams are parallel and have appr oximately the same stiffness. 4) The roadway portion of the overhang does not exceed 36 inches, unless otherwise specified. 5) The cross-section is consistent with one of the cross-sections shown in Table 4.6.2.2.1-1 in the LRFD specifications.

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53 Since the conditions specified above are met, live loads may be uniformly distributed among all of the beams. The following equation is used for determining the distribution factors for live load moment and shear. The live load distribution factor, DFLL, for moment and shear works out to be 1.467. L g L LLN N N . DF 425 0 85 0 05 0 (AASHTO Table 4.6.2.2.2b-1) DFLL = Distribution factor for Live Load, NL = Number of lane, Ng = Number of girders 467 1 3 425 0 2 3 85 0 05 0 . . DFLL In this example there are 3 design lanes (NL) and two box girders (Ng), so the ratio NL/Ng is 1.5. If this ratio exceeds 1.5, a more refine d analysis is required to take into consideration torsional effects. Since fatigue load is placed only on one lane, its distribution factor must accordingly be adjusted using the above equation. This distribution factor turns out to be 0.9 as follows: 9 0 1 425 0 2 1 85 0 05 0 . . DFFL In addition to lateral distribution, live load has to account for dynamic effects in accordance with Article 3.6.2 The dynamic load allowance f actor for the strength and fatigue limit states are 1.33 and 1.15, respectively. 5.8 Load Combinations The AASHTO LRFD load combinations consid ered for the model design were Strength I and Fatigue. The box girder section was designed for Strength I, and the shear connectors were designed for strength and fatigue. The maximum ne gative moment occurs at the interior pier supports. The maximum unfactored and factored moments for the Strength I load combination

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54 are summarized in Table 5.9. Table 5.10 summ arizes the maximum unfactored and factored shear forces at the interior pier section. In these tables, the DC1 load case represen ts dead load forces resisted by the noncomposite steel girder section only, DC2 forces are resisted by the composite steel girder and bottom slab section, the DC3 forces were genera ted by the placement of the concrete traffic barriers, DW represents loads from a future w earing surface, and LL+IM are live load plus impact forces. Table 5.9 Maximum Unfactored and Factored Moments at Interior Pier Section DC1 DC2 DC3 DW LL+IM 1.25 DC1 1.25 DC2 1.25 DC3 1.5 DW 1.75 LL+IM Max. Neg. Moment Mu 6536 12410 2670 1930 10580 8170 15513 3338 2895 18515 48430 Note: All moments are expressed in ft-kips Table 5.10 Maximum Unfactored and Factored Shear at Interior Pier Section DC1 DC2 DC3 DW LL+IM 1.25 DC1 1.25 DC2 1.25 DC3 1.5 DW 1.75 LL+IM Max. Shear Vu 206 321 70 49 302 258 401 88 74 529 1348 Note: All shear forces are expressed in kips 5.8.1 Location of Inflection Points The negative moment section extends from th e points of inflection in the end span (L1) and the main span (L2). The location of these inflection points is affected by several factors such as the type of loading (uniform or concentrated), position of load (placement of truck load for maximum effect), span geometry (interior to exterior span ratio). In this example, the ratio of the main to the end span is 1.24 (236/190). For this case, the inflection point is 0.27L1 [10, 11] from the interior support. This works out to be 0.27 x 190 = 51 ft from the interior support in the end span.

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55 The inflection point in the main span (L2) for different span ratios ranging from 1.0 to 1.7 was found to vary from 0.2L2 to 0.25L2. For this case where the ratio is 1.24, the inflection point is at a distance of 0.22L2 (52 ft) from interior support in the main span. The total length of the section under negative moment is therefore 51 ft + 52 ft = 103 ft. On a conservative note, the inflection points can be generalized to be taken as 0.3L, where L is the span length for span ratio varying from 1.2-1.4. 5.9 Section Properties The section properties of the steel box girder cross-section must be calculated for both non-composite and composite action. Composite ac tion additionally takes into consideration the effects of concrete creep for transient (i.e., shor t-term) and sustained (i.e., long-term) loading by using different values of the modular ratio, n in accordance with Article 6.10.1.1 The modular ratio is given by: 9 6 4181 29000 ksi ksi c E s E n whereby 7 20 3 n Section properties for five different sec tions must be calculated. These are noncomposite (Section A), short-term composite s ection with bottom slab (Section B), long-term composite section with bottom slab (Section C), short-term composite section considering top slab rebars, bottom slab and structural steel (Section D), and long-term composite section considering top slab rebars, bottom slab and structural steel (Section E). These properties are summarized in Table 5.11. The section property calculations can be found in Appendix A.

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56 Table 5.11 Section Properties for Noncomposite and Composite Sections Section Section Properties Crosssectional Area (in.2) Moment of Inertia (in.4) Neutral Axis (in.) Section Modulus (in.3) Bottom Top Bottom Flange Bottom Slab Top Flange A 341 340456 39.707 33.943 8574 10030 B 528 449569 28.295 45.355 16551 118390 10325 C 403 395991 34.726 38.924 11403 243044 10173 D 549 525077 30.329 55.321 17312 123529 12120 E 424 439256 37.039 48.611 11859 252302 11997 Figure 5.3 Forces in the Cross-section 5.10 Plastic Neutral Axis The location of the plastic neutral axis must be determined in order to ensure that the section meets the ductility requirement described in Article 6.10.7.3 of AASHTO LRFD. The location of the plastic neutral axis can be determined using the formulas presented in Article D6.1 of the LRFD guidelines. The following steps are used to calculate the plastic moment: YPNA Prt Prb Ptf Pw Pbs Pb f Pt f Pw Notation Prt = Force in Top Rebars Prb = Force in Bottom Rebars Ptf = Force in Top Flange Pw = Force in Web Pbs = Force in Bottom Slab Pbf = Force in Bottom Flange Note: Drawing not to scale

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57 1) Determine general location of the plastic neutra l axis (P.N.A) by comparing forces in the flanges and webs Calculate forces due to structural steel, bot tom concrete slab and reinforcement in top concrete slab. Table 5.12 shows the calcu lation of forces in the cross-section. Table 5.12 Forces in the Cross-section Force Expression Input Values Force (kips) Force in top rebars yr ts eff rtf t b P 0067 0 ksi in. in. 60 9 232 0067 0 2 841 Force in bottom rebars yr ts eff rbf t b P 0033 0 ksi in. in. 60 9 232 0033 0 3 414 Force in top flange y tf tf tfF t b P 2 ksi in. in. 50 5 2 25 2 6625 Force in web y w wF t D P 2 ksi in. in. 50 75 0 15 72 2 4 5411 Force in bottom flange y bf bf bfF t b P ksi in. in. 50 0 1 100 5000 Force in bottom slab bs bs c bst b f P 85 0 in. in. ksi . 12 99 5 6 85 0 7128 The total tension force in the top slab reba r, flanges and webs is greater than the compression force in the bottom flange and bottom c oncrete slab. Therefore, the plastic neutral axis lies somewhere in the web. Since the magnitude of force in bottom flange and bottom slab is greater the neutral axis lies in bot tom concrete slab along with web. bs bf w tf reP P P P P 2) Calculate the location of the plastic neutra l axis from the bottom of the bottom flange. The plastic neutral axis (YPNA) is taken from the bottom of the bottom flange. Its location is determined by summing forces as follows:

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58 0 cos cos t Y D P P P Y t D D P P Pbf PNA w bs bf PNA bf w w tf re Substituting values obtained in the prev ious step in the above equation, YPNA is found. 0 036 14 cos 1 15 72 43 5411 7128 5000 036 14 cos 1 70 15 72 43 5411 6625 5 1255 in. Y in. . Y in. in. in. . .PNA PNA 603 8 5 154 1325 in in. kip kip YPNA Thus, YPNA is located 8.603 in. from the extreme bottom fiber of the box girder section, which places it within the concrete bottom slab. Note: The equilibrium equation used here does not account for the loss of compressive force for the bottom slab concrete above the plastic neutra l axis. However the result is adequate for the design. 5.11 Strength I Limit State Design checks related to the Strength I limit st ate are presented in this section. The model design section must satisfy the AASHTO LRFD requirements for composite members and the design recommendations presented in Chapter 4 of this document, including limits for web slenderness, concrete compressive stress, steel top flange stress and concrete slab ductility. 5.11.1 Web Slenderness Web slenderness criterion is checked as per Article 6.10.6.2.3 of the AASHTO specifications. The following equation defines the slenderness limit of the web in composite and non-composite sections in the negative flexure region.

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59 y s w cF E t D 7 5 2 Where Dc = depth of the web in compression in th e elastic range determined as specified in Article D6.3.1. 0 5 2 64 52 90 46 ) 90 46 ( tf t c c ct d f f f D 32 30 in Dc Substituting the value of Dc in the above equation. 89 80 75 0 32 30 2 . in in S H L 27 137 50 29000 7 5 . ksi ksi S H R S H R S H L . . Therefore, the section satisfies the AASHTO web slenderness criteria. 5.11.2 Slab Ductility Requirement for Bottom Slab In order to prevent premature crushing of the concrete in the bottom slab, the ductility requirement for the bottom concrete slab must be satisfied. The following equation gives the ductility criteria to avoid premature crushing of concrete. Dp < 0.42Dt where: Dp = distance from the bottom of the concrete botto m slab to the neutral axis of the composite section at the plastic moment (in.) Dt = depth of the composite section measured from the top layer of reinforcing to the bottom of the concrete bottom slab (in.) in in in t Y Dbf PNA p603 7 0 1 603 8

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60 in in in in in in in t t t D Dts h tf w t65 82 2 9 3 65 2 70 2 092 0 5 82 603 7 in in D Dt p Therefore, the bottom slab satisfies the slab ductility requirement to avoid the premature crushing of concrete. 5.11.3 Compressive Stress in Concrete Slab As explained in Chapter 4 of this document, stress in the composite concrete bottom slab shall be limited to 0.6f’c. The maximum stress developed in the bottom slab due to factored loads is given by: bD LL bsE DW D bsC DC bsD LL bsD DW D bsB DC bsuS M S M M S M S M S M M S M f 3 2 3 2 ksi in kip f t in kip f t in kip f t fbsu97 3 123529 18515 123529 2895 3338 118391 155133 3 3 ksi ksi fbsu9 3 5 6 6 0 Eventhough, the stress in bottom concrete slab exceeds 0.6f’c by 2 %, for the purpose of this example the bottom slab is acceptable. c bsuf f 6 0 is satisfied for the bottom slab 5.11.4 Flexural Resistance of Steel Flanges The flexural resistance of the bottom steel fl ange in compression and the top steel flanges in tension to resist negative moments are checked in this section. The flexural resistance of the box flanges in negative flexure shall be determined in accordance with Article 6.11.8 of the LRFD guidelines.

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61 Assuming that torsional shear stresses in the flange are negligible, the nominal flexural resistance of the compression flange is determined in accordance with Article 6.11.8.2 y h b ncF R R F Where, Rb = 1.0, web load-shedding factor determined as specified in Article 6.10.1.10.2. Rh =1.0, hybrid factor determined as specified in Article 6.10.1.10.1. = 1.0 (assumed) ksi ksi Fnc50 50 0 1 0 1 0 1 Similarly the flexural resistance of the tension flange isy ntF F ksi Fy50 Flexural Resistance limit state of Compression Flanges y f buF f The maximum stress developed in the compressi on flange due to factored loads is given by: bD LL bE DW D bC DC bA bD LL bD DW D bB DC bA DC buS M S M M S M S M S M S M M S M S M fDC 3 2 3 2 11 ksi in kip ft in kip ft in kip ft in kip ft fbu90 46 17312 18515 11859 ) 2895 3338 ( 16551 15513 8574 81703 3 3 3 ksi ksi fbu50 50 0 1 y f buF f is satisfied for the compression flange. Similarly, the tension flange can be checked using the same criteria. Calculations for the tension flange are shown in Appendix A. 5.12 Shear Design The section must be checked for the maximum shear force. Since the maximum shear is at the interior support section, this section will be checked. Shear design of the web is in accordance with Article 6.10.9 and 6.11.9

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62 Table 5.10 indicates that the maximum factor ed shear is 1348 kips for Strength I limit state. This shear is not accounted for the imp act at ultimate limit stat e. The total shear for ultimate limit state is 1348 kips. However, this shear is equally distributed to both webs of the box girder section. Maximum shear for the single web kips V us674 The inclination of the web should also be taken into consideration. kips kips V Vus u695 036 14 cos 674 cos Therefore the maximum shear considered for design is 695 kips. 5.12.1 Nominal Shear Resistance of Unstiffened Webs The nominal shear resistance for the unstiffened webs is calculated as per Article 6.10.9 in this section. The resistance factor ( v) for shear design is 1.0 as per Article 6.5.4.2 The following steps show the shear design of the web. 1) Determine plastic shear force in accordance with Article 6.10.9.2. w y Pt D F V 58 0 in in ksi VP75 0 15 72 50 58 0 kips 1569 VP 2) Determine the nominal shear resistance of the web. p nV C V Where C is the ratio of shear buckling stress to the yield strength C should be determined in accordance with Article 6.10.9.3.2-6. If y s wF k E t D 40 1 then y s wF k E t D C257 1 Where, k = 5.0, shear buckling co-efficient.

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63 In this case, 2 96 75 0 15 72 in in t D w and 392 75 50 5 29000 40 1 40 1 ksi ksi F k Ey s Since, y s wF k E t D 40 1 hold true, the above equation for calculating C can be used. 492 0 50 5 29000 75 0 15 72 57 12 ksi ksi in in C kips Vn772 1569 492 0 kips Vn v772 772 0 1 Therefore, the nominal shear capacity of single web is 772 kips. Since, Vu = 695 kips is less than kips Vn v 772 the section satisfies the nominal shear criteria. 5.13 Shear Connectors There is no change in the design procedure of the shear connectors for the top flange in the negative flexure region. The shear connectors on the bottom flange are designed for the same provisions as the top flange in Article 6.10.10 and 6.11.10. The fatigue life and nominal fatigue resistan ce of shear connecters are designed as per Article 3.6.1.4 and Article 6.6.1.2.5. The detailed calculations for the design of shear connectors are presented in the Appendix A. However, th e steps in the design of shear connectors are summarized below. 1) Ultimate resistance of shear connectors shall be calculated in accordance with Article 6.10.10.4. 2) Number of shear connectors shall be determ ined based on the ultimate resistance of the shear connectors. 3) Determine the fatigue life of the bridge in accordance with the Article 3.6.1.4 and Article 6.6.1.2.5.

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64 4) Determine the nominal fatigue resistance of shear connectors as per Article 6.6.1.2.5 and Article 6.10.10.2 5) Lateral spacing and longitudinal pitch of shear connector should be determined as per existing LRFD guidelines. In this case, the total number of shear conn ectors required to connect the bottom slab to the bottom flange is 1940 with a longitudinal pitch of 18 in. However the bottom flange should be checked for buckling between the shear stud lines. The spacing between two shear stud lines on bottom fl ange is 18 in. Classical theory on stability of plates is used to determine plate buckling. From the analysis it was found that the longitudinal spacing of 20 in. was adequate to prevent buck ling failure. Refer Appendix G for the detailed calculations. 5.14 Temporary Bracing of Bottom Flange Temporary bracing of the bottom flange should be considered by the designer to support the dead weight of the bottom concrete slab un til it cures. The bottom flange deformation should follow the L/360 criteria for deflection and the through thickness bending stress in the bottom flange during construction should not exceed more than 20 ksi. The bottom flange should always be in accordance with the Article 6.10.3 and 6.11.3 which describes the construction related guidelines. Lateral bracing of the bottom flange s hould be removed once the bottom slab hardens. In this case, the bottom flange was bra ced with WT 8 13 members. The maximum spacing between the braced sections was 2 ft. and maximum stress was limited to 7.8 ksi. The maximum deflection of 0.287 in. was observed with bracing at 2 ft. Detailed calculations of the composite section properties, load, deflection and stress are included in the Appendix A.

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65 5.15 Material Cost Comparison The material (concrete and steel) cost of the double composite bridge was compared with the referenced AISI example having the overall di mensions, span configuration under the same loading. The difference in cost is due to the difference in the amount steel required by the negative moment region for the tw o designs. Several alternates w ith different concrete strength and different thickness of bottom flange and bottom slab were compared to select optimum section. Table 5.13 Cost Analysis of Materials used in Negative Flexure Region for Single Composite Section Qty Single Composite Section Dimensions Total Length Width Thickness X-Sect Area Volume Weight Cost (ft) (in) (in) (in2) (ft3) (lbs) ($) 4 Bottom Flange 100.0 100.0 1.375 381.94 187153 $402,378 4 Stiffener (WT 12x34) 100.0 10.0 27.78 13611 $71,458 Total $473,837

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66 Table 5.14 Cost Analysis of Materials Used in Negative Flexure Region for Double Composite Section Qty Single Composite Section Dimensions Total Length Width Thickness X-Sect Area Volume Weight Cost (ft.) (in.) (in.) (in.2) (ft.3) (lbs) ($) 4 Bottom Flange 100.0 100.0 1.0 100 278 136111 $292,639 4 Bottom Slab 100.0 99 13 1290 3575 518375 $105,926 Reinforcing Steel 17875 $19,663 1940 Shear Connectors 0.5 0.75 (diameter) 3.31 1620 $2,430 204 Temporary Bracing 8.33 3.84 33.17 22213 $19,437 Total $440,094 In the comparison, costs are based on the latest cost data; these are $ 800 per cubic yard for structural concrete and $ 2.15 per pound of st eel. The corresponding costs per cubic feet are $35 for structural concrete and $1053 for structural steel. Table 5.14 and 5.15 shows the cost analysis of the materials used in negative flexure region for both ‘single’ and ‘double’ composit e sections. The inspection of Table 5.14 and 5.15 shows that there is approximate saving of $ 33,743 in terms of materials used in negative flexure region for double composite section. This approximates to net savings of 7 %. Table 5.15 Cost Comparison of Double Composite Sections Double Composite Sections Alternate Concrete Strength (psi) Bottom Slab Thickness Bottom Flange Thickness Cost Savings ($) Cost Savings (%) 1 6500 13 1.0 33,743 7 2 7500 10 1.0 62,215 13 3 8500 9 0.875 107,375 23 4 10,000 7 0.875 126,860 27

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67 5.16 Summary The thickness of the bottom flange in the referenced AISI example was 1.375 in. and the bottom flange was stiffened by WT sections with an approximate cross-sectional area of 10 sq. in. In contrast, in the double composite section, the bottom flange thickness reduced to 1.0 in. and no stiffeners were needed. The thickness of bottom concrete slab between the contraflexure points was maintained constant at 12 in. in the proposed design. Several other alternate with high strength concrete were considered. Table 5.16 summarizes cost savings for all the different alte rnates for double composite section. In all the cases, stress in the bottom concrete slab was lim ited to 0.6f’c. Table 5.16 shows that by using high strength concrete, the thickness of bottom slab and steel bottom flange can be reduced. This increases the cost savings significantly for doub le composite sections in the negative flexure region. The double composite design required the bottom slab to be checked for the new slab ductility requirement to avoid premature crushing of the concrete slab. Also, the section was designed as non-compact in the negative flexure region. The concrete slab continuously braces the compression flange and therefore elim inates the need for lateral bracing. The bottom flange was temporarily braced every 2 ft to limit deflection and through thickness bending while it supported the weight of the weight concrete during construction.

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68 6. CONCLUSIONS AND RECOMMENDATIONS 6.1 Introduction The work reported in this thesis is fro m a cooperative research project between USF/FDOT/URS. In the project, a full-scale ‘double composite’ box girder section designed to the AASHTO specifications were tested under fa tigue, service and ultimate loads. Following completion of the testing and analysis of the da ta by USF, design rules were proposed by URS Corporation. This thesis focuses on the applicati on of these newly developed design rules for the LRFD design of double composite box girder bridges. For completeness, it also provides an overview of the experimental testing conducted by FDOT and URS’ interim design provisions. These rules will be finalized following completi on of the non-linear finite element analysis. 6.2 Conclusions Based on the information presented in the thesi s and the experience of the author, the following conclusions may be drawn: 1) The proposed rules incorporate minor cha nges to current AASHTO LRFD provisions. As such they do not add undue complexity and the design of double composite box girder bridges is simple and straight forward. 2) The envelope of the points of contraflexure was used in this study to identify the negative moment section that is made composite. In practice, it may be simpler to use a single value, e.g. 0.3L.

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69 3) The illustrative example showed that compar ed to “single” composite design, the double composite design with the use of high strengt h concrete provided cost savings up to27% and cost savings of $ 126,860 in the negative flexure region. 6.3 Future Work This study did not address all issues rela ting to the design of double composite box girders. The following issues need further investigation: Since negative moments drop off rapidly, the thickness of the bottom slab may be varied. Guidelines are needed based on the specified locations of the contraflexure point. 1) The type of reinforcement provided in the bo ttom slab needs to be evaluated. The bottom slab is restrained by the steel webs and is not subjected to locali zed wheel loads. There may be a need for additional shrinkage and temperature steel above current requirements to prevent the type of cracking th at occurred in the test specimen. 2) Guidelines should be prepared to provide information on the (1) minimum thickness of the bottom flange, (2) optimal shear connector configuration for the bottom flange and (3) grade of concrete to be used in the bottom slab. 3) Hybrid sections in which different grades of steel are used for the top and bottom flanges and the web may be the most economical. Guidelines should be developed based on appropriate numerical analysis. 4) Creep effects in the bottom slab need to be explored since it sustains larger permanent loads than the top slab.

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70 REFERENCES 1. Martinez-Calzon, Julio (1995). Strict Box Composite Bridges A New Design of the Optimum Use of Composite Topology Proceedings of the 12th Annual International Bridge Conference and Exhibition, June 19-21 Pittsburgh, PA, pub. Engineers' Society of Western Pennsylvania, pp. 258-264. 2. Saul, Reiner (1996). Bridges with Double Composite Action Structural Engineering International, International Asso ciation for Bridge and Structural Engineering, Vol. 6, No 1, pp. 32-36. 3. Saul, Reiner (1997). Design and Construction of Long Span Steel Composite Bridges in Composite Construction in Steel and Concrete III : Proceedings of an Engineering Foundation Conference, Irsee, Germany, pp. 700-712. 4. Stroh, Steven (1994). Design of a Double Deck Cable Stayed Bridge for Combined Highway and Railway Traffic Proceedings of the 10th Joint US-Japan Workshop on Performance on Strengthening of Bridge St ructures and Research Needs, Lake Tahoe, Nevada, May. 5. Stroh, Steven, and Lovett, Thomas (1995). Kap Shui Mun Cable Stayed Bridge Proceedings of the Fourth International Bridge Engineering Conference Volume I, Transportation Research Board, San Francisco, August, pp. 259-265. 6. Calzon, J.M. (1998). Strict Box Composite Bridges: A Proposal for the Optimization of Materials, in Developments in Short and Me dium Span Bridges ’98, Calgary, Canada, 1-16. 7. Saul, Reiner (1992). Longspan Bridges with Double Composite Action Composite Construction in Steel and Concrete II Proceedings of an Engineering Foundation Conference, June 14-19, Potosi, MO, Pub. ASCE New York, pp. 608-622. 8. RPX – 95 (1995). Recommendations for the Design of Composite Road Bridges Madrid, Spain. 9. Salmon, C.G. and Johnson, J.E. (1996). Steel Structures: Design and Behavior Harper Collins, NY, NY. Fourth Edition. p.639. 10. AISC Manual of Steel Construction (2007), 13th Edition, Chicago, IL, pp 3-224–3-225. 11. Retrieved on June 26, 2009, from http://www.bridgesite.com

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71 12. AASHTO LRFD Bridge Design Specifications (2004), 3rd Edition, Washington, DC. 13. Florida Structures Design Guidelines (2005), Tallahassee, FL. 14. AISI (1995). Four LRFD Design Examples of Steel Highway Bridges. Vol. II Ch 1A, Highway Structures Design Handbook, Prepared by HDR Engineering Inc, Chicago, IL.

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72 APPENDICES

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73 Appendix A: Design of a Double Composite Box Girder Bridge

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76 Appendix A (Continued) Figure A.1 Typical Cross-section of Bridge Figure A.2 Typical Cross-section of Box Girder

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101 Appendix A (Continued) Table A.3 Unfactored Shear for Negative Section in Kips

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102 Appendix A (Continued) Table A.4 Factored and Distributed Shear for Negative Section in Kips

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