Simplified Full-Depth Precast Concrete Deck Panel

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Simplified Full-Depth Precast Concrete Deck Panel Systems

DETAILS 156 pages | 8.5 x 11 | PAPERBACK ISBN 978-0-309-47997-4 | DOI 10.17226/25319

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Sameh S. Badie, George Morcous, and Maher K. Tadros; National Cooperative Highway Research Program; Transportation Research Board; National Academies of Sciences, Engineering, and Medicine

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N AT I O N A L C O O P E R AT I V E H I G H W AY R E S E A R C H P R O G R A M

NCHRP RESEARCH REPORT 895 Simplified Full-Depth Precast Concrete Deck Panel Systems Sameh S. Badie The George Washington University Washington, D.C.

George Morcous University of Nebraska–Lincoln Lincoln, NE

Maher K. Tadros e.Construct USA, LLC. Omaha, NE

Subscriber Categories

Bridges and Other Structures

Research sponsored by the American Association of State Highway and Transportation Officials in cooperation with the Federal Highway Administration

2018

Copyright National Academy of Sciences. All rights reserved.


NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM

NCHRP RESEARCH REPORT 895

Systematic, well-designed research is the most effective way to solve many problems facing highway administrators and engineers. Often, highway problems are of local interest and can best be studied by highway departments individually or in cooperation with their state universities and others. However, the accelerating growth of highway transportation results in increasingly complex problems of wide interest to highway authorities. These problems are best studied through a coordinated program of cooperative research. Recognizing this need, the leadership of the American Association of State Highway and Transportation Officials (AASHTO) in 1962 initiated an objective national highway research program using modern scientific techniques—the National Cooperative Highway Research Program (NCHRP). NCHRP is supported on a continuing basis by funds from participating member states of AASHTO and receives the full cooperation and support of the Federal Highway Administration, United States Department of Transportation. The Transportation Research Board (TRB) of the National Academies of Sciences, Engineering, and Medicine was requested by AASHTO to administer the research program because of TRB’s recognized objectivity and understanding of modern research practices. TRB is uniquely suited for this purpose for many reasons: TRB maintains an extensive committee structure from which authorities on any highway transportation subject may be drawn; TRB possesses avenues of communications and cooperation with federal, state, and local governmental agencies, universities, and industry; TRB’s relationship to the National Academies is an insurance of objectivity; and TRB maintains a full-time staff of specialists in highway transportation matters to bring the findings of research directly to those in a position to use them. The program is developed on the basis of research needs identified by chief administrators and other staff of the highway and transportation departments, by committees of AASHTO, and by the Federal Highway Administration. Topics of the highest merit are selected by the AASHTO Special Committee on Research and Innovation (R&I), and each year R&I’s recommendations are proposed to the AASHTO Board of Directors and the National Academies. Research projects to address these topics are defined by NCHRP, and qualified research agencies are selected from submitted proposals. Administration and surveillance of research contracts are the responsibilities of the National Academies and TRB. The needs for highway research are many, and NCHRP can make significant contributions to solving highway transportation problems of mutual concern to many responsible groups. The program, however, is intended to complement, rather than to substitute for or duplicate, other highway research programs.

Project 12-96 ISSN 2572-3766 (Print) ISSN 2572-3774 (Online) ISBN 978-0-309-47996-7 Library of Congress Control Number 2018961247 © 2018 National Academy of Sciences. All rights reserved.

COPYRIGHT INFORMATION Authors herein are responsible for the authenticity of their materials and for obtaining written permissions from publishers or persons who own the copyright to any previously published or copyrighted material used herein. Cooperative Research Programs (CRP) grants permission to reproduce material in this publication for classroom and not-for-profit purposes. Permission is given with the understanding that none of the material will be used to imply TRB, AASHTO, FAA, FHWA, FMCSA, FRA, FTA, Office of the Assistant Secretary for Research and Technology, PHMSA, or TDC endorsement of a particular product, method, or practice. It is expected that those reproducing the material in this document for educational and not-for-profit uses will give appropriate acknowledgment of the source of any reprinted or reproduced material. For other uses of the material, request permission from CRP.

NOTICE The research report was reviewed by the technical panel and accepted for publication according to procedures established and overseen by the Transportation Research Board and approved by the National Academies of Sciences, Engineering, and Medicine. The opinions and conclusions expressed or implied in this report are those of the researchers who performed the research and are not necessarily those of the Transportation Research Board; the National Academies of Sciences, Engineering, and Medicine; or the program sponsors. The Transportation Research Board; the National Academies of Sciences, Engineering, and Medicine; and the sponsors of the National Cooperative Highway Research Program do not endorse products or manufacturers. Trade or manufacturers’ names appear herein solely because they are considered essential to the object of the report.

Published research reports of the

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The National Academy of Sciences was established in 1863 by an Act of Congress, signed by President Lincoln, as a private, nongovernmental institution to advise the nation on issues related to science and technology. Members are elected by their peers for outstanding contributions to research. Dr. Marcia McNutt is president. The National Academy of Engineering was established in 1964 under the charter of the National Academy of Sciences to bring the practices of engineering to advising the nation. Members are elected by their peers for extraordinary contributions to engineering. Dr. C. D. Mote, Jr., is president. The National Academy of Medicine (formerly the Institute of Medicine) was established in 1970 under the charter of the National Academy of Sciences to advise the nation on medical and health issues. Members are elected by their peers for distinguished contributions to medicine and health. Dr. Victor J. Dzau is president. The three Academies work together as the National Academies of Sciences, Engineering, and Medicine to provide independent, objective analysis and advice to the nation and conduct other activities to solve complex problems and inform public policy decisions. The National Academies also encourage education and research, recognize outstanding contributions to knowledge, and increase public understanding in matters of science, engineering, and medicine. Learn more about the National Academies of Sciences, Engineering, and Medicine at www.national-academies.org.

The Transportation Research Board is one of seven major programs of the National Academies of Sciences, Engineering, and Medicine. The mission of the Transportation Research Board is to increase the benefits that transportation contributes to society by providing leadership in transportation innovation and progress through research and information exchange, conducted within a setting that is objective, interdisciplinary, and multimodal. The Board’s varied committees, task forces, and panels annually engage about 7,000 engineers, scientists, and other transportation researchers and practitioners from the public and private sectors and academia, all of whom contribute their expertise in the public interest. The program is supported by state transportation departments, federal agencies including the component administrations of the U.S. Department of Transportation, and other organizations and individuals interested in the development of transportation. Learn more about the Transportation Research Board at www.TRB.org.



COOPERATIVE RESEARCH PROGRAMS

CRP STAFF FOR NCHRP RESEARCH REPORT 895 Christopher J. Hedges, Director, Cooperative Research Programs Lori L. Sundstrom, Deputy Director, Cooperative Research Programs Waseem Dekelbab, Senior Program Officer Megan Chamberlain, Senior Program Assistant Eileen P. Delaney, Director of Publications Natalie Barnes, Associate Director of Publications

NCHRP PROJECT 12-96 PANEL Field of Design—Area of Bridges Ahmad Abu-Hawash, Iowa DOT, Ames, IA (Chair) Ihab Said Darwish, Alfred Benesch and Company, East Lansing, MI Hussam Z. “Sam” Fallaha, Florida DOT, Tallahassee, FL Michael D. Hyzak, Texas DOT, Austin, TX William N. Nickas, Precast/Prestressed Concrete Institute, Tallahassee, FL Carin L. Roberts-Wollmann, Virginia Polytechnic Institute and State University, Blacksburg, VA William P. Saffian, New Hampshire DOT, Concord, NH Benjamin A. Graybeal, FHWA Liaison Richard B. “Dick” Stoddard, NHTSA Liaison Stephen F. Maher, P.E., TRB Liaison

AUTHOR ACKNOWLEDGMENTS The research reported herein was performed under NCHRP Project 12-96 by the Department of Civil and Environmental Engineering at The George Washington University in Washington, D.C. The George Washington University was the contractor for this study. The University of Nebraska–Lincoln and e.Construct USA in Omaha, Nebraska, served as subcontractors to The George Washington University. Sameh S. Badie, professor of Civil Engineering at The George Washington University, was the project director and principal investigator. Other authors of this report are George Morcous, professor of Civil Engineering at University of Nebraska–Lincoln; and Maher K. Tadros, principal at e.Construct USA. Many thanks are due the following individuals for their help and support during various phases of the project: Majid Manzari, professor; Arzhang Zamani and Saman Mehryar, PhD students; Khaled Alfadl and Hannah Gaudet, undergraduate students; and Daniel Balacha, William Rutkowski, Thomas Punte, and Mark Wagner, laboratory technicians at George Washington University; Raed Tawadrous, Mostafa Aboelkhier, and Antony Kodsy, PhD students at University of Nebraska–Lincoln; Chuanbing Sun, PhD, and Michael Saad, PhD, of e.Construct USA; Nicholas Paleologos, John Paleologos, Michael Lenkin, and Alan Jenkins of Miller and Long DC in Washington, D.C.; Mark Lafferty of Concrete Industries, Inc., in Lincoln, Nebraska; Todd Culp of Coreslab Structures, Inc., in Plattsmouth, Nebraska; Gregory Nault of LafargeHolcim North America, Inc., in Chicago, Illinois; and Robert Cramer of Cramer and Associates in Grimes, Iowa.



FOREWORD

By Waseem Dekelbab Staff Officer Transportation Research Board

This report presents new simplified connections between full-depth precast concrete deck panels and beams. These new connections are simplified with regard to constructability, inspection during construction, reducing the impact of construction on traffic, and future deck replacement and are based on comprehensive analytical and testing programs. The new system utilizes clustered shear connectors spaced up to 6 ft and connected to the deck system using ultra-high performance concrete (UHPC). In addition, the new system utilizes discrete joint connections (i.e., noncontinuous haunch) to eliminate blind grouting. The report also presents proposed revisions to the AASHTO LRFD Bridge Design Specifications. The material in this report will be of immediate interest to bridge engineers. Full-depth precast concrete deck panels have been widely used in accelerated bridge construction (ABC) in various forms and sizes. As a prefabricated component, full-depth deck panel systems meet the objectives of ABC by expediting construction, enhancing quality and durability, improving public and worker safety, and reducing road-user impact. Typically, deck panels are connected to the supporting beams by shear connectors in formed openings in panels (i.e., shear pockets) to achieve composite action between the deck panels and beams of a bridge. The current use of shear connectors at small spacing poses several constructability challenges because of the large number of connectors and pockets, including the work associated with the blind grouting/concreting of numerous shear pockets and the longitudinal haunch between deck panels and beams. Specifically, leveling, sealing, forming, grouting, and concreting can be time-consuming and require access from above and below the deck. This access requirement may adversely affect traffic. A new deck connection that can overcome these constructability challenges by reducing the number of shear pockets and eliminating blind grouting would provide additional benefits from using this construction technique. Under NCHRP Project 12-96, George Washington University was asked to develop recommended guidelines and to propose AASHTO LRFD Bridge Design Specifications language for the design, fabrication, and construction of a new full-depth precast concrete deck panel system that simplifies the connection between deck panels and beams. A number of deliverables, provided as appendices, are not published but are available on the TRB project website at https://apps.trb.org/cmsfeed/TRBNetProjectDisplay.asp? ProjectID=3409. These appendices are titled as follows: • Appendix A—Literature Review • Appendix B—Analytical Program • Appendix C—Shop Drawings





CONTENTS

1 Summary 3

3 3 4 4 6

9 9 10 20

24

24 24 24 32 33

34 34 37 38 38 39 39 40 42 42 45 47 50 51 51 52 74 107 107 122 124

Chapter 1 Background 1.1 General 1.2 Literature Review 1.2.1 Variable-Depth Precast Deck Panel Systems 1.2.2 Slab–Girder Systems Made with Discrete Joints 1.2.3 Shear Connector Spacing and Capacity

Chapter 2 Research Goals and Approach 2.1 Introduction 2.2 Precast Deck Panel System with Longitudinal Post-Tensioning 2.3 Precast Deck Panel System with Conventional Longitudinal Reinforcement

Chapter 3 Research Findings 3.1 Analytical Program 3.1.1 Objectives of the Analytical Program 3.1.2 Design Requirement 1: Flexural Design of Deck 3.1.3 Design Requirement 2: Two-Way Shear at the Discrete Joints 3.1.4 Design Requirement 3: Two-Way Shear at Wheel Loads for Variable-Thickness Ribbed Slab 3.1.5 Design Requirement 4: Bearing Stresses 3.1.6 Analytical Model Used to Investigate Design Requirements 5 to 9 3.1.7 Design Requirement 5: One-Way Shear in the Slab 3.1.8 Design Requirement 6: Flexural Stresses of Composite Member 3.1.9 Design Requirement 7: Deflection of Composite Member 3.1.10 Design Requirement 8: Interface Shear 3.1.11 Design Requirement 9: Vertical Shear of Composite Beam 3.1.12 Design Requirement 10: Distribution Factors 3.1.13 Flexural Strength 3.1.14 Top Flange Buckling 3.1.15 Finite Element Analysis of Push-Off Specimens 3.1.16 Effect of Simplification of Deck Post-Tensioning 3.1.17 Summary and Conclusions 3.2 Experimental Program 3.2.1 Introduction to the Experimental Program 3.2.2 Investigation of Precast Deck System with Concrete Girders 3.2.3 Investigation of Precast Deck System with Steel Girders 3.3 Design Examples 3.3.1 Design of the Precast Deck Slab System 3.3.2 Longitudinal Design of Deck–Girder System for Concrete Girders 3.3.3 Longitudinal Design of Deck–Girder System with Steel Girders



131 131 132 133 133 133 133 134 134 134 135 138 138 140 140 140 141 141

142 142 144

3.4 Design Guidelines 3.4.1 Precast Deck 3.4.2 Haunch (Build-Up) Between Girders and Panels 3.4.3 Concrete Girder-to-Deck Joint 3.4.4 Steel Girder-to-Deck Joint 3.4.5 Concrete Girder Design 3.4.6 Steel Girder Design 3.5 Proposed Changes to AASHTO LRFD Bridge Design Specifications 3.5.1 Item 1: Create a New Section 2.5.2.6.4 3.5.2 Item 2: Add New Reference to Section 2.8 3.5.3 Item 3: Modify Section 5.7.4 3.5.4 Item 4: Add New Reference to Section 5.15 3.5.5 Item 5: Modify Section 6.10.10.1.2 3.5.6 Item 6: Modify Section 6.10.10.4.3 3.5.7 Item 7: Add New Reference to Section 6.17 3.5.8 Item 8: Add New Paragraphs to Section 9.7.5.3 3.5.9 Item 9: Add New Reference to Section 9.10 3.6 Economical Impact of Proposed Guidelines and Specifications

Chapter 4 Conclusions and Recommendations for Future Research 4.1 Conclusions 4.2 Recommendations for Future Research

145 Bibliography 148

Appendices A–C

Note: Photographs, figures, and tables in this report may have been converted from color to grayscale for printing. The electronic version of the report (posted on the web at www.trb.org) retains the color versions.



SUMMARY

Simplified Full-Depth Precast Concrete Deck Panel Systems Public inconvenience and loss of income during bridge construction and rehabilitation have prompted exploration of rapid construction methods. In 2001, FHWA launched the Accelerated Bridge Construction (ABC) initiative. ABC is bridge construction that uses innovative planning, design, materials, and construction methods in a safe and costeffective manner to reduce the construction time associated with maintenance of traffic when building new bridges or replacing and rehabilitating existing bridges. Cast-in-place (CIP) bridge deck slabs represent a significant part of construction of stringer-type bridge superstructures. Much of the construction time is consumed in deck forming, placement of steel bars, and placement and curing of CIP deck concrete. In addition, studies have shown that CIP decks in harsh environments where deicing chemicals are used are considered one of the major elements of highway bridges requiring frequent maintenance, including patching, sealing, and placement of overlays. CIP decks pose low durability performance because of shrinkage cracking, high permeability, and direct exposure to deicing chemicals and moisture. As a result, full-depth precast concrete deck panel systems have been increasingly used to replace CIP decks. In addition to higher construction speed, full-depth precast concrete deck panel systems have advantages such as high-quality plant production, low permeability, and much-reduced volume-change cracking caused by shrinkage and temperature drop during initial curing. High-quality precast concrete decks are often pretensioned in the transverse direction and post-tensioned in the longitudinal direction. They have relatively low life-cycle costs, even though they may have higher initial costs in some U.S. markets. Although full-depth precast concrete deck panel systems have many advantages compared to CIP decks, some challenges have been reported with these systems, including achieving full composite action with the supporting girders and durability of the CIP joints. The outcomes of this project address these issues. The goals of this project are as follows: 1. Develop a simplified full-depth precast concrete deck panel system with panel-to-panel and panel-to-girder connections that satisfy the following criteria: a. Provide satisfactory composite action with the supporting girders. b. Meet FHWA goals of ABC, which include minimal construction steps, duration of each step, and safety risks to construction workers. c. Can be assembled from the top of the bridge deck. d. Require simplified grouting between the precast deck panels and the supporting girders. e. Keep fabrication of the precast deck panels as simple as possible by minimizing shear pockets, minimizing top-surface construction joints, and relaxing tight tolerances. f. Make inspection easy for quality assurance during construction. g. Require minimal long-term maintenance. 1 Copyright National Academy of Sciences. All rights reserved.


2 Simplified Full-Depth Precast Concrete Deck Panel Systems

2. Investigate various concepts, including constructability and structural behavior of the girder–deck system under various stages of the bridge life. 3. Investigate various design and construction issues through analytical and experimental programs, and select the proper criteria to be recommended for implementation. 4. Develop guidelines and specifications for design and construction of the recommended system. 5. Carry out proposed revisions to the AASHTO LRFD Bridge Design Specifications. The outcome of the research can be summarized as follows: 1. Comprehensive literature review: Information on bridge projects built with full-depth precast concrete panel systems were collected, reviewed, and summarized. The summary provides specific information on critical issues such as grouting material, shear key details, panel-to-panel connections, panel-to-superstructure connections, design, reinforcement details, fabrication, and installation of the deck panel system. 2. A full-depth precast concrete deck panel system, which has the following features: a. Spacing between shear connector joints that is up to 6 ft. b. A discrete joint connection system that provides for full composite behavior between the deck and the supporting girders. c. Spacing between the discrete joints at the haunch between girder top face and deck soffit that can be left unfilled. d. The ability to be used with precast concrete or steel I-girders. e. The deck can be longitudinally post-tensioned using a novel, simplified, “ductin-duct” system. This system uses sheathed post-tensioned strands that do not require grouting or splicing of the post-tensioned ducts at the transverse joints between panels. f. A solid deck panel, or ribbed if deck weight reduction is desirable to improve superimposed load capacity. g. A unique collared dual rod (CDR) assembly developed and found to give excellent results for shear connection of concrete girders to the precast deck. 3. Analytical and experimental investigations of the developed full-depth precast concrete deck system. The experimental study included push-off (small-scale) specimens, as well as large-scale beams. 4. Guideline manual: Recommended guidelines for design, detailing, fabrication, installation, and construction were developed to help implement the proposed system by designers and bridge owners. 5. Proposed revisions to the AASHTO LRFD Bridge Design Specifications.



CHAPTER 1

Background

1.1 General Public inconvenience and loss of income during bridge construction and rehabilitation have prompted exploration of rapid construction methods. In 2001, FHWA launched the ABC initiative (FHWA 2011). ABC is bridge construction that uses innovative planning, design, materials, and construction methods in a safe and cost-effective manner to reduce the construction time associated with maintenance of traffic when building new bridges or replacing and rehabilitating existing bridges. CIP bridge deck slabs represent a significant part of construction of stringer-type bridge superstructures. Much of the construction time is consumed in deck forming, placement of steel bars, and placement and curing of CIP deck concrete. Also, studies conducted by bridge owners, such as the Oregon Department of Transportation (DOT), have shown that CIP decks are considered one of the major elements of highway bridges that require continuous maintenance (i.e., patching, sealing, and overlays) (Johnson 2012). CIP decks pose low durability performance because of shrinkage cracking, high permeability, and exposure to deicing chemicals and moisture. As a result, full-depth precast concrete deck panel systems have been increasingly used to replace CIP decks. In addition to high construction speed, full-depth precast concrete deck panel systems have many advantages, such as high-quality plant production under tight tolerances, low permeability, and much-reduced volume-change cracking caused by shrinkage and temperature effects during initial curing. High-quality precast concrete decks are often two-way prestressed. They have relatively low life-cycle costs, even though they may have higher initial costs in some U.S. markets.

1.2 Literature Review Development of the full-depth precast concrete deck panel systems has occurred during three distinct periods. The first period was from the early 1960s to the early 1980s, where no standard geometry, connection details, or specifications were used. The second stage was from the early 1980s to the end of the 1990s, where more experimental efforts were set towards studying the structural behavior of full-depth precast concrete deck panel systems made composite with the supporting girders (Issa et al. 1995, Issa et al. 1998). Towards the end of the second stage, innovative ideas of connecting the precast panels with the supporting girders were devised. These included the development of large 1.25-in.-diameter steel studs (Badie et al. 2002), the dovetail steel connection (Tadros and Baishya 1998), and the debonded shear key detail for concrete I-girders (Tadros et al. 2002). During this era, new rapid-construction full-depth precast concrete deck panel systems were also developed and tested (Yamane et al. 1998, Badie et al. 1998, Badie et al. 1999). 3 Copyright National Academy of Sciences. All rights reserved.



The third period started in 2000 and has continued. Most of the research activities in this period have been focused on developing standard geometry and connection details that ensure high construction speed and reduced future maintenance. Among these efforts were studies conducted at the University of Wisconsin–Madison (Carter III et al. 2007). In addition, research was conducted jointly by George Washington University in Washington, D.C., and the University of Nebraska–Lincoln (Badie and Tadros 2008). Other notable research was conducted at Purdue University in West Lafayette, Indiana (Frosch et al. 2010); Virginia Polytechnic Institute and State University in Blacksburg (Scholz et al. 2007, Sullivan et al. 2011); and Utah State University in Logan (Wells et al. 2013). In-progress research is being conducted at the University of Nebraska–Lincoln. The goals of these research projects can be summarized as follows: (1) examine the possibility of extending the spacing of the shear pockets to 48 in., (2) simplify panel-to-panel and panel-to-girder connection details, and (3) develop recommended guidelines for design, detailing, fabrication, installation, and construction for the AASHTO LRFD Bridge Design Specifications. A summary of notable connection details for full-depth precast concrete deck panel systems developed in the past 25 years is given in Appendix A. More information can be found in the following references: Issa et al. 1995, Tadros and Baishya 1998, Markowski et al. 2005, Carter III et al. 2007, Scholz et al. 2007, Badie and Tadros 2008, Sullivan et al. 2011, Frosch et al. 2010, and Wells et al. 2013. Additional information can be found in the state-of-the-art report on full-depth precast concrete deck panels (Precast/Prestressed Concrete Institute 2011A) and in NCHRP 10-71 (French et al. 2011). Although the research conducted in NCHRP 10-71 was for precast/pretensioned members connected longitudinally, some of the developed connection details can be used for full-depth precast concrete deck panels supported by concrete–steel girders. The following sections provide a summary of some of the major issues relevant to the goals of this project.

1.2.1 Variable-Depth Precast Deck Panel Systems A variable-depth precast deck panel system was developed at the University of Nebraska– Lincoln (Yamane et al. 1998, Tadros and Baishya 1998), as shown in Figure 1.1. This system had the following unique features: 1. A two-way ribbed panel was used to reduce the weight of the deck. Longitudinal ribs were provided only at the girder lines. Transverse ribs were provided at about 26-in. spacing. 2. The panels were transversely pretensioned and longitudinally post-tensioned. Longitudinal post-tensioning was provided using high-strength threaded bars installed in the longitudinal ribs at girder lines. 3. Shear key detail dimensions were optimized to reduce the amount of grout. 4. Shear pockets were hidden to minimize potential joints and color variation of the completed deck.

1.2.2 Slab–Girder Systems Made with Discrete Joints In the early 1990s, a full-depth precast concrete deck system was used on the Suehiro Viaduct at the Kansai International Airport Line in Japan (Matsui et al. 1994, Manabe and Matsui 2004). This system had the following features: • A variable-depth precast concrete panel system, as shown in Figure 1.2. The thickened ends

of the panel provide enough space to support the panel and to accommodate the leveling bolt system used to adjust panel elevation. This helped the designer to reduce the self-weight of the deck and to splice the supporting steel girders without the need to use a thick haunch.



Background 5

Figure 1.1. Details of the variable-depth precast deck panel developed in NCHRP Report 407: Rapid Replacement of Bridge Decks (Tadros and Baishya 1998) (25.4 mm = 1.0 in.).

• Shear connectors provided only at the transverse panel-to-panel joints and at a relatively wide

spacing of 4 ft, 11 in. This simplified the production of the precast panels, as no shear pockets were created in the panel. • Discrete joints. Only the space between the steel girder and the thickened ends of the panels was filled with grout, as shown in Figure 1.3. Using the discrete joints reduced the amount of labor and materials required to fill the haunch. • The precast panels were transversely pretensioned, and the completed deck was longitudinally post-tensioned. The longitudinal post-tensioning was applied after the panel-to-panel joints were grouted and cured but before the panel-to-girder joints were grouted. Therefore, the full post-tensioned force was applied only on the deck. • The superstructure was designed as a noncomposite girder, conforming to the Japanese bridge design specifications. Therefore, a small number of studs were used only to anchor

Figure 1.2. Cross section of the precast panel system used on the Suehiro Viaduct at the Kansai International Airport Line in Japan.




Figure 1.3. Precast deck during construction showing the wide spacing of the shear connectors and the grout barrier for the panel-to-girder connection.

the precast slab with the supporting girders. However, the field instrumentation and analysis conducted on the bridge found that the superstructure behaved as a partially composite system (Manabe and Matsui 2004). It is a common practice in the United States to design slab–I-girder assemblies as composite structures for superimposed dead and live loads. Article 6.10.1.2 of AASHTO LRFD Bridge Design Specifications states that noncomposite sections are not recommended but are permitted.

1.2.3 Shear Connector Spacing and Capacity Traditionally, the AASHTO LRFD Bridge Design Specifications up to the 6th edition in 2012 specified that the spacing between shear connectors for steel- and concrete-girder bridges should not exceed 24 in. The source of this limit is unclear. An investigation described in NCHRP Report 584 (Badie and Tadros 2008) on full-depth precast concrete deck panels attributes that limit to a rule of thumb in design suggested in 1943 (Newmark and Siess 1943). The 24-in. limit first appeared in 1944 in AASHTO Standard Specifications for Highway Bridges, 4th edition, and was kept without change in the following editions until the 17th edition in 2002. When the 1st edition of the AASHTO LRFD Bridge Design Specifications appeared in 1994, the 24-in. limit was kept without change in the subsequent editions until the 6th edition. It should be noted that the 24 in. recommended by Newmark and Siess (1943) was developed for shear connectors placed at relatively small spacing along the length of the supporting girders, which is common with cast-in-place decks. The research team believes that the 24-in. limit was not intended for widely spaced clusters of studs, which are now used with full-depth precast concrete deck panels. Minimizing the number of connectors and blockouts was preferred for precast panel systems to simplify production and reduce potential conflicts at the construction site (Oliva and Okumus 2013). 1.2.3.1 Composite Deck on Concrete Girders In a study conducted at Virginia Polytechnic Institute and State University, hooked reinforcing bars anchored in the girder web and embedded in the concrete deck were used to examine the possibility of extending the spacing between the shear pockets beyond the 24-inch limit (Scholz et al. 2007, Sullivan et al. 2011). A full-scale mock-up was built and tested in the laboratory, where the spacing between the shear connector clusters was set at 24 in. and 48 in. The test results showed that full composite action was achievable in both 2-ft and 4-ft pocket spacing.



Background 7

Based on the experimental investigation conducted at the University of Nebraska–Lincoln, the Nebraska Department of Roads—now the Nebraska DOT—used a full-depth precast deck panel system on the Kearney East Bypass Bridge in Kearney, Nebraska (Morcous et al. 2013). The precast deck was supported by concrete girders. The shear connectors were made of clusters of two 1.25-in.-diameter, 120-ksi threaded rods spaced at 48 in. The threaded rods were anchored in the girder web and in the precast panels using heavy nuts. Steel tubes provided special confinement of the grout around the threaded rods. 1.2.3.2 Composite Deck on Steel Girders Steel studs are typically used for composite decks supported on steel girders. Many studies were conducted between 2002 and 2015 to investigate the possibility of extending the spacing beyond the traditional 24 in. Among these studies was the work conducted by Issa et al. (2003) to investigate the effect of providing the steel studs in clusters on the capacity value for studs, which is known as the group effect. The test data obtained using push-off specimens showed up to 25% capacity reduction because of the clustering effects. AASHTO LRFD Bridge Design Specifications do not recommend any change in capacity with the number of studs in a cluster. Issa et al. (2003) recommended calculating the capacity as 85% or less of AASHTO’s value when more than two studs clustered in a pocket were recommended. Testing of panels connected to 84-ft-long steel girders with both 24-in. and 48-in. connector spacing was conducted at the University of Wisconsin–Madison (Markowski et al. 2005). That study found no reduction in composite action stiffness or strength caused by the wider spacing, even after 2 million cycles of repeated service loading. Upon testing to the theoretical ultimate capacity, no deck uplift was detected; and the 48-in. connector spacing provided an experimental ultimate load capacity higher than predicted using AASHTO procedures, even though no capacity reduction was taken for multiple studs per cluster. In NCHRP 12-65, Badie and Tadros (2008) tested two composite beams where spacing between the shear connector clusters was set at 24 in. and 48 in. The beams consisted of fulldepth precast deck panels supported on steel girders. The composite beams were exposed to 2 million cycles of fatigue load and then tested to failure. The test results showed that extending the stud spacing from 24 in. to 48 in. had no detrimental effect either on the composite beam stiffness or on the ultimate flexural capacity. However, the study recommended providing special confinement of the stud clusters to guarantee full development of the studs. A study conducted at Virginia Polytechnic Institute and State University examined the possibility of extending the spacing between the shear pockets beyond the 24-in. limit (Scholz et al. 2007, Sullivan et al. 2011). A full-scale mock-up was built and tested in the laboratory, where the spacing between the shear connector clusters was set at 24 in. and 48 in. The test results showed that full composite action was achievable using shear studs as shear connectors at both 2-ft and 4-ft spacing. Researchers at the Turner–Fairbank Highway Research Center in McLean, Virginia, evaluated whether the AASHTO Strength and Fatigue Limit States were applicable to clustered shear studs used for precast deck panel systems (Provines and Ocel 2014A, Provines and Ocel 2014B). Based on a review of the current domestic and international shear stud specifications, the researchers found that the fatigue provisions might be overly conservative, while the strength provisions might be unconservative. The experimental program included 16 large-scale tests using four configurations of shear stud spacing that ranged from a typical cast-in-place deck detail with studs every 12 in. or 24 in. to configurations more conducive to precast panels with clustered shear studs spaced at 36 in. and 48 in. Of the 16 large-scale tests, four were static and 12 were fatigue tests. Upon completion of the large-scale tests, small-scale (push-off) fatigue and static tests were also conducted. The static




tests focused on evaluating the AASHTO minimum longitudinal and transverse stud spacing, while the fatigue tests focused on evaluating the AASHTO shear stud constant amplitude fatigue limit. The test results showed that, regardless of the spacing between the clusters, the specimens were unable to reach the nominal design strength. The measured flexural strength was about 80% of the nominal design capacity. The static test results suggested a shear factor close to the 0.8 factor found in some international codes. The extended stud cluster spacing up to 48 in. did not appear to have a negative effect on either the relative slip or uplift between the concrete deck and steel beam. This is consistent with the conclusions reported in NCHRP 12-65 (Badie and Tadros 2008). No special confinement was provided to the stud clusters in the specimens tested at FHWA. The only source of confinement was provided by the slab reinforcement that was designed using the LRFD Empirical Design Method. 1.2.3.3 Current Provisions of AASHTO LRFD Bridge Design Specifications, 8th Edition Composite deck on concrete girders. Article 5.7.4.5 of the AASHTO LRFD Bridge Design Specifications permits a longitudinal spacing up to 48 in. but not greater than the beam depth. Equation 5.7.4.3-3 of Article 5.7.4 provides the formula for the nominal shear resistance that is a modified version of the basic shear friction model. In this formula, the shear resistance is proportional to the normal clamping force provided by the shear connectors through a friction coefficient. Additional shear resistance is provided by the cohesion and/or aggregate interlock, depending on the nature of the interface. Two upper bound limits of the nominal shear resistance are provided in Equation 5.7.4.3-4 and Equation 5.7.4.3-5. The AASHTO LRFD Bridge Design Specifications do not provide any provisions when the shear connectors are set in clusters nor any recommendations regarding any additional special confinement. Composite deck on steel girders. Article 6.10.10.1.2 of the AASHTO LRFD Bridge Design Specifications permits a longitudinal spacing up to 48 in. for members having a web depth greater than or equal to 24.0 in. For members with a web depth less than 24.0 in., the center-to-center pitch of shear connectors shall not exceed 24.0 in. Article 6.10.10.1.2 states that the spacing between the shear connectors is determined to satisfy the Fatigue Limit State given in Article 6.10.10.2 and the Strength Limit State given in Article 6.10.10.4. Equation 6.10.10.4.3-1 of Article 6.10.10.4.3 provides the formula for the nominal shear resistance. The formula shows that the shear connector strength is a function of both the concrete modulus of elasticity and concrete strength. The formula has an upper bound that is the product of the cross-sectional area of the connector times its ultimate tensile strength. AASHTO LRFD Bridge Design Specifications do not provide any provisions when the shear connectors are set in clusters nor any recommendations regarding additional special confinement. Article I8 of the Steel Construction Manual, 15th edition, published by the American Institute of Steel Construction (2017), uses the same formula as the AASHTO LRFD Bridge Design Specifications to determine the nominal shear capacity of the shear connectors. However, the formula applies a 75% reduction factor on the upper bound. This is consistent with the recommendation given by the study conducted at the Turner–Fairbank Highway Research Center (Provines and Ocel 2014A, Provines and Ocel 2014B).



CHAPTER 2

Research Goals and Approach

2.1 Introduction The goals of this project were as follows: 1. Develop a full-depth precast concrete deck panel system with simplified connection details. The connection details include panel-to-panel and panel-to-girder connections that, specifically, – Provide satisfactory composite action with the supporting girders; – Meet the FHWA goals of ABC. Minimal construction steps, duration of each step, and safety risk to construction workers are of utmost importance; – Can be assembled from the top of the bridge deck; – Require simplified or no grouting between the precast deck panels and the supporting girders; – Keep the fabrication of the precast deck panels as simple as possible by minimizing shear pockets, minimizing cold top-surface construction joints, and relaxing tight tolerances in achieving satisfactory interface shear behavior; – Can be inspected for quality assurance during various stages of construction; and – Require minimal long-term maintenance. 2. Establish analytical procedures to investigate various concepts, such as constructability and structural behavior of the total system under various stages of the bridge life, including overloading. 3. Develop an experimental program to examine the various concepts to validate the analytical program and to select the system (or systems) to be retained for finalization. 4. Conduct more detailed analysis and testing of the developed system to establish design and construction guidelines. 5. Develop sample guidelines–specifications for the developed system that are validated by the analytical and experimental programs. 6. Develop a draft of proposed revisions to the AASHTO LRFD Bridge Design Specifications provisions to encourage widespread use of the research results. As a result of the research conducted in this project, it has been possible to develop a fulldepth precast concrete deck panel system with shear connection spacing of up to 6 ft. Therefore, the shear pockets exist only in the transverse joints between the panels if the panels are made 6-ft long in the direction of traffic. However, the panels can be made as long as 12 ft, which generally is considered the maximum allowed dimension for shipping without special permit in most of the United States. In this case, an intermediate pocket would be required at a spacing not exceeding 6 ft. Panel width can be as much as the total bridge width or a partial bridge width for relatively wide bridge decks. The deck slab can be solid, or it can have a variable depth—that is, ribbed—to reduce deck weight and, thus, increase allowance for additional loads in situations where such an upgrade is 9 Copyright National Academy of Sciences. All rights reserved.



desirable. The deck system is pretensioned transversely and post-tensioned—or conventionally reinforced—longitudinally. The research was conducted in such a way that only the joints (pockets)—where the interface shear connectors are located—are required to be grouted. Such a system is referred to as a system with “discrete joints” between the deck and the girders. The haunch between girder and the deck may be left unfilled in the gaps between shear pocket joints. This option was used in the research to allow for both choices, regardless of whether the haunch was filled. The discrete joint system would reduce the labor and materials needed to fill the haunch. In addition, blind grouting of the haunch and associated questionable quality would be eliminated. The discrete joint system is similar to the system used in the Suehiro Viaduct at Japan’s Kansai International Airport Line (Matsui et al. 1994, Manabe and Matsui 2004). However, unlike the Japanese project, the discrete joint system developed in this project provides for composite action between the deck and the girders. However, there is some benefit to grouting the haunch. This research team is not opposed to doing that. Grouted haunches protect the space between the girders and the deck from being filled with foreign and unwanted material. After numerous trials, the research team reached a conclusion that the best material for grouting the shear pockets is ultra-high-performance concrete (UHPC) (Graybeal 2013, Graybeal 2014). Further, if the owner prefers not to introduce longitudinal post-tensioning in the field, the transverse joints should be filled with UHPC and reinforcing bars should project into the joints, as has been recently employed by New York and other states. If the deck is longitudinally post-tensioned, the transverse joint can be made much narrower, as it would not require space for splicing reinforcing bars, and it would be filled with nonshrink grout that has a compressive strength similar to the precast deck concrete. This would be much less expensive than UHPC. The innovative duct-in-duct post-tensioning method is proposed. The larger duct may be simply made of polyvinyl chloride (PVC) tube. As described in Chapter 3, the exterior tube need not extend beyond the formed edge of the panel. Once all the transverse and shear pocket joints are filled, preinstalled full bridge-length greased strands in rubber tubes are then tensioned to the required prestress. Thus, all grouting is done in one stage to simplify construction, and no duct couple or large coupling pockets are required. Analysis has shown that the loss of post-tensioning—transferred from the deck to the girder because of the full connection before post-tensioning—is insignificant. The goals of the project were achieved by executing the following steps: 1. Develop a full-depth precast concrete ribbed slab deck panel system. 2. Analytically investigate performance of the system. 3. Experimentally investigate the behavior of the beam–deck connection using push-off specimens. 4. Investigate the behavior of the full beam–deck system using full-scale composite beam–deck specimens. 5. Develop design examples and guidelines to facilitate implementation of the proposed system.

2.2 Precast Deck Panel System with Longitudinal Post-Tensioning An 8.5-in.-thick ribbed panel—as shown in Figure 2.1 and Figure 2.2—is proposed. The ribbed panel has longitudinal ribs between adjacent girder lines, spaced at 3 ft or less. In addition, there are longitudinal ribs directly over the girder lines. If necessary, the panel overhangs




Figure 2.1. Plan view of the 6-ft- and 12-ft-long panel.



Figure 2.2. Precast deck panel system: Section A-A, B-B, and C-C.


Research Goals and Approach 13

are expected to be made of full 8.5-in. thickness to resist impact loading on the bridge railing (Precast/Prestressed Concrete Institute 2011A). The longitudinal ribs and the solid overhang help eliminate the potential for torsional stresses caused by moving truckloads. The precast concrete panel was designed with 6-ksi-specified concrete strength at service. The panel can be made 6-ft long to avoid in-panel shear pockets. Alternately, the panels can be 12-ft long with shear pocket at mid-length (6-ft) spacing, as shown in Figure 2.1. Depending on the bridge design, other panel lengths are possible. This project gives evidence that connection spacing can be as large as 6 ft, but it does not dictate the length of each panel or whether each panel is a ribbed slab or a solid slab. Figure 2.2 and Figure 2.3 show the cross sections of the panel, which has a shear key at the transverse joint. At the top, the shear key has a 2.5-inch-wide gap between panels to fill the transverse joint with grout. If the deck is not post-tensioned and a UHPC conventionally reinforced joint is desired, the shear key is intentionally roughened by applying a retarder to expose the aggregates and enhance the bond between the panel and the grout, according to Iowa DOT (Wipf et al. 2011). Feedback from the precaster of the panels used on this project indicated that a simplification could be achieved by reducing the projection of the bottom lip of the shear key because that length is relatively thin and could crack during handling and shipping of the panels. The research team agrees with this improvement and recommends a modified shear key geometry, as given in Figure 2.2. The precast panel is pretensioned in the transverse direction. Experience has shown that about 250-psi average effective prestress produces adequate capacity in this direction for handling and service loads. Additional reinforcement is needed to help distribute wheel loads to the transverse ribs. The longitudinal post-tensioning system is made of sheathed 0.6-in.-diameter post-tensioned tendons placed in larger PVC tubes. The post-tensioned tendons are designed to introduce a minimum average compressive prestress of 250 psi at the transverse joints. The net stress after allowance for the effects of superimposed loads in continuous span bridge decks should be designed to be less than the limit permitted by the AASHTO LRFD Bridge Design Specifications. For continuous spans expected to have negative moments at the piers, the post-tensioned compressive stress may be as large as 600 psi to 700 psi. The tendons are unbonded seven-wire strands coated with corrosion-inhibiting grease, regardless of whether transverse joint grout flows into the outer PVC ducts. The strands are continuously encased in polyethylene sheathing, according to ASTM A416 and as shown in Figure 2.4. Thus, post-tensioning is guaranteed to extend for the full length of the tendons and across the transverse joints, even after all joints are filled with grout. The strands would have an excellent multilayer corrosion-protection system. Traditional metal or plastic corrugated duct materials have traditionally been used and can still be used if the designer desires. However, a simple, locally available PVC tube can be used, as its function is only to create space for the fully encapsulated groups of strands to go through the deck end-to-end. This system of unbonded tendons was successfully used on the Arbor Rail Line Bridge replacement in Nebraska City, Nebraska (Hennessey and Bexten 2002), and later on bridges in Oregon and Michigan. UHPC is recommended to fill the shear pockets. In addition, it can be used to fill the transverse joints if no longitudinal post-tensioning is employed. The proposed minimum compressive strength at the time of grinding the joint and opening the bridge to traffic is 12 ksi. The UHPC mix used for this project was supplied by Lafarge North America. While able to use custom-designed mixes with local materials, the research team opted to use the bagged mix from this experienced supplier to minimize variability in the project. Future users of the system may opt to develop their own mixes, as long as the material meets the UHPC criteria




Figure 2.3. Precast deck panel system: Section D-D on concrete and steel girders.



Figure 2.4. Unbonded seven-wire strand coated with corrosion-inhibiting grease and encased in polyethylene sheathing.

set by FHWA (Graybeal 2013, Graybeal 2014). If a flowable fill is used to fill the haunches over the girders, holes in the panel would be needed to place the grout and vent the air. The two cases for the interface shear pockets considered in this project were 1. Panel-to-concrete girder connection (Figure 2.5): An innovative shear connector assembly was developed for this project. Based on numerous trials and iterations, the new CDR connection hardware was developed in this research. It consists of two 1½-in.-diameter (ASTM A193 B7: minimum specified yield strength = 105 ksi, minimum tensile strength = 125 ksi) threaded rods that are connected with a collar and a ½-in.-thick horizontal top plate assembly. The collar is made of two tubes (outer diameter = 2 in., inner diameter = 15⁄8 in.) welded to a ½-in.-thick vertical plate. The collar assembly is 7-in. tall and is embedded 3⁄4 in. into the top flange of the concrete girder, as shown in Figure 2.5. A 3-D print of the shear connector assembly was made to help understand and communicate its features, as shown in Figure 2.6. Note that the CDR is placed in the precast girder before girder concrete is placed. The two threaded rods are made 12-in. long to allow for field cutting to proper length and for haunch variability. Additional No. 4 rebars were added at the base of the collar in the girder top flange to protect the concrete from crushing because of the high bearing stress produced by the threaded rods and the collar assembly, as shown in Figure 2.5. Nonlinear finite element models were developed to examine the behavior of this unique collar assembly, and the results are shown in Figure 2.7. As can be seen, the collar helps reduce the bending of threaded rods and the stress concentration in the grout. 2. Panel to steel girder connection (Figure 2.8): The shear connector assembly consists of nine 1.0-in.-diameter studs (ASTM A108, Fy,min = 51 ksi, Fu,min = 65 ksi). The studs are welded to the top flange of the steel girder. Transverse and longitudinal spacing between the studs satisfy the minimum spacing requirement given by the AASHTO LRFD Bridge Design Specifications of four times the stud diameter. Although the testing was performed on 1-in.-diameter studs, it can be shown analytically that ¾-in.-, 7⁄8-in.-, and 1¼-in.-diameter studs can be used, as long as the stud cluster does not exceed nine studs. If a larger number of studs in a cluster is necessary, it is recommended that further experiments be undertaken to determine the group effect. The precast panel is provided with additional reinforcement around the pocket—as shown in View C-C of Figure 2.5 and Figure 2.8—to help confine the concrete in this zone of high-concentrated shearing force.




Figure 2.5. Details of the panel-to-concrete girder connection.




(a) Components

(b) Full assembly

Figure 2.6. A 3-D print of the shear connector assembly for concrete girders.




Assembly with collar

Assembly without collar

(a) Von Mises stresses in the grout around the shear connector assembly (with collar, smaller red area is in high stress).

(b) Von Mises stresses in the shear connector assembly (with collar, smaller red area of the stud is in high stress).

(c) Von Mises stresses in the shear connector assembly at the girder–haunch interface (with collar, stresses in the rods are smaller).

Figure 2.7. Von Mises stresses in the grouted shear pocket and the shear connector assembly.




Figure 2.8. Details of the panel-to-steel girder connection.




Figure 2.9. 3-D rendering of the complete deck.

Since the width of the transverse joints is narrow and the shear pockets are covered, the complete deck has a uniform width joint, as shown in Figure 2.9.

2.3 Precast Deck Panel System with Conventional Longitudinal Reinforcement The proposed system can be used without longitudinal post-tensioning. Figure 2.10 shows the plan view of the panel. The longitudinal reinforcement of the panels would be coupled rebars across the transverse joints. The top layer of rebar is made of No. 5 at 10 in. in the 5-in.-thick slab. The bottom layer is made of two No. 6 rebars at each of the longitudinal ribs, which are spaced at 3 ft or less, as shown in Figure 2.11 and Figure 2.12. Top and bottom layers are provided with two 3⁄8-in. and 2-in. concrete covers, respectively. Additional longitudinal reinforcement over the piers in continuous span bridges may be required by design. The longitudinal reinforcement extends into the transverse grouted joint, as shown in Figure 2.13. Because of the use of UHPC, the length of the joint to produce full continuity in the bars is greatly reduced compared with conventional concrete or nonfiber reinforced grouts. To avoid interference between the spliced bars, the bars may be bent horizontally at 15 degrees or staggered in production. A similar splicing concept has been found to provide full development of the spliced bars by FHWA (Graybeal 2014). Figure 2.13 shows a plan view of the spliced longitudinal reinforcement bars in the panel-to-panel joint.




B

Figure 2.10. Plan view of the precast panel with conventional reinforcement (for clarity, reinforcement is not shown).

Figure 2.11. Precast panel with conventional reinforcement: Section A-A.




Figure 2.12. Precast panel with conventional reinforcement: Section B-B.



Figure 2.13. Splice of longitudinal rebars at the panel-to-panel joint.



CHAPTER 3

Research Findings

This chapter presents the results of the analytical and experimental programs conducted to validate the full-depth precast concrete panel system proposed in Chapter 2 and to offer guidelines for its design. The affected sections in the AASHTO LRFD Bridge Design Specifications and proposed revisions to these sections are also presented.

3.1 Analytical Program 3.1.1 Objectives of the Analytical Program As stated in Chapter 2, the goal of this project was to extend the limit for spacing between shear connector clusters to 6 ft from the current limit of 4 ft. Investigation was done using discrete connections between the deck and the girder, with the remainder of the haunch in the space between connectors kept unfilled. However, the research team has no objection to filling the haunches with a flowable cementitious material. All details and conclusions reached in this research would equally apply to both options. Table 3.1 provides a summary of the design requirements and the parameters used in the analytical program. The design requirements were divided into two groups: design requirements related to the precast deck and design requirements related to the composite slab–beam system. The analysis was conducted for spacing between the shear connector clusters ranging from 2 ft to 8 ft. In the analytical investigation, the case of 8-ft spacing was considered to have a more comprehensive understanding of trends in the results.

3.1.2 Design Requirement 1: Flexural Design of Deck 3.1.2.1 Solid Slabs Supported by Discrete Supports The purpose of this analysis was to investigate the effect of using discrete joints at 2-ft, 4-ft, 6-ft, and 8-ft spacing on the design of concrete decks. This investigation was conducted for three values of girder spacing (6 ft, 9 ft, and 12 ft), which are labeled G6, G9, and G12 in this study. An 8-in.-thick slab was considered for all cases. The concrete compressive strength of the deck was set at 6,000 psi. The number of girder lines and size of the deck considered are shown in Table 3.2. The following values of spacing for the shear connectors were considered: • C0: Represents a continuous haunch. • C2, C4, C6, and C8: Represent discrete joints at 2-ft, 4-ft, 6-ft, and 8-ft spacing, respectively.

The analysis was conducted using a commercial finite element analysis software. The slab was modeled using 6 in. × 6 in. shell elements. The deck supports were point supports along the 24 Copyright National Academy of Sciences. All rights reserved.


Research Findings 25 Table 3.1. Design requirements and matrix of parameters used in the analytical investigation. Design Parameters and Corresponding Range Bridge Component

Design Requirements

Analysis Method

Bridge Span (ft)

Girder Spacing (ft)

Span-toGirder Depth Ratio

Girder Strength (ksi)

Haunch Spacing (ft)

1. Flexure design

(I) Precast concrete deck

2. Two-way shear at discrete joints 3. Two-way shear at wheel loads

6, 9, 12 FEA

2, 4, 6, 8

na

na

na

Deck Thickness (in.)

Deck Strength (ksi)

na

6, 8, 10 in. (solid) and 5.5/8.5 in. (variable)a

na

na

2, 4, 6, 8 12 x 12, 24 x 24

6, 9, 12

4, 8

5. One-way shear 6. Flexure design 7. Deflection (II) Composite slab–beam

Haunch Thickness (in.)

12 x 12, 24 x 24

na

na

4. Bearing stresses

Haunch Size (in.)

8. Interface shear

Vierendeel Model and Simplified Beam Analysis

80, 144, 216

6, 12

20, 35

6, 12

2, 4, 6, 8

12 x 12, 24 x 24

2, 6

7.5, 10

6

3-D FEA

100, 120, 160, 216

6, 9, 10, 12.75

20, 35

6, 12

2, 4, 6, 8

12-in. long, 2, 6 24-in. long

7.5, 10

4, 8

9. Vertical shear 10. Distribution factors

Note: FEA = finite element analysis; na = not applicable. a 5.5/8.5 in. indicates the thickness of the thin part to the thickness of the thick part of the variable thickness slab .

girder lines. The point supports allowed rotation in all directions, while restraining displacement in all directions. Loading was applied using the rear axle of an HL93 truck. It represents 32 kips per axle, or 16 kips per wheel. The tire contact area was 24 in. × 12 in. to match the size of the finite element mesh used in the analysis, which is close to the AASHTO recommended area of 20 in. × 10 in. Uniform pressure of 8 k/ft2 was applied to the contact area to provide 16 kips per wheel. Single and double trucks were used in the analysis to determine the maximum effects for each case. A multiple presence factor of 1.2 for one-lane loaded and 1.0 for two-lane loaded was applied. Dynamic load allowance of 1.33 was considered. Analysis of G6C8 using 6-in.- and 10-in.-thick slabs was also conducted to study the effect of the slab thickness on the flexural behavior. Results of the study are summarized in Table 3.3 and Table 3.4. The following observations were obtained from the finite element analysis: 1. As the spacing between the discrete joints increases, the slab behavior approaches a columnsupported two-way slab. Bending moment in the transverse direction deviates from that

Table 3.2. Number of girder lines and size of the deck. Case

Girder Spacing (ft)

Number of Girder Lines

Deck Width (ft)

G6 G9 G12

6 9 12

9 7 5

48 54 48

Deck Length (ft) 36 36 36



Transverse Direction

Case

Girder Spacing (ft)

Spacing Between Joints (ft)

G6C0 G6C2 G6C4 G6C6

6 6 6 6

Uniform 2 4 6

G6C8 G9C0 G9C2 G9C4 G9C6 G9C8

6 9 9 9 9 9

8 Uniform 2 4 6 8

G12C0 G12C2 G12C4 G12C6 G12C8

12 12 12 12 12

Uniform 2 4 6 8

LRFD Table A4-1 (k-ft/ft) M+ve

4.83

6.29

8.01

M-ve @ 12 in.

-2.31

-3.71

-6.74

M-ve @ 6 in.

-3.5

-5.13

-8.51

FEA (k-ft/ft) M-ve @ 12 in. 24 x 24-in. haunch

M+ve

Longitudinal Direction (k-ft/ft) M-ve @ 6 in. 12 x 12-in. haunch

M+ve

M-ve @ 12 in. 12 x 12-in. haunch M long./ FEA M trans. @ 6 in. (%) 0.000 0.00 -0.985 31.55 -2.445 64.16 -2.977 69.96

FEA

%

FEA

%

FEA

%

FEA

4.533 4.558 4.718 4.892

6.1 5.6 2.3 -1.3

-2.480 -2.501 -2.571 -2.806

-7.4 -8.3 -11.3 -21.5

-2.795 -3.122 -3.811 -4.255

20.1 10.8 -8.9 -21.6

2.388 2.451 2.519 2.557

M long./ M trans. (%) 52.68 53.77 53.39 52.27

4.983 5.907 5.972 6.030 6.252 6.410

-3.2 6.1 5.1 4.1 0.6 -1.9

-2.933 -3.530 -3.575 -3.853 -4.234 -4.493

-27.0 4.9 3.6 -3.9 -14.1 -21.1

-4.469 -4.475 -4.576 -5.228 -6.042 -6.456

-27.7 12.8 10.8 -1.9 -17.8 -25.8

2.630 3.554 4.025 4.750 5.822 6.360

52.78 60.17 67.40 78.77 93.12 99.22

-3.813 0.000 -1.325 -3.139 -4.394 -5.131

85.32 0.00 28.96 60.04 72.72 79.48

7.155 7.241 7.246 7.431 7.658

10.7 9.6 9.5 7.2 4.4

-4.456 -4.896 -5.369 -5.621 -6.101

33.9 27.4 20.3 16.6 9.5

-5.303 -5.611 -6.989 -7.614 -8.340

37.7 34.1 17.9 10.5 2.0

4.341 4.860 5.008 6.260 6.682

60.67 67.12 69.11 84.24 87.26

0.000 -1.468 -3.398 -4.790 -5.655

0.00 26.16 48.62 62.91 67.81

Note: M = moment; M+ve = positive moment; M-ve = negative moment; long. = longitude; trans. = transverse.


Table 3.3. Maximum bending moment caused by the rear axle of HL93 truck for solid-thickness slab.


Research Findings 27 Table 3.4. Checking the effect of the slab thickness on the behavior of slabs supported by discrete joints. Results of FEA

Case

Girder Spacing (ft)

Slab Thickness (in)

Spacing between joints (ft)

FEA

%

FEA

%

G6C8

6

6

8

4.944

99.2

-2.994

102.1

-4.547

101.7

2.595

98.7

-3.862

101.3

G6C8 Baseline

6

8

8

4.983

100.0

-2.933

100.0

-4.469

100.0

2.630

100.0

-3.813

100.0

G6C8

6

10

8

5.028

100.9

-2.857

97.4

-4.373

97.9

2.67

101.5

-3.763

98.7

M+ve FEA

Tranverse Direction (k-ft/ft) M-ve @ 12 in. M-ve @ 6 in. M+ve 24 x 24-in. haunch 12 x 12-in. haunch % FEA % FEA %

Longitudinal Direction (k-ft/ft) M+ve

M-ve

given by Table A4.1 of the AASHTO LRFD Bridge Design Specifications, where one-way slab behavior is considered. 2. Discrete joints have a more pronounced effect on the negative moment than on the positive moment. 3. Discrete joints create significant values of positive and negative moments in the longitudinal (secondary) direction and should not be ignored. 4. In all cases, the longitudinal (secondary) positive and negative moments are smaller than corresponding transverse (primary) moments. 5. Changing the thickness of the slab from 6 in. to 10 in. does not have a significant effect on the moment in both directions. 6. Since the analysis was conducted assuming that the slab behaves perfectly elastic, changing the concrete strength of the slab had no effect on the flexural behavior of the slab. 3.1.2.2 Variable-Thickness Ribbed Slabs Supported by Discrete Joints Figure 3.1 shows the longitudinal cross section of the finite element model used for analysis of the variable-thickness slab. Two longitudinal ribs between the girder lines were considered. The analysis was conducted using a commercial finite element analysis package. Parameters of the model were similar to those used in the analysis of the solid panel system. Analysis showed that the slab behaves similarly to a solid-thickness slab in the longitudinal and transverse direction. Based on the finite element analysis results, a set of design tools were developed to aid the design of solid-thickness and variable-thickness slabs. Table 3.5 summarizes the design tools. The design tools provide the longitudinal and transverse bending moments and reactions caused by the rear axle of the HL93 truck and 100 psf. Figure 3.2 to Figure 3.4 show the force effects caused by the rear axle of the HL93 truck. Figure 3.5 to Figure 3.7 show the force effects caused by 100 psf uniform load.

Figure 3.1. Longitudinal cross section of the finite element model used for analysis of the variable-thickness slab.




Table 3.5. Summary of tools developed for design of solid-thickness and variable-thickness ribbed slabs supported by discrete joints. Design Aid Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7

Description Transverse bending moment caused by rear axle of an HL93 truck (including multiple presence factor and dynamic allowance) Longitudinal bending moment caused by rear axle of an HL93 truck (including multiple presence factor and dynamic allowance) for solid-thickness slab Reaction caused by rear axle of an HL93 truck (including multiple presence factor and dynamic allowance) Transverse bending moment caused by 100 psf uniform load Longitudinal bending moment caused by 100 psf uniform load Reaction caused by 100 psf uniform load

Transverse Positive Moment 2.5 6 ft GS 9 ft GS 12 ft GS

Moment (kip-ft/ft)

2.0 1.5 1.0 0.5 0.0

2

3

4 5 Connector Spacing (ft)

6

7

8

7

8

(a)

0.0 -1.0

2

Transverse Negative Moment (12 x 12 in. haunches) 3 4 5 6 Connector Spacing (ft)

6 ft GS 9 ft GS 12 ft GS

Moment (kip-ft/ft)

-2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 (b)

Figure 3.2. Transverse bending moment caused by the rear axle of the HL93 truck (including multiple presence factor and dynamic allowance) for solid-thickness and variable-thickness ribbed slabs (GS = girder spacing).



Research Findings 29 Transverse Negative Moment (24 x 24 in. haunches) 0.0

2

3

4

5

6

7

Connector Spacing (ft) 6 ft GS 9 ft GS 12 ft GS

-1.0 Moment (kip-ft/ft)

8

-2.0 -3.0 -4.0 -5.0 -6.0 -7.0 (c)

Figure 3.2. (Continued). Longitudinal Positive Moment 8.0 7.0 Moment (kip-ft/ft)

6.0 5.0


4.0 3.0 2.0 1.0 0.0

2

3

4


7

8

7

8

(a)

0.0

2

3

Longitudinal Negative Moment 4 5 6 Connector Spacing (ft)

Moment (kip-ft/ft)

-1.0


-2.0 -3.0 -4.0 -5.0 -6.0 (b)

Figure 3.3. Longitudinal bending moment caused by the rear axle of the HL93 truck (including multiple presence factor and dynamic allowance) for solid-thickness and variable-thickness ribbed slabs.



30 Simplified Full-Depth Precast Concrete Deck Panel Systems Reaction 60.0

Reaction (kips)

50.0 40.0 30.0 20.0

6 ft GS 9 ft GS

10.0

12 ft GS

0.0

2

3

4


7

8

Figure 3.4. Reaction caused by the rear axle of the HL93 truck (including multiple presence factor and dynamic allowance) for solid-thickness and variable-thickness ribbed slabs. Transverse Positive Moment

2.5 6 ft GS 9 ft GS 12 ft GS

Moment (kip-ft/ft)

2.0 1.5 1.0 0.5 0.0

2

3

4


7

8

7

8

(a)

0.0

2

3

Transverse Negative Moment at 6 in. 4 5 6 Connector Spacing (ft)

Moment (kip-ft/ft)

-0.5 -1.0 -1.5 -2.0


-2.5 (b)

Figure 3.5. Transverse bending moment caused by 100 psf uniform load for solid-thickness and variable-thickness ribbed slabs. Copyright National Academy of Sciences. All rights reserved.


Research Findings 31

0.0

2

3

Transverse Negative Moment at 12 in. 4 5 6

7

8

7

8

7

8

Connector Spacing (ft)

Moment (kip-ft/ft)

-0.5 -1.0 -1.5 6 ft GS 9 ft GS 12 ft GS

-2.0 -2.5

(c)

Figure 3.5. (Continued). Longitudinal Positive Moment

Moment (kip-ft/ft)

2.0 6 ft GS 9 ft GS 12 ft GS

1.5

1.0

0.5

0.0

2

3

4

5 6 Connector Spacing (ft) (a)

Moment (kip-ft/ft)

0.0

2

3

Longitudinal Negative Moment 4 5 6 Connector Spacing (ft)

-0.5

-1.0

-1.5

-2.0

6 ft GS 9 ft GS 12 ft GS (b)

Figure 3.6. Longitudinal bending moment caused by 100 psf uniform load for solid-thickness and variable-thickness ribbed slabs.



32 Simplified Full-Depth Precast Concrete Deck Panel Systems Reaction

12.0 6 ft GS

10.0 Reaction (kips)

9 ft GS 8.0

12 ft GS

6.0 4.0 2.0 0.0

2

3

4


7

8

Figure 3.7. Reaction caused by 100 psf uniform load for solid-thickness and variable-thickness ribbed slabs.

3.1.3 Design Requirement 2: Two-Way Shear at the Discrete Joints Since the deck slab is supported by discrete joints, two-way (punching) shear of the slab should be checked around the joint. The check for the two-way shear should follow the provisions given by Article 5.12.8.6.3 of the AASHTO LRFD Bridge Design Specifications. The analysis showed that an 8.5-in.-thick slab with 2.0 in. of clear concrete cover provides adequate capacity to resist the two-way shear around the joint. Input criteria: 12-ft girder spacing, 6-ft haunch spacing, and 1-ft × 1-ft haunch: Case G12C6. This case was selected because it produces the highest reaction at the connection. Deck minimum specified concrete strength = 6 ksi 8.5-in. solid-thickness panel: Slab weight = ( 8.5 12 ft )(150 pcf ) = 106 psf Barrier weight = ( 2 barriers )( 300 lb ft barrier ) (5 girder lines ) = 120 lb/ft = (120 lb ft ) (12-ft girder spacing ) = 10 psf DC load = 106 + 10 = 116 psf DW load: 2-inch Wearing surface load = ( 2 12 ft )(150 pcf ) = 25 psf LL + I load: HS20 truck with multiple presence factor and dynamic allowance DC = component and attachment, DW = wearing surfaces and utilities, LL = live load, and I = dynamic allowance. Solution: Reaction due to 100 psf = 8.8 kips (Figure 3.7) Reaction due to HS20 truck (with multiple presence factor and dynamic allowance) = 45 kips (Figure 3.4)




Factored two-way shear: Vu = 1.25( 8.8 kips )( DC =116 psf ) (100 psf ) + 1.50( DW = 25 psf ) (100 psf ) + 1.75( 45 kips ) = 12.76 + 0.38 + 78.75 = 91.9 kips The nominal shear resistance Vn for sections without transverse reinforcement: 0.126   Vn =  0.063 +   βc 

f c′bodv ≤ 0.126 f c′bodv

( LRFD Equation 5.12.8.6.3 − 1)

Footprint of the discrete joint = 14 in. × 20 in. βc = 20 14 = 1.43, dv = 8.5 − 2.0 = 6.5 in., bo = 2(14 + 20) = 68 in. Therefore: Vn = 0.126 f c′ bodv = 0.126 6 ( 68 )( 6.5 ) = 136.4 kips φVn = 0.9(136.4 ) = 122.8 kips > 91.9 kips OK where βc = ratio of long side to short side of the rectangle through which the concentrated load or reaction force is transmitted, f c′ = compressive strength of concrete for use in design (ksi), bo = the perimeter of the critical section for shear (in.), dv = effective shear depth (in.), and φVn = design shear capacity.

3.1.4 Design Requirement 3: Two-Way Shear at Wheel Loads for Variable-Thickness Ribbed Slab Two-way shear caused by the 16-kips wheel load of the rear axle of the HL93 truck should be checked according to Article 5.12.8.6.3 of the AASHTO LRFD Bridge Design Specifications. The footprint of the wheel load should be determined using Article 3.6.1.2.5 Tire Contact Area of the AASHTO LRFD Bridge Design Specifications. The analysis showed that a 5-in.-thick slab with 2.0 in. of clear concrete cover provides adequate capacity to resist the two-way shear generated by the 16-kip wheel load. Tire contact area (LRFD Article 3.6.1.2.5): Tire width = P 0.8 = 16 kips 0.8 = 20 in. = 1.66 ft Tire length = 6.4γ (1 + IM 100 ) = 6.4 (1.75 )(1 + 0.33) = 14.90 in. = 1.24 ft Thickness of thin slab = 5 in. Vu ( due to HL93, DC and DW loads ) = 1.25( 0.116 k ft 2 )(1.66 × 1.24 ft 2 ) + 1.5( 0.025 k ft 2 )(1.66 × 1.24 ft 2 ) + 1.75(16 kips )(1+33 100 ) = 37.62 kips




βc = 1.34, dv = 5.0 − 3.0 = 2.0 in., bo (at level of reinforcement assuming 45-degree distribution) = 2[( 20 + 4 ) + (14.90 + 4 )] = 85.8 in. Therefore: Vn = 0.126 f c′ bodv = 0.126 6 ( 85.8 )( 2.0 ) = 53.0 kips φVn = 0.9(53.0) = 47.7 kips > 37.62 kips OK

3.1.5 Design Requirement 4: Bearing Stresses Since the slab is supported by discrete joints, bearing stresses between the joint and the supporting girders should be checked. Bearing stress resistance should be determined according to Article 5.6.5 of AASHTO LRFD Bridge Design Specifications. The analysis showed that haunches and concrete girders made with 6-ksi minimum specified concrete strength provide adequate capacity to resist the bearing stresses. Factored reaction at the connection (Section 3.1.3) = 91.9 kips Pn = 0.85 f c′ A1m f c′ = 6 ksi (as a conservative approach) A1 (bearing area, i.e., size of the joint) = 14 × 20 = 280 in.2 m = 1.0 (as a conservative approach) Pn = (0.85 )(6 )( 280 )(1.0 ) = 1428 kips φPn = (0.7 )(1428 ) = 999.6 kips >> 91.9 kips OK where Pn = nominal bearing resistance (kips), A1 = area under bearing device (in.2), m = confinement modification factor, φPn = factored bearing resistance, and f c′ = compressive strength of concrete for use in design (ksi).

3.1.6 Analytical Model Used to Investigate Design Requirements 5 to 9 The goal of the following analysis is to investigate whether it is reasonable to use the Euler– Bernoulli Beam Theory—generally used by designers—or whether correction factors would be required because of the use of discrete joints between the beams and the slab at the shear connectors. A slab–girder system—where the deck slab is supported by discrete joints—can be modeled as a Vierendeel structure, as shown in Figure 3.8. The top cord of the Vierendeel represents the slab




Figure 3.8. Vierendeel Model of a slab–girder composite system with discrete joints.

at its own centroid. Geometrical properties of the top chord are determined based on the slab thickness and effective flange width. The bottom cord of the Vierendeel represents the girder at its own centroid. Area and inertia of the bottom chord are taken as the geometrical properties of the girder. Vertical members of the Vierendeel structure are located at the joints. The vertical members are modeled in three individual parts: (1) a rigid link that spans the distance from the centroid of the girder (i.e., bottom chord) to the bottom surface of the haunch, (2) a flexible member that spans the height of the joint, and (3) a rigid link that spans the distance from the top surface of the haunch to the centroid of the slab (i.e., top chord). Area and moment of inertia of the rigid links are set to infinity (relatively very large values), while the area and inertia of the flexible vertical member that represents the haunch are determined based on of the footprint dimensions of the haunch. Supports of the Vierendeel Model are assumed to be provided at the bottom surface of the girder. Therefore, additional rigid links are provided at ends of the Vierendeel Model to span the distance between the centroid of the girder (i.e., bottom chord) and bottom surface of the girder. The bottom node of these rigid links represents a roller support at one end and a pin support at the other end of the Vierendeel Model to emulate a simply supported span bridge. The proposed Vierendeel Model is similar to a simplified spine model used to design highway bridges (i.e., the superstructure and the supporting abutments and piers of bridges) (California DOT 2015). The proposed Vierendeel Model was calibrated using Example 9.1(a) of the PCI Bridge Design Manual (Precast/Prestressed Concrete Institute 2011B), where the Euler–Bernoulli Beam Theory is used. The calibration showed that the Vierendeel Model was able to represent the composite action with a high degree of accuracy, as shown in Table 3.6. The Vierendeel Model was used to study the effect of using the discrete joint system on the following design requirements listed in Table 3.1: • • • • •

One-way shear in deck (Design Requirement 5), Flexural design (Design Requirement 6), Deflection (Design Requirement 7), Interface shear (Design Requirement 8), and Vertical shear (Design Requirement 9).



36 Simplified Full-Depth Precast Concrete Deck Panel Systems Table 3.6. Comparison between the results obtained from the Vierendeel Model and those reported in Example 9.1(a) of the PCI Bridge Design Manual. Condition Moment caused by lane load only (kip-ft) Deflection caused by HL93 truck (in.) Maximum horizontal shear caused by superimposed dead and live load (kip/in)

(A) Euler–Bernoulli Beam Theory 843.30 0.41

(B) Vierendeel Model 843.259 0.405

2.86

2.83

(B – A)/A (%) 0.0 -1.2 -1.0

In addition, the Vierendeel Model was used to study the effect of varying the following parameters on the design requirements: • • • • • • • •

Span length = 80 ft to 216 ft, Span-to-girder depth ratio = 15 to 35, Girder spacing = 6 ft to 12 ft, Girder material = concrete girders (6 ksi and 12 ksi) and steel girders, Spacing between shear connectors = 2 ft to 8 ft, Size of the bearing area at shear connections = 12 in. × 12 in. and 24 in. × 24 in., Thickness of the haunch = 2 in. to 6 in., and Thickness of the slab = 7.5 in. to 10 in.

The following procedure was used in the parametric study to select the girder size and determine its properties: 1. 2. 3. 4.

A span length was selected. A span-to-girder depth ratio was selected. The depth of the girder was determined using information from Steps 1 and 2. The type of girder was selected as follows: – Concrete. The baseline for concrete strength is set at 6 ksi. The geometrical properties of the girder were determined using the area and inertia of typical top and bottom flanges—Washington State wide flange girder, for example—and the depth of the girder determined in Step 3. – Steel. The following dimensions were used to determine the geometrical properties of the girder: top and bottom flanges of 1.25-in.-thick × 20-in.-wide plates, respectively. Web: 0.75-inch thick. Height was determined from Step 3 after subtracting the thickness of the top and bottom flanges. 5. The following parameters were selected as the baseline: 6-ft girder spacing (concrete girder: f c′ = 6 ksi steel girder: yield strength Fy = 50 ksi), 24-in. × 24-in. joint bearing, 2-in.-thick haunch, and 7.5-in.-thick slab with f c′ = 6 ksi. 6. The analysis was conducted for a group of selected values for the joint spacing (between 2 ft and 8 ft). 7. Based on the results obtained from the baseline assumptions (Step 5), one of the parameters was changed to the opposite extreme to study the effect of that parameter on the behavior. For example, change the thickness of the slab from 7.5 in. to 10 in., or change the thickness of the haunch from 2 in. to 6 in., and so on. 8. In all cases, the results obtained from the Vierendeel Model were compared with those obtained from the simple Euler–Bernoulli Beam Theory that is typically used by designers. The Euler–Bernoulli Beam Model parameters were determined by assuming full composite action between the slab and the beam. Table 3.7 shows the criteria used for the parametric study.



Research Findings 37 Table 3.7. Design criteria for the parametric study using the Vierendeel Model. Span Length Span-to-girder depth ratio Girder type Girder depth (in.) Area of girder (in.2) Inertia of girder (in.4)

80 ft 144 ft 20 35 20 35 Concrete Concrete Concrete Concrete 48.00 27.43 86.40 49.37 767 641 1,002 776 257,356 62,565 1,075,089 275,803

216 ft 20 35 Steel Steel 129.60 74.06 145 104 334,254 89,167

3.1.7 Design Requirement 5: One-Way Shear in the Slab The Vierendeel Model was loaded with the following combination of factored loads: DC Loads: Slab weight = (area of the slab ft2)(0.150 kcf) Barrier weight = (2 barriers)(0.3 k/ft/barrier)/(6 beams) DW Loads: Wearing surface = (girder spacing)(2-in.-thick layer)(0.150 kcf) LL: HS20 truck with distribution factor for shear determined using the AASHTO LRFD Bridge Design Specifications. The HS20 load was applied as a movable load with 1.33 dynamic allowance and 1.2 multiple presence factor. Strength I Limit State was used to determine the load effect. The vertical shear force in the top cord (i.e., the slab) was recorded at a distance dv from the face of the joint, where dv is the shear depth. The shear depth dv was set to 6 in. for the 7.5-in.-thick slabs and 8.5 in. for the 10-in.-thick slabs. The results obtained from the Vierendeel Model were compared with those obtained from a Simple Beam Model that was built assuming the slab behaves as a multispan beam supported by a group of point supports at every joint. The vertical shear obtained from the simplified model was reported at the critical section and at the center line of the end support. Table 3.8 and Table 3.9 show the results of the Vierendeel and simplified models. The comparison showed that it is reasonable to use the Simple Beam Model to determine the one-way shear in the slab, where the shear force is to be determined at the center line of the support.

Table 3.8. Results of vertical shear in the slab. Parameter Haunch spacing Span to depth = 20 80-ft-span bridge Concrete girder, f c' = 6 ksi 2-in.-thick haunch 24-in. x 24-in. x 2-in. haunch 7.5-in. slab thickness 6-ft girder spacing Change haunch thickness to 6 in. Change haunch to 12 in. x 12 in. x 2 in. Change slab thickness to 10 in. Change span length to 144 ft Change girder spacing to 12 ft Change f c' to 12 ksi

Vertical Shear (kips) by Vierendeel Model (at critical section) 4 ft

59.28

59.05

Vertical Shear (kips) by Simplified Model (at critical section/at center line) 8 ft 4 ft 8 ft

63.78 45.44/64.29

58.23/66.88

45.80/64.85 45.44/64.29 67.63/95.36 45.44/64.29

59.50/68.02 58.23/66.88 81.15/98.54 58.23/66.88

63.23

65.32

67.10

69.15 64.59 97.31 54.81

69.41 65.15 98.34 62.26



38 Simplified Full-Depth Precast Concrete Deck Panel Systems Table 3.9. Vertical shear in the slab: Effect of changing the span length, girder type, and span-to-girder depth ratio on vertical shear of the slab. 8-ft haunch spacing 2-in.-thick haunch 24 in. x 24 in. x 2 in. joint 6-ft girder spacing Span-to-girder depth ratio = 20 Span-to-girder depth ratio = 35

Simplified Model (at critical section/at center line) 80 ft 144 ft 216 ft (concrete (concrete (steel girder) girder) girder)

Vierendeel Model (at critical section) 80 ft (concrete girder)

144 ft (concrete girder)

216 ft (steel girder)

63.78 kips

65.15 kips

56.06 kips

66.23 kips

65.99 kips

56.66 kips

58.23/66.88

3.1.8 Design Requirement 6: Flexural Stresses of Composite Member Service I Limit State was used to determine the load effects. The following procedure was used to obtain the flexural stresses from the Vierendeel Model. At the section where the highest moment in the girder was recorded, moment in the top chord (slab) and in the bottom chord (beam) was recorded. The moment was used to determine the flexural stresses in the slab and the girder using their individual inertia and geometrical properties. Table 3.10 shows the matrix used in the parametric study. Details of the study and comparison tables are given in Appendix B. Comparison between the Vierendeel and simplified models showed that the Simple Beam Model gives very comparable results to the Vierendeel Model, where the average difference was ±3%. Therefore, it is reasonable to use the Simple Beam Model to determine the flexural stresses in the composite beam due to the superimposed dead and live loads.

3.1.9 Design Requirement 7: Deflection of Composite Member The Vierendeel Model was loaded only with the live load (i.e., HL93 model) with distribution factor for moment (DFM) = 1.0, 1.33 dynamic effect added to the HL93 truck, and 1.0 load factor. The load was applied on the top chord of the Vierendeel Model. The matrix shown in Table 3.10 was used in the investigation. Details of the study and comparison tables are given in Appendix B. Table 3.10. Matrix of the parametric study for flexure design of the composite section. Case No. 1 (Baseline) 2 3 4 5 6 7 (Baseline) 8 9 10 11 12

Span-toDepth Ratio

Span (ft)

20

80, 144, and 216

35

Girder Spacing (ft)

Slab Thickness (in.)

Haunch Thickness (in.)

Joint Size (ft x ft)

6

7.5

2

2x2

6 6 12 6 6

7.5 7.5 7.5 10 10

6 2 2 2 6

2x2 1x1 2x2 2x2 2x2

6

7.5

2

2x2

6 6 12 6 6

7.5 7.5 7.5 10 10

6 2 2 2 6

2x2 1x1 2x2 2x2 2x2


Joint Spacing (ft)

2, 4, 6, and 8



Comparison between the Vierendeel and simplified models revealed that the Vierendeel Model showed a 5% to 7% increase in the deflection, compared to the Simple Beam Model when: (1) a thicker deck or haunch was used, (2) a higher span-to-depth ratio was used, and (3) wider spacing between the shear connector joints was used. This observation showed that the Simple Beam Model still can be used to determine the deflection of the composite beam after considering a proper reduction factor for the composite beam stiffness. This observation is acknowledged by the Steel Construction Manual (American Institute of Steel Construction 2017), where Section I3 states that, “Comparison to short-term deflection tests indicate that the effective moment of inertia, Ieff, is 15% to 30% lower than that calculated based on linear elastic theory, Iequiv. Therefore, for realistic deflection calculations, Ieff should be taken 0.75 Iequiv .” This issue was further investigated in the experimental program and a more accurate reduction factor of the composite beam stiffness was developed, as shown in Section 3.2 and Section 3.3 of the report.

3.1.10 Design Requirement 8: Interface Shear Strength I Limit State was used to determine the load effects. The matrix shown in Table 3.10 was used in the investigation. Comparison between the Vierendeel Model and Simple Beam Model showed that the interface shear determined by the Simple Beam Model was always higher than the interface shear determined by the Vierendeel Model. Ratio of shear flow determined by the Simple Beam Model to the shear flow determined by the Vierendeel Model was about 1.15 to 1.30 across the board. Therefore, it is reasonable to use the simplified model as an approximate approach. In this case, it is expected that the horizontal shear reinforcement will be somewhat overestimated. A more accurate estimate of the interface shear can be determined using the Vierendeel Model.

3.1.11 Design Requirement 9: Vertical Shear of Composite Beam In a typical bridge, the noncomposite loads (i.e., beam, haunch, and slab weight) are supported by the girder, while the composite loads (i.e., parapet, wearing surface, and transient loads) are supported on the composite slab–girder system. The shear force caused by the noncomposite loads can be easily determined using the simple Euler–Bernoulli Beam Theory. The shear force caused by the composite loads can be determined using one of the following models. The first model is the Vierendeel Model, as discussed earlier. This model gives a more realistic picture of the behavior of the slab–beam system because the slab is connected with the girder only at the locations of the discrete joints. In this case, the shear force that is reported in the bottom chord of the Vierendeel Model (i.e., the girder) should be used to design for the vertical shear in the girder. The second model is the simplified model using the simple Euler–Bernoulli Beam Theory. Details of the study and comparison tables are given in Appendix B. Analysis of the results showed that the shear force caused by the composite loads obtained from the Simple Beam Model is about 10% higher than the shear forces obtained from the Vierendeel Model, regardless of the haunch spacing, haunch dimensions, girder spacing, or thickness of the slab. However, this increase has a small effect on the spacing of the shear reinforcement. Therefore, it is reasonable to use the simplified model to determine the vertical shear caused by composite loads. As will be shown from the full-scale experiments, separation between the girder and the deck when the haunches are not filled with concrete did not cause a deficiency in the shear capacity of the slab–beam system. Until additional evidence is available, it may be prudent to count on the beam depth alone in calculating the vertical shear reinforcement.




3.1.12 Design Requirement 10: Distribution Factors DFM and shear are key components for design of a bridge superstructure. Article 4.6.2.2 of the AASHTO LRFD Bridge Design Specifications provides a group of tables that are used to determine these factors for interior and exterior beams of slab–beam bridges. Provisions of this article come primarily from the research conducted by Zokaie et al. (1991), where the slab was assumed to be supported by a continuous haunch. The following investigation was conducted to make sure that the provisions of Article 4.6.2.2 are reasonable to be used with slab–beam bridges where the slab is supported by discrete joints. 3.1.12.1 Analytical Model A 3-D finite element model was used in the investigation. In this model, the full super structure of a bridge was modeled. The slab and the haunch were modeled using the eight-node linear reduced-integration brick elements (C3D8R). Each supporting girder was modeled using a set of equivalent beams spread over a distance equal to the width of the top flange of the girder. The equivalent beams were modeled using 3-D frame elements that take into consideration the shift of the girder centroid from the bottom soffit of the haunch in their stiffness matrix. Geometrical properties of each set of equivalent beams—including height, moment of inertia, and cross-sectional area—were equal to those of a single beam line. The contact surfaces between the slab and the discrete joints and between the discrete joints and the girders were fully tied to emulate full-composite action. Figure 3.9 shows a schematic of the Finite Element Model used in the investigation. Discrete joints were spaced on center at 2 ft, 4 ft, 6 ft, and 8 ft. The models were built with an advanced commercial finite element package. The following steps were used to determine the live load DFM: 1. Each Finite Element Model was analyzed because of noncomposite and composite dead loads plus the LRFD HL93 live load. Three live load scenarios were considered: one lane loaded, two lanes loaded, and three lanes loaded. In each live load scenario, stresses at the point of maximum bending moment of the interior girder were collected and the resulting bending moment was calculated. 2. DFM was determined as follows: DFM j =

( M j )(m ) n

∑ Mi i =1

Figure 3.9. Details of the Finite Element Model used in the investigation for the distribution factors.




where DFMj = live load distribution factor for moment of girder j, Mj = live load bending moment of girder j (determined from Step 1), n

Σ M i = sum of live load moment for all girders, and i =1

m = LRFD multiple presence factor = 1.2 for one lane loaded, 1.0 for two lanes loaded, and 0.85 for three lanes loaded. The steps used to determine the live load distribution factor for shear (DFV) were similar to the steps used to determine the DFM, except that the location of the HL93 live load model was adjusted to maximize the shear force toward the end of the girder. DFV was calculated as follows: DFV j =

(Vj )(m ) n

∑Vi i =1

where DFVj = live load distribution factor for shear of girder j, Vj = live load shear of girder j, n

Σ Vi = sum of live load shear for all girders, and i =1

m = LRFD multiple presence factor = 1.2 for one lane loaded, 1.0 for two lanes loaded, and 0.85 for three lanes loaded. 3.1.12.2 Parametric Study Four design examples that represent a wide range of parameters that are commonly used on bridges today were selected. Table 3.11 summarizes the basic design criteria of these examples. Example 2 was adopted from Design Example 9.1(b) of the PCI Bridge Design Manual (Precast/Prestressed Concrete Institute 2011B), and Example 3 was adopted from Design

Table 3.11. Basic criteria of the design examples used in the distribution factor investigation. Example Span (ft) Span–Girder depth ratio Thickness (in.) Sacrificial slab (in.) Concrete strength (ksi) Inertia (in.4 ) Modulus of elasticity (ksi) Thickness (in.) Width (in.) Length (in.) Concrete Strength (ksi) Material Type Spacing (ft) Depth (in.)

1

2

3

4

100

120

160

216

26

30

9.0 0.5 6 9,294.75 4,695.98

8.0 0.5 5 5,120.00 4,286.83

2.0 23 12 4

2.0 24 12 5

33 20 Subcriteria 7.5 7.5 0.5 0.5 4 4 2,531.25 3,796.88 3,834.25 3,834.25 Joint Criteria 2.0 0.5 48 42 12 12 4 4 Girder Criteria Concrete Concrete New PCI BT-72 FIB-36 6 9 36 72

Steel Built up 12.75 73

Steel Built up 10 86.5



42 Simplified Full-Depth Precast Concrete Deck Panel Systems Table 3.12. Criteria of the parametric investigation on the distribution factor. Parameters 1–Girder concrete strength 2–Slab concrete strength 3–Slab thickness 4–Haunch length 5–Haunch thickness

Example Considered in Investigation 1 1 1 3 3

Change 8 ksi to 12 ksi 4 ksi to 8 ksi 7.5 in. to 10 in. 12 in. to 24 in. 2 in. to 6 in.

Example 1 of Highway Structures Design Handbook (American Iron and Steel Institute 1999), with some minor changes. The DFM and DFV determined for the four examples were compared with the distribution factors determined according to the AASHTO LRFD Bridge Design Specifications. For each case, the analysis was conducted for a case with a continuous haunch and joint spacing from 2 ft to 8 ft. To study the effect of changing some of the basic criteria on the distribution factors, a parametric investigation was also conducted, as shown in Table 3.12. Appendix B includes the calibration of the Finite Element Model, details of the study, and comparison tables and figures. The finite element investigation of the distribution factors showed that the DFM and shear of the AASHTO LRFD Bridge Design Specifications were always higher than the DFM and shear obtained by the finite element analysis, regardless of the number of loaded lanes, spacing between the discrete joints, type of the supporting girders, and span length of the bridge. Therefore, it is conservative and reasonable to use the DFM and shear given by the AASHTO LRFD Bridge Design Specifications for slab–I-beam bridges, where the slab is supported by discrete joints up to 8-ft spacing. This observation is consistent with the results obtained from similar previous studies, including May (2008) and Gheitasi and Harris (2014). Modeling the slab as a continuum using solid brick elements allowed the analysis to capture the arching effect inside the slab and to realistically distribute the live load to a relatively large number of girders. In addition, the grillage analysis that was used in the early 1990s to develop the formulas for the distribution factors and adopted by the AASHTO LRFD Bridge Design Specifications modeled the slab as a wire frame element and, therefore, did not fully capture the multidimensional behavior of the slab (Zokaie et al. 1991). It provided relatively conservative values of distribution factors.

3.1.13 Flexural Strength The design at failure typically uses the Whitney Equivalent Compression Block on the compression side of the section and the resultant of the tensile force on the other side. Therefore, the slab–beam composite system—which used discrete joints—will follow this typical behavior, and the flexural capacity of the system can be determined using the same procedure that is currently used with regular slab–beam composite systems. This issue was confirmed by the results obtained from the experimental program and is discussed later in this chapter.

3.1.14 Top Flange Buckling In slab–beam bridges built with precast deck panels and discrete joints, there are two stages at which buckling of the top flange of steel girders need to be checked. Stage 1: After the precast deck is installed on the bridge but not connected with the steel girders. At this stage, the steel girder will support the slab weight, its self-weight, and the construction load. The unsupported buckling length of the top flange is almost the full length




of the span. This stage is typically checked, regardless of whether a continuous or discrete joint system is used. Stage 2: After the deck is connected with the steel girder and the bridge is open to traffic. The superimposed dead and live loads will create additional compressive stresses in the flange, but the unsupported buckling length of the flange will be the 6-ft spacing between haunches. The following sections provide discussion related to buckling of the top compression flange of steel and concrete girders for this stage. 3.1.14.1 Composite Beams with Steel Girders The top flange should be checked against lateral torsional buckling (LTB), as stated in Article 6.10.8.2.3 of the AASHTO LRFD Bridge Design Specifications; and flange local buckling (FLB), as stated in Article 6.10.8.2.2 of the AASHTO LRFD Bridge Design Specifications, as follows: LTB: Article 6.10.8.2.3 of the AASHTO LRFD Bridge Design Specifications states that the compression flange is considered compact if: E Fyc

L p ≤ 1.0rt

( LRFD Equation 6.10.8.2.3-4 )

where Lp = unbraced length of the compression flange (6 ft, in this case), E = modulus of elasticity of the top flange = 29,000 ksi, Fyc = yield strength of the top flange = 50 ksi, and rt = effective radius of gyration for LTB =

If

b fc

( LRFD Equation 6.10.8.2.3-9)

 1Dc t w  12  1 +  3b fc t fc 

Dc tw is taken conservatively as a representative value of 2.0 (LRFD C6.10.8.2.3), then bfc t fc

rt = 0.22 b fc where bfc = the width of the top flange, Dc = depth of the web in compression in the elastic range (in.), tw = web thickness (in.), and tfc = thickness of the compression flange (in.). Therefore, to protect the top compression flange from LTB when the shear connector clusters are provided at 6 ft (i.e., 72 in.), the following condition must be satisfied: 72 in ≤ (1.0 )( 0.22 b fc )

29,000 50

b fc ≥ 13.39 in. For most practical cases of highway bridges, width of the top flange of the steel girder is greater than 13.39 in.




FLB: Article 6.10.8.2.2 of the AASHTO LRFD Bridge Design Specifications states that the compression flange is considered compact if: b fc E ≤ 0.38 2tfc Fyc

( LRFD Equation 6.10.8.2.2-3 and LRFD Equation 6.10.8.2.2-4 )

29,000 b fc ≤ 0.38 2tfc 50 t fc ≥ 0.055b fc where bfc = full width of the compression flange (in.), E = modulus of elasticity of the deck concrete (ksi), and Fyc = specified minimum yield strength of a compression flange (ksi). Therefore, the minimum thickness of the compression flange will be as shown in Table 3.13. 3.1.14.2 Composite Beams with Concrete Girders The AASHTO LRFD Bridge Design Specifications do not provide any limits on the thickness or width of the compression flange to protect it against buckling. The following limits were found in the literature. Article 9.2.3.1(a) of the ACI318-14 Building Code: Lb ≤ 50 b where Lb = unbraced length of the compression flange Lb (72 in., in this case) and b = least width of the compression flange or face. It is presumed that this provision was intended to safeguard the compression flange against lateral instability failures. This provision has been in the ACI318 Building Code since the 1956 edition. However, no discussion has been provided on the background of this limit.  72  b ≥  = 1.44 in.  50  This limit is satisfied for all types of I-shape girders used on highway bridges (Timoshenko 1936).

Table 3.13. Flange width and corresponding thickness. Parameter

Case 1

Case 2

Case 3

Case 4

bfc (in.)

13.39

15

20

25

tfc (in.)

0.74

0.825

1.10

1.38




Timoshenko has shown that the bending moment that is required to cause lateral bending can be expressed as follows: M buckling =

Π EI yGK t Lb

(1)

where Lb = unbraced length of the compression flange Lb (6 ft, in this case), E = modulus of elasticity, E G = shear modulus = , 2 (1 + v ) n = Possion ratio (about 0.2 for concrete), Iy = moment of inertia of the beam about its vertical axis, and 1 Kt = torsional constant = Σbi t i3 for I-shape beam, where bi and ti are the long and the short 3 dimensions of the top and bottom flanges and vertical web. Since this equation is only applicable for homogeneous uncracked beams, a reduction factor of 0.35 is presented to Iy and Kt to account for a cracked concrete beam. Therefore, Equation 1 can be rewritten in the following form: M buckling =

0.41E I y ( ∑ bi t i3 ) Lb

In order to see the magnitude of Mbuckling, Example 9.1b of the PCI Bridge Design Manual (Precast/Prestressed Concrete Institute 2011B) was used: Concrete girder: BT-72 Span = 120 ft E = 4,617 ksi Lb = 72 in. Iy = 37,971 in.4 ∑bi t i3 = 28,803 in.4 (The following dimensions were considered: top flange = 42 in. × 4.5 in., vertical web = 54 in. × 6 in., and bottom flange = 26 in. × 8 in.) Then, Mbuckling = 72,367 k-ft The flexural design capacity of the beam φMn = 11,364 k-ft Comparing Mbuckling with φMn shows that this beam will fail in flexure a long time before it fails from lateral buckling.

3.1.15 Finite Element Analysis of Push-Off Specimens Nonlinear finite element analysis was used to investigate the behavior of the tested push-off specimens. The results obtained from the finite element analysis were compared with the results




obtained from the push-off specimens and the predicted capacity. An advanced commercial finite element package was used in the analysis (ABAQUS 6.13 package). The analysis was conducted at the Colonial One High-Performance Computing Facility at George Washington University. All elements of the model—concrete deck, concrete or steel girder, and shear connectors (steel studs or threaded rods)—were modeled using the eight-node C3D8R brick elements, where “C” denotes concrete, “3D” denotes three dimensional, “8” denotes total number of nodes, and “R” denotes a reduced integration element, which brings down the number of integration points reducing running time without an unreasonable sacrifice of accuracy. Each node has three displacement degrees of freedom in the x, y, and z directions. The “x” direction is parallel to the girder longitudinal axis, the “y” direction is transverse to the girder longitudinal axis, and the “z” direction is parallel to the girder height. The stress-strain relationships for the deck panels and grout shown in Figure 3.10 were used. Tension softening of the deck and grout material enabled the simulation of cracking. Once the tensile stress reaches the tensile limit, the material relieves its stress. A very steep release path will create instability, whereas too shallow a curve will slow down the stress release. In addition to the stress–strain relationship, the Concrete Damage Plasticity Model used in ABAQUS for the deck and grout material requires defining the following parameters (Stephen 2006, Arab et al. 2011): • Dilation angle in degrees, β:

 f c′−  6sin φ  β = tan −1  , φ = tan −1   3 − sin φ   f c′+  f c′−  6sin φ  − 1 − 1 β = tan   , φ = tan   3 − sin φ f c′+ where f c′ = Specified compressive strength

fr  fr  fr  fr 

fr = Modulus of rupture f c′ = Specified compressive strength fr = Modulus of rupture

Figure 3.10. Stress–strain relationship for the deck panel concrete mix and grout used for the finite element analysis.



Research Findings 47 • Ratio of the second stress invariant on the tensile meridian to that on the compressive meridian

at initial yield, Kc: 0.5 < K c =

3 − sin φ < 1.0 3 + sin φ

• Flow potential eccentricity e: A default value of 0.1 was used. • Ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress:

A default value of 1.16 was used. • Viscosity parameter: A default value of 0.00001 was used.

A contact surface was used at the interface between 1. The shear connectors (studs or threaded rods) and surrounding grout, 2. The threaded rods and the surrounding concrete of the girder (only for specimens supported by concrete girders), 3. The bottom face of the grout in the shear pocket and top surface of the grout in the haunch (deck–haunch interface), and 4. The bottom face of the haunch and top surface of the supporting girder (girder–haunch interface). The input parameters of the contact surface include the coefficient of friction and cohesion. The magnitude of these parameters was taken from Article 5.7.4.5 (Shear Friction Theory) of the AASHTO LRFD Bridge Design Specifications, as shown in Table 3.14. The contact surface allows relative slippage between the neighboring components once the shear stresses become higher than the specified cohesion strength. The size of the finite element mesh was optimized by creating a fine mesh at the shear connection area and a relatively course mesh in the supporting girders. Figure 3.11 shows an overall view of the finite element mesh used for the model with steel girders, while Figure 3.12 shows the finite element mesh inside the shear pocket of the same specimen. Boundary conditions of the model are: • Pin supports at all of the nodes of the bottom surface of the supporting girder. These supports

restrain all vertical and horizontal movement of bottom surface of the girder. • Line of pin supports on the left side of the supporting girder. These supports were positioned

at mid height of the reaction plate provided in the test setup. The load was applied as pressure on the right-hand face of the deck. Figure 3.13 shows the boundary conditions and pressure load applied on the deck.

3.1.16 Effect of Simplification of Deck Post-Tensioning Post-tensioning of precast concrete deck panels in the longitudinal direction is an effective way of controlling transverse cracking, which is a common problem with cast-in-place decks. Table 3.14. Coefficient of friction and cohesion of the contact surfaces. Contact Surface Shear connectors and surrounding grout or concrete of the supporting girder Deck–haunch interface Steel girder–haunch interface Concrete girder–haunch interface

Coefficient of Friction

Cohesion (ksi)

0.7

0.025

1.4 0.7 1.0

0.400 0.025 0.240




Figure 3.11. Overall view of the finite element mesh of CD3 on a steel girder.

Figure 3.12. The finite element mesh inside the shear pocket of CD3 on a steel girder.




Figure 3.13. Boundary conditions and pressure load applied on the deck.

However, the common method of deck panel post-tensioning has created challenges. The common method requires that multistrand ducts be placed in the precast panels. Because of the relatively small thickness of the panels, the maximum number of strands per tendon cannot exceed three or four strands in order to allow a 2-in.- to 3-in.-diameter duct to be used. As a result, a large number of multistrand tendons are used. When the panels are placed in the field, often the duct ends do not align well, and splicing becomes time-consuming, difficult, and a cause for additional friction losses. In addition, the pockets needed for workers to splice the ducts cause a large area of the deck at the transverse joints to require grouting. After the transverse joints are made and cured, post-tensioning is performed. Another step—to grout the post-tensioning ducts—is often required. These multiple steps have caused contractors to question the speed of construction claimed by the full-depth precast deck panel system. These multiple steps are also a primary reason for initiation of this project. The commentary to Article C9.7.5.3 of the AASHTO LRFD Bridge Design Specifications encourages use of this sequencing by stating that, “post-tensioning should be applied before the panel-to-girder connection is established.” This recommendation is called into question in the analysis that follows. It will be shown that designers should actually try to avoid multistage field grouting created by this sequencing, even if the cost is a few extra strands in the beam, the deck, or both. The research team for this project has decided to introduce a novel system that has been used successfully on a number of bridges for transverse post-tensioning of adjacent box beams. Sun et al. (2018) provide an example. Two unique features are introduced: 1. Post-tensioning employs duct-in-duct and unbonded greased strand tendons, as described in Chapter 2. 2. If the bridge is constructed as simple spans, post-tensioning is introduced after all grouting has taken place in a single operation. Thus, the girder is already fully composite with the deck at the time of post-tensioning. In this case, some of the prestressing effect is lost to the beam and not fully introduced to the deck. Table 3.15 shows the ratio of post-tensioned deck stresses in a composite deck (posttensioning is applied after the deck becomes composite with concrete girder) to posttensioned stresses of noncomposite deck (post-tensioning is applied before the deck becomes composite with concrete girder). In this table, the ratio is calculated for girders ranging from NU900 to NU2000 and girder spacing ranging from 8 ft to 12 ft.



50 Simplified Full-Depth Precast Concrete Deck Panel Systems Table 3.15. Ratio of deck post-tensioned stress in composite simple-span bridge compared to deck post-tensioned stress in noncomposite deck (post-tensioning is applied before the deck is connected to the girder). Girder Section NU900 NU1100 NU1350 NU1600 NU1800 NU2000

8 95% 91% 87% 84% 82% 80%

Girder Spacing (ft) 10 98% 94% 91% 88% 86% 84%

12 100% 97% 93% 91% 89% 87%

Table 3.15 shows that this ratio is dependent on the girder stiffness and girder spacing. However, the smallest ratio in this table is 80%, which means that at the most only 20% of post-tensioning effect is lost to the girder because of the composite action. Thus, it is advisable to simplify construction by applying the deck post-tensioning after all field grouting is completed. In all calculations, it is assumed that girder compressive strength is 8 ksi, precast deck compressive strength is 6 ksi, total losses are 20%, and post-tensioning is required to maintain a minimum of 250 psi across the transverse joints. 3. If the bridge is constructed as continuous span at the time of deck post-tensioning, the effect of applying post-tensioning to the composite member may be significantly different than that for simple spans. Statically indeterminate secondary moments caused by deck post-tensioning may create detrimental negative moments at the interior pier supports. This situation would need careful analysis on a case-by-case basis—including possible adjustments of the tendon profile—before a decision is made on whether to post-tension the deck before or after it is connected with the girder.

3.1.17 Summary and Conclusions 1. The analytical investigation shows the viability of increasing the shear connection spacing to 6 ft without significant change in behavior. 2. For two-way decks that are only supported at discrete joints along the girder lines, design aids are given in Section 3.2.2.3 of this report to facilitate design of the reinforcement, especially in the longitudinal direction. 3. The analytical investigation shows that the behavior of the beam in the longitudinal direction is reasonably predicted using the Euler–Bernoulli Beam Theory, which is the common design practice at this time. However, there is one exception. In calculating live load deflection, a reduction factor of the composite member stiffness may be required to provide accurate deflection estimate. This issue is further investigated in the experimental program. 4. Because the system is less stiff with unfilled haunches, as shown from the Vierendeel Model, the research team concluded that the experimental investigation could be conducted with unfilled haunches. 5. Finite element analysis indicates that the strength of the grouting material of the shear connection joints is the most critical factor in ensuring adequate structural capacity. Therefore, the research team decided to employ UHPC as the final recommended joint material. 6. Two options were studied with regard to the longitudinal reinforcement. – The first option was to use longitudinal post-tensioning to provide adequate design against transverse cracking. For that option, the research team determined that (a) posttensioning can be applied after all field cast joints are made, without significant loss of




effective prestress; and (b) it is not necessary to fill the transverse joint with more than the conventional concrete used for the deck material. However, UHPC is still used to fill the shear connector pockets. – The second option was to eliminate field post-tensioning. In this option, the research team recommended the use of UHPC to fill the transverse joints, as well as the shear connector pockets and overlapped reinforcing bars in the transverse joint.

3.2 Experimental Program 3.2.1 Introduction to the Experimental Program As demonstrated in the analytical investigation in Section 3.1, the research team developed an experimental program to verify the developed system shown in Chapter 2 and confirm the design guidelines established in the analytical phase. Two parallel experimental studies were conducted. The first study presents the work on the precast concrete girder–deck system. The second study is on the structural steel girder–deck system. The developed system has the unique feature of allowing horizontal shear connection spacing to be as wide as 6 ft. It has retained the 6-ft-long precast ribbed-slab deck to avoid shear blockouts within the panel. However, a deck panel that is 12-ft long can still be used with one blockout at mid length of the panel and with the same exact connection hardware being tested as reported in the following sections. Another feature of the system retained for further evaluation is to allow the option of not filling the girder–deck haunch space between connection joints. This would allow the research team to show evidence that filling that haunch is not critical for the system and that no need exists for requiring high-strength grout or UHPC to fill the haunch. Table 3.16 shows the details of the experimental program, which consists of testing six pushoff specimens and two large-scale composite beams. Half of the specimens were supported on concrete girders, and the second half of the specimens were supported on steel girders. The objective of the push-off testing is to determine the interface shear resistance of the proposed UHPC connection between the deck and I-girders. Push-off specimens generally give low interface shearing resistance, as they do not fully represent the highly redundant conditions in a composite beam (Issa et al. 2003, Issa et al. 2006, Badie and Tadros 2008). Also, push-off Table 3.16. Plan of the experimental program. Girder Concrete

Push-Off Specimens

Large-Scale Composite Beam One beam

Three specimens each Variable-depth ribbed panels Variable-depth ribbed panels Tested for strength Tested for strength Without longitudinal post-tensioning

With longitudinal post-tensioning One beam

Steel Variable-depth ribbed panels Tested for fatigue and strength Without longitudinal post-tensioning




specimens, as designed for this testing program, inherently have overturning forces that tend to have an opposite effect on the compression induced by the deck weight and additional loads in a composite beam test. Thus, results of push-off specimens are shown here to be on the low side, which is consistent with testing done in previous projects. The goals of testing full-scale specimens of precast concrete deck panels and I-girders are to verify the interface shearing capacity from the push-off testing and to evaluate the structural behavior of the composite girder in beam flexure and shear when discrete connections are used at 6-ft spacing. Stresses and strains in different system components—as well as displacements— are measured and compared with those predicted using analytical methods and the simpler push-off specimens. In addition, failure modes and ultimate load capacity are measured and compared with theoretical values. The precast panels used in the specimens were professionally fabricated by Coreslab Structures, Inc., a certified precast concrete plant in Omaha, Nebraska. Shop drawing details and pictures taken during fabrication of the precast panels are provided in Appendix C. Two-inch-nominal diameter schedule 80 PVC pipes were used in each panel as ducts for the longitudinal post-tensioning. The precast concrete panels were made using normal weight self-consolidated concrete (SCC) that has a specified stripping strength of 3.5 ksi and 28-day compressive strength of 6 ksi. Measured average concrete strength of the precast deck panel was 7.7 ksi at 28 days. The shear keys and pockets were sandblasted in the storage yard to provide better bond with the UHPC mix filling the transverse joints between panels. The precast prestressed concrete girder used for the large-scale composite beam with concrete girder was fabricated by Concrete Industries, Inc., a certified precast concrete plant in Lincoln, Nebraska. The steel studs used for the push-off specimens on steel girders were welded by a certified welder using a Nelson stud gun. The studs used for the large-scale composite beam with steel girder were also welded by a certified welder.

3.2.2 Investigation of Precast Deck System with Concrete Girders 3.2.2.1 Push-Off Specimens The current AASHTO LRFD Bridge Design Specifications does not have provisions for use of UHPC for deck-to-girder connections in composite systems. The interface shear resistance provisions in Section 5.7.4 of the AASHTO LRFD Bridge Design Specifications were developed for conventional concrete and are not applicable without revisions. However, these provisions, as well as additional fundamental analysis, were used to estimate the connection capacity prior to testing. The predicted horizontal shear capacity was found to be 236 kips. Three identical push-off specimens were tested, and the results were compared with the predicted capacity. Because the connector hardware developed in this project was used for the first time, fundamental theory and finite element analysis were also used to attempt to understand and verify its behavior. Table 3.17 shows the configuration of the three push-off specimens tested to evaluate the constructability and structural performance of the revised connection.

Table 3.17. List of the push-off specimens on concrete girders. Specimen ID UHPC C1 UHPC C2 UHPC C3

Girder Type Concrete block Concrete T-section Concrete T-section

Connector Type and Size Two 1.5-in.-diameter A193 B7 threaded rods held by a steel collar and washers


Deck Panels Two 4 ft x 3 ft x 8.5 in. precast concrete panels



Figure 3.14 and Figure 3.15 show the dimensions of the three push-off specimens. The first specimen, shown in Figure 3.14, was made using a concrete block that was lightly reinforced. Although the UHPC connection far exceeded expectations, failure occurred in the concrete block and controlled the maximum load applied on the specimen. As a result, the design of the concrete block was changed from a rectangular block to a T-section beam that was adequately reinforced compared to the block in UHPC C1. Figure 3.15 shows the second and third specimens. In all specimens, a discrete 20-in. × 14-in. × 3-in. haunch joint was formed around the shear connector. The concrete girders were cast at the laboratory using a ready-mixed SCC with an average slump flow of 22 in. The average 28-day compressive strength was 6.8 ksi, 8.3 ksi, and 8.3 ksi for the first, second, and third specimens, respectively. Average measured concrete strength at 28 days was 7.9 ksi. The UHPC used in grouting the new connection was mixed by the research team at the laboratory using the commercial mix Ductal JS1000 produced by Lafarge North America. For each push-off specimen, 2.6 ft3 was made using seven bags of Ductal JS1000. Table 3.18 shows

Figure 3.14. Details of the first push-off test specimen.




Figure 3.15. Details of the second and third push-off test specimens.

the ingredients of the mix per bag. The mixed UHPC had a slump flow of 10 in., according to ASTM C1856, at a temperature of 80°F and relative humidity of 50%. A trial mix was tested prior to casting the three connections to evaluate the mechanical properties of the UHPC mix. The results of testing three cylinders and prisms according to ASTM C1856 indicated that UHPC has an average compressive strength of 14.8 ksi at 4 days and 26.3 ksi at 28 days, 1.6 ksi precracking splitting strength, 2.67 ksi postcracking splitting, and 2.6 ksi flexural strength. Table 3.18. UHPC mix proportions per bag. Ingredients Ductal JS1000 Water/Ice HRWRA Steel fibers Yield volume

Quantity 50 lbs (one bag) 2.96 lbs 0.69 lbs 3.6 lbs 0.37 ft3

NOTE: HRWRA = high-range waterreducing admixture.




Compressive Srength (ksi)

30 25 20 15

Specimen 1

10

Specimen 2

5

Specimen 3

0 0

7

14 Age (days)

21

28

Figure 3.16. Compressive strength of UHPC used in push-off specimens.

Figure 3.16 shows the compressive strength versus age for the UHPC mix used in each of the three push-off specimens. This figure indicates consistency of the UHPC performance. The 1.5-in.-diameter threaded rods used as shear connectors were made of ASTM A193 Grade B7 steel with yield strength of 105 ksi and ultimate strength of 125 ksi. All other steel components (collars and washer plates) were made of Grade 50 A572 steel with E70 electrode welding. Figure 3.17 and Figure 3.18 show the setup used for push-off testing of the three specimens. The hydraulic jack and load cell were aligned to apply a horizontal force at the center of the concrete deck panels. To avoid specimen rotation caused by eccentricity between the applied force and the reaction, hold-down straps were used to anchor the specimen to the floor, as shown in Figure 3.17 and Figure 3.18. All specimens were instrumented to measure the relative displacement between the concrete deck panels and the supporting girder at the connection location using linear variable differential transformers (LVDTs) in both horizontal and vertical directions. Two LVDTs were installed on each side, as shown in Figure 3.19. Electric resistance strain gauges were also installed diagonally on one side at the center of the steel collar to monitor the strain during testing, as shown in Figure 3.20.

Figure 3.17. Setup showing the rectangular block used in testing of the first specimen.




Figure 3.18. Setup showing the tee-section beams used in testing the second and third specimens (LVDT = linear variable differential transformer).

Figure 3.19. Location of vertical and horizontal LVDTs.

Stain Gauge

Figure 3.20. Diagonal steel strain gauge on the steel collar.




Figure 3.21. Concrete block premature failure in push-off Specimen UHPC C1.

Specimen UHPC C1: In this test, the load was applied incrementally at an approximate rate of 5 kips/s. The UHPC compressive strength at the time of testing (4 days old) was 15.7 ksi. During testing and before reaching the predicted capacity, the concrete block started to bend upward, forming vertical cracks at the edge of the connection, as shown in Figure 3.21. These flexural cracks are likely caused by the bending moments generated by the clamping force on the concrete block and the lack of longitudinal reinforcement provided in the concrete block. In a typical bridge I-girder, it is expected that longitudinal and transverse reinforcement exist, especially at the highly concentrated forces imparted by the connection. Unfortunately, the unusually high capacity with UHPC was not anticipated, and the concrete block was not properly reinforced. Therefore, before testing the remaining specimens, the design of the concrete block was revised where a T-shape was selected instead of the rectangular block, and significant reinforcement was added in the tee-section beam flange. Figure 3.22 shows the load-displacement plots for the horizontal and vertical relative displacements at the deck–haunch interface of the specimen. The maximum recorded load was 232 kips, which is slightly lower than the 236-kip predicted capacity. The maximum measured strain in the steel collar was 341 microstrain (i.e., 9.8 ksi). Figure 3.23 shows the two parts of the damaged specimen during disposal. The top portion includes the deck panels, UHPC connection, and threaded rods. Visual inspection indicated no sign of cracking in the UHPC connection and some cracking at the bottom of the deck. The 350 300 Load (kip)

250 200 150 100

Horizontal Displacement

50 0.00

Vertical Displacement 0.01

0.02

0.03

0.04 0.05 0.06 Displacement (in.)

0.07

0.08

0.09

0.10

Figure 3.22. Horizontal and vertical relative displacement for push-off Specimen UHPC C1.




Girder cracks

Grouted haunch Threaded rods

Deck panel cracks (b) Concrete block

(a) Deck panels

Figure 3.23. Damaged push-off Specimen UHPC C1.

bottom portion includes the damaged concrete block with significant cracking. This behavior indicated that the use of lightly reinforced concrete block was inadequate, and the specimen anchorage system to the floor needs to be revised to reduce the bending moment resulting from load eccentricity. These changes were implemented in the second and third push-off specimens. Specimen UHPC C2: The compressive strength of UHPC at the time of testing (3 days old) was 13.5 ksi. The deck panels were supported by a concrete T-girder that had top flange reinforcement and web reinforcement similar to that of a typical concrete bridge I-girder. In addition, the girder was tied down to the strong floor using nylon straps at both ends to prevent it from moving up. Failure happened when wide cracks were generated in the concrete deck panel at the loading side, as shown in Figure 3.24. Again, the extremely strong UHPC was not the weak link, and failure shifted from the beam to the deck panels. At this moment, the measured load started to drop. The maximum recorded load was 312 kips, which exceeded the 236 kip predicted capacity. No visible cracks on either the UHPC connection or the T-girder were reported. Figure 3.25 shows the load-displacement plots for the horizontal and vertical relative displacement at the deck–haunch interface. The maximum measured strain in the steel collar was 310 microstrains (8.99 ksi), which is very small.

Deck Panel Cracks

Figure 3.24. Concrete deck panel failure in push-off Specimen UHPC C2.




350 300

Load (kip)

250 200 150


100 Vertical Displacement

50 0.00

0.01

0.02

0.03

0.04 0.05 0.06 Displacement (in.)

0.07

0.08

0.09

0.10

Figure 3.25. Horizontal and vertical relative displacement of push-off Specimen UHPC C2.

Specimen UHPC C3: In this test, the load was also applied incrementally at an approximate rate of 5 kips/s. The compressive strength of UHPC at the time of testing (4 days old) was 15.1 ksi. The specimen had the same concrete T-girder and anchorage system used in Specimen UHPC C2. As predicted, based on Specimen 2 testing, failure happened in the deck panels. Wide cracks were generated in the concrete deck panel at the loading side, as shown in Figure 3.26. At this moment, the measured load started to drop. The maximum recorded load was 342 kips, which again exceeded the theoretical 236 kip predicted capacity, with no visible cracks occurring in either the UHPC connection or the T-girder. Figure 3.27 shows the load-displacement plots for the horizontal and vertical relative displacement at the deck–haunch interface. The displacements and strains were consistent with those obtained from Specimen C2. Table 3.19 presents the summary of test results of the push-off specimens. Finite element analysis was conducted to study the behavior of the UHPC joint and areas of stress concentration. The finite element analysis was conducted using ABAQUS (V6.13-3).

Deck Panel Cracks

Figure 3.26. Concrete deck panel failure in push-off Specimen UHPC C3.




350 300

Load (kip)

250 200 150


100

Vertical Displacement

50 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

Displacement (in.)

Figure 3.27. Horizontal and vertical relative displacement of push-off Specimen UHPC C3.

Figure 3.28 shows the load-displacement plots of the three push-off specimens, as well as the one obtained from finite element analysis. The figure indicates the accuracy of the Finite Element Model in representing the behavior of the tested specimen and, therefore, its reliability. The developed model was then used to evaluate stress levels in the various components of the connection. Figure 3.29 shows the stress contours of the steel threaded rods, collar, washer plate, and nuts. This plot indicates that the highest stresses occur at the collar tube attached to the threaded rod that is located on the loading side. Figure 3.30 shows the stress contours of the concrete components (deck panels, UHPC connection and haunch, and girder). This plot indicates that the highest stresses are bearing compressive stresses that occur at the UHPC surrounding the steel collar. It also shows—as expected—high compressive stresses at the concrete girder top flange around the shear connectors. 3.2.2.2 Large-Scale Composite Beam The NU900 precast prestressed concrete girder used for the large-scale composite beam was fabricated by Concrete Industries Inc., a certified precast concrete plant in Lincoln, Nebraska. The NU900 girder was reinforced with sixteen 0.6-in.-diameter strands in the bottom flange, and four ½-in.-diameter strands in the top flange. Details and photos taken during fabrication of the precast panels are provided in Appendix C. The NU900 girder was fabricated using SCC with specified compressive strength at release of 6 ksi and 8 ksi at 28 days. Figure 3.31 shows the average compressive strength measured for the girder over time. When the girder was tested, its compressive strength was 8.8 ksi. The composite beam specimen was 40-ft long. NU900 precast prestressed concrete girder with seven shear connectors was used to support the precast deck panels. Figure 3.32 shows the elevation and cross-section views of the NU900 girder. Eight precast concrete deck panels Table 3.19. Summary of the results obtained from the push-off specimens. Specimen ID UHPC C1 on concrete block UHPC C2 on concrete tee-section beam UHPC C3 on concrete tee-section beam

Failure Load and UHPC Strength 232 kips, 15.7 ksi 312 kips, 13.5 ksi 342 kips, 15.1 ksi

Average

Prediction Capacity

295.3 kips, 14.8 ksi

236 kips



Research Findings 61 350 300

Load (kip)

250 200 150 Specimen 1 Specimen 2 Specimen 3 FE

100 50 0 0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

Horizontal Displacement (in.)

Figure 3.28. Load–displacement relationships of the three push-off specimens and Finite Element Model.

were used for this specimen. Eight precast concrete deck panels were used for this specimen, including six 6-ft-long panels between the seven connectors and two 2-ft-long end panels with the post-tensioning anchor blocks. Figure 3.33 shows plan and sectional views of the typical and end panels. These deck panels do not have steel reinforcement projecting into the transverse joints as the panels of push-off specimens did because they are longitudinally post-tensioned. Two 2-in.-diameter Schedule 80 PVC pipes were used in each panel as ducts for longitudinal post-tensioning. The panels were installed on 20-in. × 14-in. × 3-in. haunches that were around each connector. Wood forms, backer rods, and liquid nails were used to make watertight haunch forms. The bottom gaps between transverse joints were closed using backer rods, and the ends of transverse joints were formed using plywood bulkheads. All seven discrete joints at the shear connection and all transverse joints were grouted using UHPC. The longitudinal post-tensioning strands, which were greased and enclosed in continuous rubber sheathing, were installed and nominally tensioned at 10% of final prestress before the concrete surfaces were pre-wet and

Figure 3.29. Finite element stress contours in the steel components.



(a) Von Mises stresses in the deck and girder

(c) Von Mises stresses in the deck panels

(b) Von Mises stresses in the UHPC

Figure 3.30. Stress contours in the concrete components. 10

Compressive Strength (ksi)

9 8 7 6 5 4 3 2 1 0

0

7

14

21 28 Age (days)

35

42

49

56

Figure 3.31. Compressive strength of NU900 concrete girder.




Figure 3.32. Elevation (top) and cross-section (bottom) views of the NU900 girder.



(a) 6-ft-long precast panel

(b) 2-ft-long precast panel

Figure 3.33. Details of the 6-ft- and 2-ft-long precast concrete deck panels.




UHPC placed. Each transverse joint was overfilled with UHPC using ¾-in. plywood forms to ensure adequate filling of joints after the UHPC settlement. The joints were covered with plywood sheets for curing. Excess UHPC was ground immediately after curing. Four 0.6-in.-diameter Grade 270 low-relaxation strands (two strands in each duct) were used to post-tension the full-scale specimen. The strands were tensioned to only 53% of their ultimate strength to achieve an effective stress of 250 psi across the transverse joints after considering prestress losses. It is important to note that the final post-tensioning was applied after the panels have been made composite with the girder. This is a deviation from the standard practice where transverse joint concrete is poured and cured, post-tensioning is applied, and then the shear connections are grouted to achieve the composite section. The proposed procedure is expected to reduce construction time, as the grouting of the transverse joints and shear connections is conducted using a single pour. Analysis of the effect of post-tensioning on the composite section indicated the adequacy of this procedure with respect to deck compressive stresses and girder tensile stresses. Composite section properties were used in calculating post-tensioning stresses as the posttensioning force was applied after the deck panels were made composite with the girder. Having the strands greased and sheathed with rubber tubes not only allowed post-tensioning to be applied after grouting the transverse joints and shear pockets but also simplified the precast deck production and increased the level of protection to these strands. In addition, the PVC tubes that house the post-tensioned tendons do not have to be extended beyond the edges of the precast panels or coupled at the transverse joints, which increases the construction speed. Sheathing was removed from the ends of each strand, and a grease-removing agent was applied to achieve proper gripping between strands and seating wedges. Each of the four strands was post-tensioned individually. Figure 3.34 shows post-tensioning of the last strand. Figure 3.35 shows the stresses measured at different locations of the composite section while post-tensioning the last strand out of the four post-tensioned strands. These plots indicate the effectiveness of post-tensioning the composite system, as they show stress values up to 100 psi in the deck due to one strand. Therefore, it was estimated that the four strands would result in net compressive stress = 4 × 100 × 0.7 = 280 psi, which was more than the minimum desired 250 psi. The 0.7 reduction factor was used to account for the elastic-shortening losses caused by staged post-tensioning process and time-dependent losses.

Figure 3.34. Post-tensioning of the last strand.




Time (s)

Figure 3.35. Concrete strains at Section 2 caused by post-tensioning of last strand.

Table 3.20 lists the cracking moment, cracking deflection, ultimate moment, and ultimate vertical shear predicted according to AASHTO LRFD Bridge Design Specifications for both fully composite and noncomposite sections. The corresponding midspan point load for each case is also listed. These values were compared against those obtained from testing. The UHPC existing in the discrete haunches was conservatively ignored in calculating the composite section properties discrete joint system used. At the time of testing, the concrete strength of the NU900 girder was 8.7 ksi, and the average concrete strength of the precast deck panel was 7.7 ksi. The seven UHPC discrete joints and transverse joints were cast in five batches of 3.6 ft3 each, using the same proportions given in Table 3.18. The ambient temperature and relative humidity during mixing were 55°F and 84%, respectively. The slump flow test and preparation of 3-in. × 6-in. cylinders were conducted according to ASTM C1856. UHPC cylinders were kept inside the molds and air cured in the same conditions of the specimen, which resulted in slower and lower strength gain—compared to the UHPC mix used for the push-off specimens—caused by the low ambient temperature and relative humidity of the laboratory. Table 3.20. Predicted capacities of the specimen for both composite and noncomposite cases. Composite Section Property

Cracking moment (kip-ft) Cracking deflection (in.) Ultimate moment (kip-ft) Ultimate vertical shear (kip)

Noncomposite Section

Predicted Values

Corresponding Applied Load at Midspan (kip)

Predicted Values

Corresponding Applied Load at Midspan (kip)

2,200 0.32 3,401 221

226 226 327 415

1,275 0.47 2,508 163

131 131 236 300




Figure 3.36 shows the average compressive strength of UHPC with age. This figure indicates that compressive strength reached 18.3 ksi after 28 days, which is significantly lower than that of the push-off specimens. Figure 3.37 shows the test setup and instrumentation of the full-scale specimen. A vertical load was applied to the top surface of the composite girder at the midpoint of the 39-ft span. The girder was simply supported by two rollers on two concrete blocks. Concrete strain gauges were applied at the two sections on the top of the deck, bottom of the deck, top of the girder, and bottom of the girder, as shown in Figure 3.38. Electric resistance strain gauges were installed diagonally on one side of the collar at three steel connectors similar to that in the push-off test specimens. The relative displacement in both horizontal and vertical directions between the deck panels and girder were measured using six LVDTs, as shown in Figure 3.39. Also, the deflection of the girder at midpoint and quarter point were measured using two LVDTs. Bearing plates, bearing pads, a 430-kip hydraulic jack, a load cell, and a spreader beam were used to load the full-scale specimen at the midspan, as shown in Figure 3.40. Test 1 (Flexure Test): The load was applied in 25-kip increments, and the cracks were marked on the specimen. Diagonal shear cracks were observed at a 200-kip load, as shown in Figure 3.41, while vertical flexure cracks in addition to diagonal shear cracks were observed at a 225-kip load, as shown in Figure 3.42. When the applied load reached 338 kips, deflection increased with no significant increase in the applied load, which indicates yielding of flexure reinforcement. This load resulted in an ultimate moment of 3,505 kip-ft, which is higher than the 3,401 kip-ft predicted capacity shown in Table 3.20. The LVDT was unable to record deflection higher than 3.3 in. at the midpoint. Therefore, the test was stopped without visible failure. Figure 3.43 and Figure 3.44 show the load–deflection and load–displacement relationships, respectively, measured using LVDTs. The load–deflection relationship indicates that the cracking load was approximately 225 kips, which was very close to the predicted value for the fully composite section, as listed in Table 3.20. The load–displacement relationships indicated that the relative displacement between the deck panels and girder are negligible (2,000 MPa/ 290 psi). 3. Admixture: high-range water reducer/third generation. 4. Water and ice. The following proportions of mix components were used, based on the supplier’s recommendations: 1. 2. 3. 4.

Premix: 3,700 lbs/yd3. Steel fiber: 263 lbs/yd3. Super plasticizer liquid: 51 lbs/yd3. Water: 219 lbs/yd3 (one-third of the water was replaced with ice).

The mixed UHPC had a slump flow of 10 in., according to ASTM C1856, at a temperature of 78°F and relative humidity of 55%. The research team prepared 3 in. × 6 in. cylinders of the mix to monitor the concrete strength of the mix over 28 days, as shown in Figure 3.54. The UHPC reached the desired strength for testing (12 ksi to 14 ksi) in about 3 to 4 days. Figure 3.55 shows the setup used for the push-off testing of the three specimens. The hydraulic jack and load cell were aligned to apply a horizontal force at the center of the

Figure 3.53. Welding the steel studs using a Nelson stud gun.



78 Simplified Full-Depth Precast Concrete Deck Panel Systems 28 UHPC Mix at GWU_Push-Off Specimens 24

Average Strength (ksi)

20 16 12 8 4 0

0

2

4

6

8

10

12

14 16 Age (days)

18

20

22

24

26

28

Figure 3.54. UHPC strength versus time.

concrete deck panels, while the steel girder was restrained against horizontal movement using a horizontal steel frame. To avoid specimen rotation caused by eccentricity between the hydraulic jack and the horizontal frame, vertical steel frames were built around both ends of the precast deck. A ½-in.-thick steel bearing plate was installed in front of the load cell to distribute the load uniformly across the width of the panel. The push-off specimens were tied back to the wall using two 1¼-in.-diameter, 120-ksi-yield strength bars. The 1¼-in.-diameter bars were the maximum size bars that could be fed through the sleeves provided in the strong wall. The capacity of the setup was controlled by the 295-kips yield strength of the bars, which was 7% higher than the predicted shear capacity of the connection. Strain gauges were installed on five studs, as shown in Figure 3.56. In addition, strain gauges were installed on the vertical Dywidag bars holding the panel close to the applied load to monitor

Figure 3.55. Setup of the push-off specimens (N = north; S = south).




Figure 3.56. Strain gauges installed on the steel studs (NW = northwest; SW = southwest; NE = northeast; and SE = southeast).

the tension force generated in these bars. Two LVDTs were installed—one LVDT at each side of the specimen—to measure the relative horizontal displacement between the panels and the top surface of the steel beam. Specimen UHPC S1: The UHPC mix was 4 days old when the specimen was tested. Load was applied continuously at 2 kips/s until failure or maximum capacity of the setup was reached. At 265 kips, the measured load started to decline and the specimen was not able to receive any more load because the steel bearing plate in front of the load cell was bent. As a result, the concrete panel in front of the hydraulic jack was split horizontally, as shown in Figure 3.57. No signs of distress were observed in the UHPC joint between the panels and the steel beam or in the transverse connection between the panels. Figure 3.58 shows the relationship between the applied load and the relative displacement between the bottom surface of the precast panel and the top surface of the steel beam, obtained from the test and compared with the finite element simulation. The parameters of the UHPC in the finite element simulation were taken as follows: compressive strength = 14 ksi, and modulus of elasticity = 6,500 ksi. The test and finite element results showed linear elastic behavior up to 150 kips and plastic behavior afterward. The finite element results were consistent with the test results up to the 150-kip end of the linear elastic stage. Figure 3.59 shows the axial tensile stresses in the studs at the panel–haunch interface, obtained from the strain gauges installed on the studs. Figure 3.59 shows that the applied load was not uniformly distributed between the nine studs. Stud N, the center stud on the first row, carried more load than the corner studs. The maximum stress was about 37 ksi. The strain gauges installed on the vertical Dywidag bars used to tie down the panels to the strong floor showed maximum stress of 0.4 ksi, which was equivalent to 1.6 kips of axial tensile force per bar. Specimen UHPC S2: The UHPC was 3.5 days old when the specimen was tested. Load was applied continuously at 2 kips/s until failure or maximum capacity of the setup was reached. The research team provided two 1-in.-thick plates between the load cell and the panel to distribute the applied load




Applied load

(b) Precast panel split horizontally

(a) Steel bearing plate was bent

Applied load

Applied load

(c) Crushing failure of the loaded panel

(d) No signs of distress or failure observed in the UHPC joint

Figure 3.57. Reported failure mode of Specimen UHPC S1.




Push-Off, Steel Girder, Sp. No. 1

Figure 3.58. Load–relative displacement relationship obtained from the test and finite element simulation.

Figure 3.59. Axial tensile stress in the studs at the panel–haunch interface.




Applied Load Applied Load

(a)

(b)

Figure 3.60. Specimen UHPC S2: No signs of distress or failure were reported at the UHPC joint or the panels at 295 kips.

uniformly across the width of the panel. The research team loaded the specimen up to 295 kips, which was the yield capacity of the Dywidag bars tying the specimen to the strong wall. No signs of distress or failure were reported at the UHPC joint, the transverse joint, or the panels, as shown in Figure 3.60. The research team stopped the test at this point because the Dywidag bars started to show unequal plastic deformation, and the specimen started to rotate horizontally. Figure 3.61 shows the relationship between the applied load and the relative displacement between the bottom surface of the precast panel and the top surface of the steel beam, obtained from the test and the finite element simulation. The test results showed linear elastic behavior up to 295 kips, while the finite element simulation showed some plastic behavior starting at 220 kips. The test results showed higher relative displacement than the finite element results. Figure 3.62 shows the axial tensile stresses in the studs at the panel–haunch interface. The applied load was not uniformly distributed between the nine studs. Stud N, the center stud of Push-Off, Steel Girder, Sp. No. 2

Figure 3.61. Load–relative displacement relationship obtained from the test and finite element simulation.





Figure 3.62. Axial tensile stress in the studs at the panel–haunch interface.

the first row, carried more load than the corner studs. The maximum reported stud stress at the panel–haunch interface was about 27 ksi. Specimen UHPC S3: UHPC was 4 days old when the specimen was tested. Load was applied continuously at 2 kips/s. The research team provided two 1-in.-thick plates between the load cell and the panel to distribute the applied load uniformly across the width of the panel. The specimen was loaded up to 278.1 kips. At that load, the top flange of the steel beam at the far end of the specimen, where the reaction beam was located, started to bend and the specimen started to rotate horizontally. The rotation developed uneven force in the horizontal Dywidag bars, and the Dywidag bar on the east side started to show some plastic deformation. Therefore, the test was stopped at this point. No signs of distress or failure were reported in the UHPC joint, the transverse joint, or the panels up to 278.1 kips, as shown in Figure 3.63. Figure 3.64 shows the relationship between the applied load and the relative displacement between the bottom surface of the precast panel and the top surface of the steel beam, obtained from the test and the finite element simulation. The test showed linear elastic behavior up to 150 kips, while the finite element simulation showed linear elastic behavior up to 220 ksi and plastic behavior afterward up to 278.1 kips. The test results showed relatively higher displacement than the finite element results. Figure 3.65 shows the axial tensile stresses in the studs at the panel–haunch interface. This figure shows that the applied load was not uniformly distributed between the nine studs. Stud N, the center stud of the first row, carried more load than the corner studs. The maximum reported stress at this elevation was about 31 ksi. Table 3.22 gives a summary of the test results. The test results showed that the connection was able to sustain a capacity at least equal to that predicted by Article 5.7.4 of the AASHTO LRFD Bridge Design Specifications, with an average measured capacity of 279.4 kips. However, as the




(a)

(b)

Figure 3.63. Specimen UHPC S3 after testing: No signs of distress or failure were reported at the UHPC joint or the panels at 278.1 kips.

table shows, the three tests could not result in failure of the connection itself. Thus, the true connection capacity, as will be further illustrated in the beam testing, is higher than that obtained from the push-off tests. It also illustrates that UHPC causes the weak link to be away from the connection and into the conventional concrete connected elements. To monitor the stress distribution in the UHPC joint and the steel studs, the finite element simulation was used to run up to 279.4 kips. Figure 3.66 and Figure 3.67 show the Von Mises stresses in the UHPC joint and in the panels, respectively. The maximum-recorded stress in the UHPC joint and the precast panels was about 10 ksi and 6 ksi, respectively. The Von Mises stress is the equivalent uniaxial tensile/compression stress of a multiaxial state of stress. It is typically used to accurately detect stress distribution in 3-D continuum.


Figure 3.64. Load–relative displacement relationship obtained from the test and finite element simulation (FE = finite element).





Figure 3.65. Axial tensile stress in the studs at the panel–haunch interface. Table 3.22. Summary of the test results of the push-off specimens.

Specimen

Capacity Mode of failure Relative horizontal displacement

UHPC S1

UHPC S2

265.0 kips 295.0 kips Average capacity = 279.4 kips Crushing of the Reaching precast panel in maximum front of the capacity of the hydraulic jack test setup 0.095 in. 0.058 in.

UHPC S3

Nominal Capacity by AASHTO LRFD Bridge Design Specifications

278.1 kips Instability of the test specimen 0.065 in.

Article 5.7.4, 276.5 kips Article 6.10.10.4.3, 510.79 kips

Average relative horizontal displacement = 0.073

Applied Load

Figure 3.66. Von Mises stresses in the UHPC joint at 279.5 kips. Copyright National Academy of Sciences. All rights reserved.



Figure 3.67. Von Mises stresses in the UHPC joint at 279.4 kips.

Figure 3.68 and Figure 3.69 show the Von Mises stresses in the steel studs at the panel–haunch interface and the base of the studs, respectively. These figures show that the maximum tensile stress in the studs was at the base, and it was about 33 ksi in the center stud of the first row. 3.2.3.2 Large-Scale Composite Beam The composite beam was made of a 34-ft, 6-in.-long W24 × 104, A992-50 steel beam that supports seven 4-ft-wide precast panels. The steel beam was provided with stiffeners at the midspan and at the location of the end supports. Mechanical properties of the steel were tensile strength = 67.8 ksi and yield strength = 50.3 ksi. The steel beam was provided with six groups of steel studs at 6-ft spacing. Each group had nine 1-in.-diameter studs. The studs within each group were provided at 5-in. and 4-in. spacing in the longitudinal and transverse directions,

Figure 3.68. Von Mises stresses (psi) in the studs at panel–haunch interface at 279.5 kips.




Figure 3.69. Von Mises stresses (psi) at the base of the studs at 279.5 kips.

respectively. Height of the studs was 8 in. after welding. Studs were made of ASTM C1015 steel. Properties of studs were as given earlier in the push of testing description. The beam was fabricated by a certified steel fabrication company. Quality of the welding was checked by successfully bending four test studs to 45 degrees, as shown in Figure 3.70. Details of the composite beam and final setup are shown in Figure 3.71. The composite beam was supported on two end supports resulting in a simply supported 33-ft, 5-in. span. Load was applied at the midspan point. A concrete pad was provided between the panel and the steel beam at the midspan location to protect the center panel from flexural failure. Figure 3.72 shows the UHPC connections between the steel beam and the precast deck.

Figure 3.70. Quality control test of the stud welding.




(a)

(b)

Figure 3.71. Test setup of the large-scale beam.



Figure 3.72. UHPC connection between the steel beam and the precast deck.

Ductal JS1000 mix was produced by Lafarge North America. The mix is the same as has been used for the push testing and for the concrete girder-to-deck panel testing. Stress gain was monitored using 3-in. × 6-in. cylinders, as shown in Figure 3.73. The following instruments were installed in the specimen: • Strain gauges on the steel studs (Figure 3.74a): The strain gauges were installed on the steel

studs (Stud Groups A, B, and C) on the west side of the beam. • Horizontal LVDTs (Figure 3.74a): Three LVDTs were installed on the west side of the beam

to measure the relative horizontal displacement between the precast slab and the stop surface of the steel beam. • Vertical LVDT (Figure 3.74b): An LVDT was installed on the west side of the beam to measure the relative vertical displacement between the precast slab and the stop surface of the steel beam. • String pots (Figure 3.74c): Five string pots were installed on the west side of the beam to measure the vertical displacement of the composite beam. • Strain gauges on the composite beam (Figure 3.74d): Three groups of strain gauges were installed on the west side of the beam to measure the normal stresses of the composite beam. Each group contains five gauges. 28 UHPC Mix at Large-Scale Composite Beam

Average Strength (ksi)

24 20 16 12 8 4 0

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

Age (days)

Figure 3.73. UHPC strength versus time.




String Pot D5

String Pot D4

String Pot D3

String Pot D2

String Pot D1

(a) Locations of the strain gauges on the steel studs and horizontal LVDTs

(b) Location of the vertical LVDT

String Pot D4

String Pot D3

String Pot D2

String Pot D1

(c) Locations of the string pots

(d) Locations of the strain gauges on the composite beam

Figure 3.74. Instrument installed on the large-scale beam.



String Pot D5



Modes of failure: Three modes of failure were investigated: (1) flexural failure based on the plastic flexural capacity of the composite beam, (2) vertical shear failure based on the shear capacity of the web of the steel beam, and (3) horizontal shear failure based on the plastic flexural capacity of the composite beam, as shown in Table 3.23. For the first and second modes of failure, the corresponding horizontal shear force generated for each group of studs was calculated. For the third mode of failure, the horizontal shear capacity was determined using Article 5.7.4 and Article 6.10.10 of the AASHTO LRFD Bridge Design Specifications. In addition, Table 3.23 shows the corresponding concentrated applied load at midspan of the test specimen for every mode. Table 3.23 shows that—if full composite action is maintained between the precast deck and the steel beam—the specimen would fail in flexure. The corresponding applied horizontal shear force would be 432.4 kips per cluster of studs. This horizontal shear force is 156% and 85% of the capacity determined by Article 5.7.4 and Article 6.10.10 of the AASHTO LRFD Bridge Design Specifications, respectively. Fatigue testing: The large-scale beam was subjected to fatigue load and was then tested for strength. The fatigue load range was determined using an actual 60-ft bridge that would deliver a flexural strength equal to the plastic moment strength of the composite beam (3,581.95 kip-ft). Other criteria of this bridge were as follows: girder spacing = 9 ft, slab thickness = 8.5 in., slab compressive strength = 7.06 ksi, haunch thickness = 2.5 in., steel beam built-up section = W24 × 104 + PL (11 in. × 0.75 in.), Grade 50 steel, groups of nine 1-in.-diameter studs at 72-in. spacing. Moment due to Fatigue I Limit State was determined. It corresponded to a 49.55-kip load range applied at midspan. To expedite the fatigue test, this load was magnified by a factor of 1.534. This approach was used by NCHRP Project 10-72 (Connor et al. 2012). The magnified load range = 1.534 × 49.55 = 76.0 kips. To maintain stability of the test setup, a minimum load of 5 kips was applied. Therefore, the maximum and minimum applied fatigue loads were 81.0 kips and 5.0 kips, respectively. Article 6.6.1.2.5 of the AASHTO LRFD Bridge Design Specifications states that, with regard to cycles, the fatigue resistance above the constant amplitude fatigue threshold is inversely proportional to the cube of the stress range, as follows: 1

 A3 ( ∆F )n =   N

(LRFD Eq. 6.6.1.2.5-2)

Table 3.23. Comparison between possible modes of failure. Mode of Failure 1. Flexure plastic moment Composite behavior = 3,581.9 k-ft Noncomposite behavior = 1,632.6 k-ft 2. Vertical shear strength = 360.0 kips 3. Horizontal shear Article 5.7.4 AASHTO LRFD Bridge Design Specifications = Article 6.10.10 AASHTO LRFD Bridge Design Specifications = Based on push-off test results =

Horizontal Shear per Group of Studs (kips)

Corresponding Load at Midspan (kips)

432.4 na 726.2

428.7 195.4 720.0

276.5

274.0

510.8 279.4

505.0 277.0

Note: na = not applicable.




Therefore, if the fatigue test is conducted for 1,900,000 cycles (according to ASTM D6275-98) at the magnified load level, it is equivalent to = (1.900 × 106) (1.534)3 = 6.86 × 106 design fatigue cycles. The magnified applied load range that was applied on the test specimen resulted in 8.52 kips of horizontal shear force per stud. This was higher than the nominal fatigue resistance given by the AASHTO LRFD Bridge Design Specifications for Fatigue I and Fatigue II Limit States. Analysis has shown that the studs in the experimental investigation were stressed beyond the limits given by Fatigue I and Fatigue II Limit States of the AASHTO LRFD Bridge Design Specifications. Thus, the current AASHTO fatigue limits are conservative. The fatigue load was applied at 1.5 cycles/s. The composite beam was visually inspected for signs of distress every 50,000 cycles. Measurement data from the LVDTs, strain gauges, and string pots were collected at zero cycles, and then at every 250,000 running cycles. The data were collected while the composite beam was loaded with a monotonic load at 1 kip/s up to 81.0 kips. At 800,000 cycles, while the composite beam was exposed to the magnified fatigue load (equivalent to 2,888,000 cycles of design fatigue load), some hairline cracks developed on the top surface of the deck at the transverse joints at Stud Group B and Stud Group F, as shown in Figure 3.75. Also, at 800,000 cycles, a crack extended on the top surface of the deck and on the bottom surface of the thin slab on the north end of the deck, as shown in Figure 3.76.

(a) At Stud Group B

(b) At Stud Group F

Figure 3.75. Top deck cracks developed at 800,000 running cycles at Stud Group B and Stud Group F.




Midspan East Side

West Side

Midspan Midspan

Figure 3.76. Deck cracks developed at 800,000 running cycles at midspan.

No further cracks were observed when 1,900,000 cycles were reached, which is equivalent to 6,860,000 unmagnified fatigue cycles. At the full fatigue limit of 1,900,000 magnified cycles, a crack started to appear at the bottom face of the steel beam. It propagated quickly to mid height of the web, as shown in Figure 3.77. The test was immediately stopped. Temporary supports were installed on both sides of the crack. A professional welding company was called to fix the crack, as shown in Figure 3.78 and Figure 3.79. The quality of the weld was carefully checked using ultrasonic inspection. Steel plates were welded on both sides of the web, and steel bars were welded to the bottom flange, as shown in Figure 3.80. The steel bars were extended only 4 ft on each side of the crack. Therefore, the flexural capacity of the composite beam at midspan was not affected.




Midspan East Side

West Side

String Pot D5

String Pot D4

String Pot D3

String Pot D2

String Pot D1

Figure 3.77. Fracture fatigue crack developed in the steel beam.

Figure 3.81 to Figure 3.85 show the change in the measurements collected versus the number of cycles. Examining these figures shows clearly that no significant change of the behavior of the composite beam occurred because of application of the fatigue load. No cracks were observed in the UHPC filling the transverse joints between panels or the discrete joints filling the haunch between the deck and the steel beam. Figure 3.86 shows the distribution of flexural stresses at Locations 1, 2, and 3. The figure presents a comparison between the flexural stresses obtained from analysis, assuming full composite action and the average flexural stresses obtained from the fatigue test. Figure 3.86 also shows that the stress distribution obtained from the fatigue test has a single neutral axis, which is an indication that the full composite action was maintained at the three locations.




Figure 3.78. Preparation of the crack before welding.

Figure 3.79. The crack after welding.




Figure 3.80. The steel beam after welding the web plates and the bottom steel bars.

Vertical Deflection Versus Number of Cycles

String Pot D5

String Pot D4

String Pot D3

String Pot D2

String Pot D1

Number of Cycles (millions) (fatigue design load)

Figure 3.81. Deflection of the composite beam versus the number of cycles (D = deflection).




Relative Vertical Displacement Versus Number of Cycles


Figure 3.82. Vertical separation between the steel beam and the deck versus the number of cycles (VS = vertical separation).

Relative Horizontal Displacement Versus Number of Cycles


Figure 3.83. Relative horizontal movement between the steel beam and the deck versus the number of cycles.




Flexural Stress (ksi)

Flexural Stresses G1 Versus Number of Cycles


Figure 3.84. Flexural stresses in the composite beam at Location 1.

Axial Tensile Stresses in Studs of Group A

String Pot D5

String Pot D4

String Pot D3

String Pot D2

String Pot D1


Figure 3.85. Axial tensile stresses in studs of Group A.



A

B

Figure 3.86. Flexural stresses of the composite beam (81 kips).

C

D


Midspan West Side



Figure 3.87 shows a comparison between the deflection obtained by analysis (using the Euler–Bernoulli Beam Theory, along with the full composite section properties) and the fatigue test. The comparison between the measured and predicted deflection shows that an 80% reduction of the beam model stiffness would bring the analytical results close to the experimental result. This observation is acknowledged by the Steel Construction Manual (American Institute of Steel Construction 2017), where Section I3 states that “comparison to short-term deflection tests indicate that the effective moment of inertia, Ieff, is 15 to 30% lower than that calculated based on linear elastic theory, Iequiv. Therefore, for realistic deflection calculations, Ieff should be taken 0.75 Iequiv .” Strength test: After the fatigue test was completed, the composite beam was exposed to a monotonic load until failure. The load was applied using a 500-kip hydraulic jack, as shown in Figure 3.88. The applied load was monitored using a load cell installed at the hydraulic jack and a pressure gauge installed on the hydraulic pump. The load was applied at 2 kips/s until the maximum capacity of the setup was reached at 450 kips. At 322 kips, some hairline cracks started to appear on the north side of the deck at Joint B. A single crack appeared on the bottom surface of the deck around the shear pocket, one vertical crack on the side of the deck in the UHPC joint, and one crack on top of the deck in the UHPC joint, as shown in Figure 3.89. At 375 kips, wide cracks started to develop on the bottom surface of the deck at Joints C, D, and E. Figure 3.90 shows the cracks formed on the bottom surface of the deck by the end of the test. The test was stopped at 450 kips when the applied load reached the maximum capacity of

Vertical Deflection at Midspan (D1)

String Pot D5

String Pot D4

String Pot D3

String Pot D2

String Pot D1


Figure 3.87. Deflection at midspan caused by fatigue test and composite beam analysis.




Figure 3.88. Setup of the strength test.

West

East

B

B

West

East (a)

(b)

West East

West

North

East (d)

(c)

Figure 3.89. Hair cracks appeared on the north side of Joint B at 305 kips.




D B West East

West

East

(a) Joint B (south side)

(b) Joint D (south side)

E

E

West

East

West

East

(c) Joint E (south side)

(d) Joint E (north side)

D

West

East East

West

C

(e) Joint D (north side)

(f) Joint C (north side)

Figure 3.90. Cracks appeared on the bottom surface of the deck at 450 kips.




the setup. No cracks were observed on the top surface of the deck except the crack that appeared at Joint B at 322 kips. In addition, no cracks were observed around Joints A and F. In all cases, the UHPC material filling the transverse joints between panels and the discrete joints between the slab and the beam appeared to shift distress away from it. The recorded deflection at midspan was 2.377 in. The beam showed 0.665 in. residual deflection after the applied load was fully removed. Measurements obtained from the strength test are shown in the following figures: (1) Figure 3.91 shows the deflection of the beam at midspan, (2) Figure 3.92 shows the relative horizontal displacement between the bottom surface of the deck and the top surface of the steel beam, and (3) Figure 3.93 shows the relative vertical displacement between the bottom surface of the deck and the top surface of the steel beam. In these figures, the corresponding load to Service I, Service II, and Strength I Limit States of the 60-ft bridge are presented for comparison. Figure 3.91 shows that the beam continues to show elastic behavior up to 380 kips, where the recorded stresses at the bottom face of the steel built-up section reached the yield strength 50 ksi. In addition, Figure 3.91 shows the predicted deflection at midspan using Euler–Bernoulli

Deflection at Midspan

String Pot D5

String Pot D4

String Pot D3

Figure 3.91. Deflection at midspan.


String Pot D2

String Pot D1



Load Versus Relative Horizontal Displacement

Figure 3.92. Relative horizontal displacement between the deck and the steel beam.

Elastic Beam Analysis with 100% EI, 80% EI, and 75% EI, where EI is the stiffness of the composite beam. The comparison between the measured and predicted deflection shows that an 80% reduction of the stiffness should be used in the beam model to accurately predict the short-term deflection. This observation is consistent with the observation reported during the fatigue test and the recommendation given by the American Institute of Steel Construction (2017). Figure 3.92 and Figure 3.93 show an insignificant amount of relative horizontal and vertical displacement between the deck and the steel beam at Fatigue, Service, and Strength Limit States. 3.2.3.3 Summary and Conclusions Based on the results obtained from the push-off and the large-scale beam specimens, the following conclusions are drawn: 1. Fatigue load has no detrimental effect on the composite action of the slab–beam system. 2. No changes are proposed for the fatigue design of the shear connectors given in Article 6.10.10.2 of the AASHTO LRFD Bridge Design Specifications. 3. Table 3.24 gives a summary of the shear connector capacity. The push-off specimens had an average capacity of 279.4 kips. When averaged with the horizontal shear capacity of a stud cluster in the beam specimen, the overall experimental connection capacity is 366.6 kips. This capacity can be well represented by Equation 6.10.10.4.3-1 of the AASHTO LRFD




Load Versus Relative Vertical Displacement

Figure 3.93. Relative vertical displacement between the deck and the steel beam.

Table 3.24. Summary of the test results of push-off specimens and large-scale beam specimens.

Criteria

Push-Off Specimens (average of 3 specimens)

Large-Scale Beam Specimens

279.5 kips

453.8 kips

Article 5.7.4 (276.5 kips)

Average = 366.6 kips

Capacity

Nominal Capacity by AASHTO LRFD Bridge Design Specifications (Qn)

366.6 kips = 133% of Qn by LRFD Article 5.7.4 366.6 kips = 72% of Qn by LRFD Article 6.10.10.4.3

Mode of Failure

Relative Horizontal Displacement

Crushing of precast panel in front of hydraulic jack

Article 6.10.10.4.3 (510.79 kips)

Reaching Reaching maximum Instability maximum capacity of test capacity of of test specimen test setup setup

0.073 in.

0.100 in.

Average = 0.086 in.




Bridge Design Specifications if a group effect factor of 0.72 is applied. Thus, the modified formula is Qn = 0.5 Asc f c′Ec ≤ 0.72 Asc Fu where Qn = nominal shear resistance of the stud shear connectors in the cluster (kips), Asc = cross-sectional area of the stud shear connectors in the cluster (in.2), Ec = modulus of elasticity of the deck concrete (ksi), and Fu = specified minimum tensile strength of the stud shear connectors (ksi). 4. Full composite action is expected at all Service and Strength Limit States. No reduction of the full composite beam stiffness is warranted. 5. For deflection calculations, a 75% factor should be applied to the full composite beam stiffness.

3.3 Design Examples 3.3.1 Design of the Precast Deck Slab System 3.3.1.1 Design Criteria Figure 3.94 to Figure 3.96 show the details of the deck. The deck is made of ribbed precast concrete panels. The panels are 6-ft long and 51-ft wide. The precast deck panels are pretensioned transversely and post-tensioned longitudinally. Girder spacing = 9 ft. Actual thickness of the panel = 9.0 in. The top ½ in. of the panel thickness is assumed to be a wearing surface and is not included in the structural resistance. Structural thickness: Top skin ts = 5.0 and total rib depth = 8.5 in. The cantilevers are made of a solid section. Concrete: Normal-weight concrete, unit weight = 150 pcf; concrete strength at pretension release = 4 ksi; concrete strength at 28 days = 6 ksi; and relative humidity, H = 70%.

Figure 3.94. Cross section of the bridge.




Figure 3.95. Details of the precast deck (transverse section).

Figure 3.96. Longitudinal cross section of the precast panel.




3.3.1.2 Loads Deck weight (DC): Deck weight between girders: Volume=( 9 × 12′′ )( 6 × 12′′ )( 9′′ ) − ( 2 × 12′′ )( 4 × 12′′ )( 3.5′′ ) = 69,984 − 12,096 = 57,888 in.3 = 33.50 ft 3 Deck weight = ( 33.50 ft 3 )( 0.150 kcf ) = 5.025 kips =

5.025 kips = 0.093 k/ft 2 ( 6 ft )( 9 ft )

 8.5  Deck weight at the cantilever = ( 6 ft ) ft ( 0.150 kcf ) = 0.638 k ft 6-ft long panel  12  = 0.106 k/ft 2  2  Wearing surface ( DW ): DW = ( 6 ft ) ft  ( 0.150 kcf ) = 0.150 k ft 6-ft long panel = 0.025 k/ft 2  12  LL: Rear axle of the AASHTO HL93 standard truck. 3.3.1.3 Flexural Design in the Transverse Direction Positive transverse moment: Figure 3.2 and Figure 3.5 give the transverse moment due to HL93 (including the multiple presence factor and dynamic allowance) and 100 psf, respectively. DC loads: Panel weight:

 93  M DC = ( 0.75 ) = 0.70 k-ft/ft  100 

DW loads: Wearing surface:

 25  M DW = ( 0.75 ) = 0.20 k-ft/ft  100 

LL: HS20:

MLL+I = 6.2 k-ft/ft

Mservice I = 0.70 + 0.20 + 6.2 = 7.10 k-ft/ft = 42.6 k-ft/6-ft long panel Mservice III = 0.70 + 0.20 + 0.8 × 6.2 = 5.86 k-ft/ft = 35.2 k-ft/6-ft long panel Mstrength I = 1.25 × 0.7 + 1.5 × 0.2 + 1.75 × 6.2 = 12.1 k-ft/ft = 72.2 k-ft/6-ft long panel Negative transverse moment: Figure 3.3 and Figure 3.6 give the transverse moment due to HL93 (including the multiple presence factor and dynamic allowance) and 100 psf, respectively. DC loads: Panel weight:

 93  M DC = (1.20 ) = 1.11 k-ft/ft  100 


 25  M DW = (1.20 ) = 0.30 k-ft/ft  100 

LL: HS20

MLL+I = 6.0 k-ft/ft




Mservice I = 1.11 + 0.30 + 6.0 = 7.41 k-ft/ft = 44.46 k-ft/6-ft long panel Mservice III = 1.11 + 0.30 + 0.8 × 6.0 = 6.21 k-ft/ft = 37.26 k-ft/6-ft long panel Mstrength I = 1.25 × 1.11 + 1.5 × 0.30 + 1.75 × 6.0 = 12.34 k-ft/ft = 74.03 k-ft/6-ft long panel Geometrical properties of the panel in positive moment zone between girder lines: Variable-thickness panel (Figure 3.96): Ag = (6 × 12″)(8.5″) – (4 × 12″)(3.5″) = 612 – 168 = 444 in.2 Using the bottom fiber as the reference line: Moment of the area about the bottom fiber = 612 ×

y bottom =

8.5 3.5 − 168 × = 2307 in.3 2 2

2307 2307 = 5.20 in., y top = 8.5 − = 3.30 in. 444 444

8.5  ( 6 × 12 )( 8.5′′ ) 3.5  ( 4 × 12′′ )( 3.5′′ )   Ig = ( 612 ) 5.2 − + − (168 ) 5.2 − − = 2066 in.4    2  12 2  12 2

S top =

3

2

3

2066 2066 = 397.3 in.3 = 626.1 in.3 , S bottom = 3.3 5.2

where Ag = gross section area, ybottom = distance from the centroid to the bottom fiber, ytop = distance from the centroid to the top fiber, Ig = moment of inertia, Stop = section modulus at top fiber, and Sbottom = section modulus at bottom fiber. The panel is reinforced transversely with six 1/2-in.-diameter, 270-ksi strands per panel, placed on two layers, as shown in Figure 3.96. Centroid of the six strands is at 3.92 in. from the top fiber of the panel. Therefore, the centroid of the strands is below the centroid of the cross section. ep = 3.92 – 3.30 = 0.62 in., where ep is the distance from the centroid to the top fiber. Geometrical properties of the panel in the negative moment zone (8.5-in.-thick solid section): Ag = ( 6 × 12 )( 8.5 ) = 612 in.2 ytop = ybottom = 4.25 in. Ig =

( 6 × 12)( 8.5)3 12

Stop = Sbottom =

= 3684.8 in.4

3684.8 = 867 in.3 4.25




Centroid of the six strands is at 3.92 in. from the top fiber of the panel. Therefore, the centroid of the strands is above the centroid of the cross section. e p = 4.25 − 3.92 = 0.33 in. Prestress losses. (a) Elastic shortening losses: Ep ∆ fpES =   fcgp  Ect 

( LRFD Equation 5.9.3.2.3a-1)

where Dfpes = prestress loss due to elastic shortening (ksi), Ep = modulus of elasticity of prestressing strands = 28,500 ksi, Ect = modulus of elasticity of panel at transfer = 3,834 ksi, and fcgp = the concrete stress at the center of gravity of the prestressing strands due to the prestressing force immediately after transfer and self-weight of the member at the section of maximum moment. The Commentary to Article 5.9.5.2.3a of the AASHTO LRFD Bridge Design Specifications states that fcgp may be assumed to be 90% of the initial prestress before transfer and the analysis iterated until acceptable accuracy is achieved. However, because of the very light prestress used, 1% initial loss is assumed and then checked. Strand stress immediately after release = 202.5 (1.00 − 0.01) = 200.475 ksi Pi = total prestressing force at release = ( 6 strands )( 0.153 in.2 strand )( 200.475 ksi ) = 184.036 kips fcgp = + =+

2 ( M deck ) e p Pi Pe i p + − Ag Ig Ig

184.036 184.036 × 0.622 ( 3.97 × 12 )0.62 + − = +0.415 + 0.034 − 0.014 = 0.435 ksi 444 2066 2066

Therefore, loss due to elastic shortening:  28000  f pES =  ( 0.435) = 3.177 ksi  3834  Initial prestress loss =

3.177 × 100 = 1.57% 202.5

The initial prestress loss is very close to the assumed value, so a second iteration is not necessary. Strand stress immediately after release = 202.5 – 3.177 = 199.323 ksi Pi = total prestressing force at release = (6 strands)(0.153 in.2/strand)(199.323 ksi) = 182.979 kips




(b) Long-term prestress losses: Using Section 5.9.3.3 of the AASHTO LRFD Bridge Design Specifications, time-dependent losses can be estimated as follows: ∆ f pLT = 10.0

f pi Aps γ h γ st + 12.0 γ h γ st + ∆f pR Ag

( LRFD Equation 5.9.3.3-1)

where fpi = Prestress immediately prior to transfer = 2020.5 ksi, Aps = Area of prestress reinforcement = 6 × 0.153 = 0.918 in.2, Ag = Gross concrete section area = 444 in.2, gh = 1.7 – 0.01(H) = 1.7 – 0.01(70) = 1.0, 5 5 = = 1.0 , gst = (1 + f ci′ ) (1 + 4 ) fci = concrete strength at release = 4.0 ksi., DfpR = 2.4 ksi, and ( 202.5 × 0.918 ) ∆ fpLT = 10 (1.0 )(1.0 ) + 12(1.0 )(1.0 ) + 2.4 = 18.586 ksi 444 Total prestress losses at service = 3.177 + 18.586 = 21.764 ksi Effective prestress at service fpe = 202.5 – 21.794 = 180.736 ksi Effective prestress force Ppe = (6 strands)(0.153 in.2/strand)(180.736 ksi) = 165.916 kips Check of concrete stresses at service at the positive moment area. Effective prestress force at service Ppe = 165.916 kips Stress limits for concrete (LRFD Article 5.9.4.2): Compression stress, Service I, top fiber. Compression stress limit due to LL and 50% of the sum of effective prestress and permanent loads = 0.40 f c′ = (0.40)(6.0) = + 2.4 ksi M service I = 0.5 × 0.7 + 0.5 × 0.2 + 6.2 = 6.65 k-ft/ft = 39.90 k-ft/6-ft-long panel ftop = + 0.5 × = + 0.5 ×

Ppe ( Ppe e p ) ytop ( M service ) ytop − 0.5 × + Ag I I 165.916 (165.916 × 0.62)( 3.3) (39.90 × 12 )(3.3) − 0.5 × + 444 2066 2066

=+ 0.5 × 0.374 − 0.5 × 0.164 + 0.764 = +0.869 ksi < 2.4 ksi Compression stress limit due to sum of effective prestress and permanent loads = 0.45 f c′= ( 0.45)( 6.0 ) = + 2.7 ksi M service I = 0.7 + 0.2 = 0.9 k-ft/ft = 5.40 k-ft/6-ft-long panel




f top = +

165.916 (165.916 × 0.62)( 3.3) (5.40 × 12 )( 3.3) Ppe ( Ppe e p ) ytop ( M service ) ytop − + =+ − + 444 2066 2066 Ag I I

= + 0.374 − 0.164 + 0.104 = 0.314 ksi < 2.7 ksi Compression stress limit due to effective prestress, permanent loads, and transient loads = 0.6 f c′ = ( 0.6 )( 6.0 ) = +3.6 ksi M service III = 0.70 + 0.20 + 6.2 = 7.10 k-ft/ft = 42.60 k-ft/6-ft-long panel f top = +

165.916 (165.916 × 0.62 )( 3.3) ( 42.60 × 12 )(3.3) Ppe ( Ppe e p ) ytop ( M service ) ytop − + =+ − + 444 2066 2066 Ag I I

= + 0.374 − 0.164 + 0.817 = +1.027 ksi < 3.6 ksi Tensile stress, Service III, bottom fiber: Tensile stress limit = 0.19 f c′ = 0.19 6.0 = − 0.465 ksi M service III = 0.7 + 0.2 + 0.8 × 6.2 = 5.86 k-ft/ft = 35.16 k-ft/6-ft long panel fbottom = + =+

Ppe ( Ppe e p ) ybottom ( M service ) ybottom + − Ag I I 165.916 (165.916 × 0.62)(5.2 ) ( 35.16 × 12 )(5.2 ) + − 444 2066 2066

= + 0.374 + 0.259 − 0.674 = − 0.041 ksi < − 0.465 ksi Check of concrete stresses at service at the negative moment area: Prestressing force at service Ppe = 165.916 kips ep = 4.25 − 3.92 = 0.33 in. Stress limits for concrete (LRFD Article 5.9.2.3): (a) Compression stress, Service I, bottom fiber: Compression stress limit due to live load and 50% of the sum of effective prestress and permanent loads = 0.40 f c′ = ( 0.40 )( 6.0 ) = + 2.4 ksi M service I = 0.5 × 1.11 + 0.5 × 0.30 + 6.0 = 6.71 k-ft/ft = 40.23 k-ft/6-ft long panel fbottom = + 0.5 × = + 0.5 ×

Ppe ( Ppe e p ) ybottom ( M service ) ybottom − 0.5 × + Ag I I 165.916 (165.916 × 0.33)( 4.25) ( 40.23 × 12 )( 4.25) − 0.5 × + 612 3684.8 3684.8

= + 0.5 × 0.271 − 0.5 × 0.063 + 0.556 = + 0.660 ksi < 2.4 ksi




Compression stress limit due to sum of effective prestress and permanent loads = 0.45 f c′ = ( 0.45)( 6.0 ) = + 2.7 ksi M service I = 1.11 + 0.30 = 1.41 k-ft/ft = 8.46 k-ft/6-ft-long panel Ppe ( Ppe e p ) ybottom ( M service ) ybottom − + Ag I I

fbottom = + =+

165.916 (165.916 × 0.33)( 4.25) ( 4.77 × 12 )( 4.25) − + 612 3684.8 3684.8

= +0.271 − 0.063 + 0.066 = +0.274 ksi < 2.7 ksi Compression stress limit due to effective prestress, permanent loads, and transient loads = 0.6 f c′ = ( 0.6 )( 6.0 ) = + 3.6 ksi M service I = 1.11 + 0.30 + 6.0 = 7.41 k-ft/ft = 44.46 k-ft/6-ft-long panel fbottom = + =+

Ppe ( Ppe e p ) ybottom ( M service ) ybottom − + Ag I I

165.916 (165.916 × 0.33)( 4.25) ( 44.46 × 12 )( 4.25) − + 612 3684.8 3684.8

= + 0.271 − 0.063 + 0.615 = +0.823 ksi < 3.6 ksi (b) Tensile stress, Service III, top fiber: Tensile stress limit = 0.19 f ′c = 0.19 6.0 = −0.465 ksi M service III = 1.11 + 0.30 + 0.8 × 6.0 = 6.21 k-ft/ft = 37.26 k-ft/6-ft-long panel f top = + =+

Ppe ( Ppe e p ) ytop ( M service ) ytop + − Ag I I 165.916 (165.916 × 0.33)( 4.25) ( 37.26 × 12 )( 4.25) + − 761 3684.8 3684.8

= + 0.218 + 0.063 − 0.516 = − 0.235 ksi > − 0.465 ksi Strength Limit State at the positive moment area: Mstrength I = 1.25 × 0.7 + 1.5 × 0.2 + 1.75 × 6.2 = 12.03 k-ft/ft = 72.18 k-ft/6-ft-long panel Using Strain Compatibility analysis: Depth of the equivalent compression block = 0.636 in. Depth of the neutral axis = 0.636/0.75 = 0.847 in. Nominal flexural strength Mn = 72.383 k-ft/6-ft-long panel φMn = 1.0 × 72.383 = 72.383 k-ft/6-ft-long panel




Strength Limit State at the negative moment area: Mstrength I = 1.25 × 1.11 + 1.5 × 0.30 + 1.75 × 6.0 = 12.34 k-ft/ft = 74.03 k-ft/6-ft-long panel Cross section: 8.5-in. solid section Using Strain Compatibility analysis: Depth of the equivalent compression block = 0.625 in. Depth of the neutral axis = 0.625/0.75 = 0.833 in. Nominal flexural strength Mn = 86.173 k-ft/6-ft-long panel φMn = 1.0 × 72.383 = 86.173 k-ft/6-ft-long panel 3.3.1.4 Flexural Design in the Longitudinal Direction Positive longitudinal moment: Figure 3.4 and Figure 3.7 give the longitudinal moment caused by the HL93 truck (including the multiple presence factor and dynamic allowance) and 100 psf, respectively. DC loads: Panel weight:

 93  M DC = ( 0.6 ) = 0.56 k-ft/ft  100 


 25  M DW =( 0.6 ) = 0.15 k-ft/ft  100 

Live load: HS20 truck:

M LL+I = 5.95 k-ft/ft

Mservice I = 0.56 + 0.15 + 5.95 = 6.66 k-ft/ft = 59.94 k-ft/9-ft Mservice III = 0.56 + 0.15 + 0.8 × 5.95 = 5.47 k-ft/ft = 49.23 k-ft/9-ft Mstrength I = 1.25 × 0.56 + 1.5 × 0.15 + 1.75 × 5.95 = 11.34 k-ft/ft = 102.04 k-ft/9-ft Negative longitudinal moment: Figure 3.3 and Figure 3.6 give the longitudinal moment due to HL93 (including the multiple presence factor and dynamic allowance) and 100 psf, respectively. DC loads: Panel weight:

 93  M DC = ( 0.80 ) = 0.75 k-ft/ft  100 


 25  = 0.20 k-ft/ft M DW =( 0.80)  100 

Live load: HS20:

M LL+I = 4.2 k-ft/ft




Mservice I = 0.75 + 0.20 + 4.2 = 5.15 k-ft/ft = 46.35 k-ft/9-ft Mservice III = 0.75 + 0.20 + 0.8 × 4.2 = 4.31 k-ft/ft = 38.79 k-ft/9-ft Mstrength I = 1.25 × 0.75 + 1.5 × 0.20 + 1.75 × 4.2 = 8.59 k-ft/ft = 77.29 k-ft/9-ft Geometrical properties of the panel in positive moment zone (Figure 3.95, shaded area): Height = 8.5 in., Area = 618 in.2, Inertia = 2782.5 in.4, ytop = 3.125 in., ybottom = 5.375 in. The panel is post-tensioned longitudinally with twelve ½-in.-diameter, 270-ksi encapsulated strands per girder spacing. The strands are provided in four ducts, three strands per duct. The centroid of the ducts is at 4.25 in. from the top and bottom fiber of the panel. Therefore, the centroid of the strands is below the centroid of the cross section. e p = 5.375 – 4.25 = 1.125 in. Geometrical properties of the panel in negative moment zone (8.5-in.-thick solid section): Ag = (9 × 12′′)(8.5) = 918 in.2 ytop = ybottom = 4.25 in. I g = (9 × 12)(8.5)3 12 = 5527.1 in.4 Stop = Sbottom =

5527.1 = 1300.5 in.3 4.25

The centroid of the 12 strands is at the same level as the centroid of the cross section. Therefore: ep = zero Prestress losses: In this example, it is assumed that the four groups of strands will be tensioned one group at a time. In addition, the strands are post-tensioned from both ends of the 120-ft-long span. (a) Elastic shortening losses: ∆ f pES =

N − 1  Ep    fcgp 2 N  Ect 

( LRFD Equation 5.9.3.2.3b-1)

where N = number of identical tendons = 4, Ep = modulus of elasticity of prestressing strands = 28,500 ksi, Ect = modulus of elasticity of panel at transfer = 3,834 ksi, and fcgp = concrete stress at the center of gravity of the prestressing strands due to the prestressing force after jacking and self-weight of the member at the section of maximum moment. In this example, 1% initial loss is assumed and then checked later. Strand stress immediately after release = 202.5 (1.00 − 0.01) = 200.475 ksi Pi = total prestressing force at release = (12 strands)(0.153 in.2/strand)(200.475 ksi) = 368.1 kips




fcgp = +

2 Pi Pe 368.1 368.1 × 1.1252 ( 0.56 × 12 )1.125 ( M deck )e p i p + − =+ + − = + 0.760 ksi Ag Ig Ig 618 2782.5 2782.5

Therefore, loss due to elastic shortening: f pES =

4 − 1  28000  ( 0.745) = 2.119 ksi 2 × 4  3834 

Initial prestress loss =

2.119 × 100 = 1.04% 202.5

The initial prestress loss is very close to the assumed value, so a second iteration is not necessary. Strand stress immediately after release = 202.5 – 2.119 = 200.381 ksi Pi = total prestressing force at release = (12 strands)(0.153 in.2/strand)(200.381 ksi) = 367.9 kips (b) Friction losses: ∆ f pF = f pj (1 − e −( Kx+µ α ) ) ∆ f pF = 202.5 (1 − e −(0.0002×60+0) ) = 2.415 ksi where DfpF = losses due to friction, fpj = stress in the prestressing steel at jacking (ksi), x = length of a prestressing tendon from the jacking end to any point under consideration (ft), K = wobble friction coefficient (per ft of tendon), µ = friction factor, α = sum of the absolute values of angular change of prestressing steel path from jacking end, or from the nearest jacking end if tensioning is done equally at both ends to the point under investigation (rad), and e = base of natural logarithms. (c) Anchorage seating losses: ∆f pA =

∆A E ps L

∆f pA =

0.25 ( 28500 ) = 9.896 ksi 60 × 12

where Dfpa = losses due to anchorage seating, DA = anchor set, L = length of the post-tensioned strand, and Eps = modulus of elasticity of the strand.




(d) Long-term losses: Using Section 5.9.5.3 of the AASHTO LRFD Bridge Design Specifications, the time-dependent losses can be estimated as follows: ∆f pLT = 10.0

f pi Aps γ h γ st + 12.0 γ h γ st + ∆f pR Ag


where fpi = Prestress immediately prior to transfer = 2020.5 ksi, Aps = Area of prestress reinforcement = 12 × 0.153 = 1.836 in.2, Ag = Gross concrete section area = 618 in.2, gh = 1.7 – 0.01(H) = 1.7 – 0.01(70) = 1.0, 5 5 = = 1.0 , gst = (1 + f ci′ ) (1 + 4) DfpR = 2.4 ksi, and ( 202.5 × 1.836 ) ∆f pLT = 10 (1.0 )(1.0 ) + 12(1.0 )(1.0 ) + 2.4 = 20.416 ksi 618 Total prestress losses at service = 2.119 + 2.415 + 9.896 + 20.416 = 34.846 ksi Effective prestress fpe = 202.5 – 34.846 = 167.654 ksi Effective prestress force Ppe = (12 strands)(0.153 in.2/strand)(167.654 ksi) = 307.812 kips DfpR = an estimate of relaxation loss taken as 2.4 ksi for low relaxation strand, and DfpLT = long-term prestress loss. Check of the post-tensioned (PT) effective prestress: Section 9.7.5.3 of the AASHTO LRFD Bridge Design Specifications states that minimum average effective prestress shall not be less than 0.25 ksi. Solid section area = 918 in.2 Minimum required effective PT force = (918 in.2)(0.250 ksi) = 229.5 kips Minimum required PT area = (229.5 kips)/(167.654 ksi) = 1.37 in.2 Number of ½-in.-diameter strands = (1.37 in.2)/(0.153 in.2) = 8.95 strands In this example, 12 – ½-in.-diameter, 270-ksi strands are used that will deliver effective prestress = (250 ksi)(12/8.95) = 335 ksi OK Check of concrete stresses at service at the positive moment area: (a) Compression stress, Service I, top fiber: Compression stress limit due to effective prestress, permanent loads, and transient loads = 0.6 f c′ = ( 0.6 )( 6.0 ) = + 3.6 ksi




M service I = 0.56 + 0.15 + 5.95 = 6.66 k-ft/ft = 59.94 k-ft/9-ft f top = + =+

Ppe ( Ppe e p ) ytop ( M service ) ytop − + Ag I I 307.812 ( 307.812 × 1.125)( 3.125) (59.94 × 12 )( 3.125) − + 618 2782.5 2782.5

= + 0.498 − 0.389 + 0.808 = +0.917 ksi < 3.6 ksi (b) Tensile stress, Service III, bottom fiber: Tensile stress limit = 0.19 f c′ = 0.19 6.0 = −0.465 ksi M service III = 0.56 + 0.15 + 0.8 × 5.95 = 5.47 k-ft/ft = 49.23 k-ft/9-ft fbottom = + =+

Ppe ( Ppe e p ) ybottom ( M service ) ybottom + − Ag I I 307.812 ( 307.812 × 1.125)(5.375) ( 49.23 × 12 )(5.375) + − 618 2782.5 2782.5

= +0.498 + 0.669 − 1.141 = +0.026 ksi < 3.6 ksi Check of concrete stresses at service at the negative moment area: (a) Compression stress, Service I, bottom fiber: Compression stress limit due to effective prestress, permanent loads, and transient loads = 0.6 f c′ = ( 0.6 )( 6.0 ) = + 3.6 ksi M service I = 0.75 + 0.20 + 4.2 = 5.15 k-ft/ft = 46.35 k-ft/9-ft fbottom = +

Ppe ( M service ) ybottom 307.812 ( 46.35 × 12 )( 4.25) + =+ + Ag I 918 5527.1

= + 0.335 + 0.428 = +0.763 ksi < 3.6 ksi (b) Tensile stress, Service III, bottom fiber: Tensile stress limit = 0.19 f c′ = 0.19 6.0 = − 0.465 ksi M service III = 0.75 + 0.20 + 0.8 × 4.2 = 4.31 k-ft/ft = 38.79 k-ft/9-ft fbottom = +

Ppe ( M service ) ybottom 307.812 ( 38.79 × 12 )( 4.25) − =+ − Ag I 918 5527.1

= +0.335 − 0.358 = − 0.023 ksi > − 0.465 ksi Strength Limit State at the positive moment area: Mstrength I = 1.25 × 0.56 + 1.5 × 0.15 + 1.75 × 5.95 = 11.34 k-ft/ft = 102.04 k-ft/9-ft Cross section: Ribbed section (Figure 3.96)




Using Strain Compatibility analysis: Depth of the equivalent compression block = 0.855 in. Depth of the neutral axis = 0.855/0.75 = 1.14 in. Nominal flexural strength Mn = 149.857 k-ft/9-ft Strain at extreme tensile layer of reinforcement = 0.0141 φMn = 1.0 × 149.857 = 149.857 k-ft/6-ft-long panel Strength Limit State at the negative moment area: Mstrength I = 1.25 × 0.75 + 1.5 × 0.20 + 1.75 × 4.2 = 8.59 k-ft/ft = 77.29 k-ft/9-ft Cross section: 8.5-in. solid section Depth of the equivalent compression block = 0.855 in. Depth of the neutral axis = 0.855/0.75 = 1.14 in. Nominal flexural strength Mn = 149.857 k-ft/9-ft Strain at extreme tensile layer of reinforcement = 0.0141 φMn = 1.0 × 149.857= 149.857 k-ft/6-ft-long panel 3.3.1.5 Two-Way Shear (Punching Shear) Two-way shear at the discrete joints: Since the deck slab is supported by a discrete system of haunches, two-way shear of the slab should be checked around the haunches. The check for the two-way shear should follow the provisions given by Article 5.12.8.6.3 of AASHTO LRFD Bridge Design Specifications. The factored two-way shear force caused by the HL93 truck and 100 psf uniform distributed load can be determined using Figure 3.4 and Figure 3.7. Reaction due to HL93 truck (with multiple presence factor and dynamic allowance) = 37.2 kips Reaction due to 100 psf = 6.5 kips As a conservative approach and to simplify the calculations, the following assumptions were made for this section: (1) the slab is an 8.5-in.-thick solid slab, and (2) the haunch is 12 in. × 12 in. Factored two-way shear:  106.3   25  Vu = 1.25( 6.5 ) + 1.5( 6.5 ) + 1.75( 37.2) = 76.2 kips   100   100  The nominal shear resistance Vn: 0.126   Vn =  0.063 +   βc 

f c′ bodv ≤ 0.126 f c′ bodv





βc = 1.0 dv = 6 in. bo = 4(12 + 6) = 72 in. Therefore: Vn = 0.126 f c′ bodv = 0.126 6 ( 72 )( 6 ) = 133.3 kips The design shear resistance: φVn = 0.9(133.3) = 119.9 kips > 76.2 kips OK Two-way shear at wheel loads: Two-way shear of the thin slab (i.e., 5-in. slab) caused by the 16-kip wheel load of the HL93 truck should be checked according to Article 5.12.8.6.3 of the AASHTO LRFD Bridge Design Specifications (2017). The footprint of the wheel load is determined using Article 3.6.1.2.5 “Tire Contact Area” of the AASHTO LRFD Bridge Design Specifications (2015), where the wheel load of the design truck is distributed uniformly on a 20-in. × 10-in. area. Factored load due to HS20, Vu = 1.75 × 1.33 × 16 = 37.24 kips The nominal shear resistance Vn: 0.126   Vn =  0.063 +   βc 

f c′ bodv ≤ 0.126 f c′ bodv


βc = 1.0 dv = 5.0 – 1.5 = 3.5 in. bo = 2(20 + 2) + 2(10 + 2) = 68 in. Therefore: Vn = 0.126 f c′ bodv = 0.126 6 ( 68 )( 3.5 ) = 73.5 kips The design shear resistance: φVn = 0.9(73.5) = 66.15 kips > 37.24 kips OK 3.3.1.6 Bearing Stresses Since the slab is supported by a discrete system of haunches, bearing stresses between the haunch and the supporting girders should be checked. Bearing stresses resistance should be determined according to Article 5.6.5 of AASHTO LRFD Bridge Design Specifications. Bearing stresses caused by the weight of the slab, wearing surface, and HS20 truck = 76.2 kips Pn = 0.85 f c′A1m f c′ = 6 ksi




A1 = 12 × 12 = 144 in.2 m = 1.0(to simplify the calculations) Pn = (0.85)(6)(144)(1.0) = 734 kips φPn = (0.7)(734) = 514.1 kips >> 76.2 kips OK

3.3.2 Longitudinal Design of Deck–Girder System for Concrete Girders 3.3.2.1 Parametric Study In this investigation, several prestressed concrete I-girder bridges were analyzed to determine the interface shear demand per unit length. Table 3.25 summarizes the basic information of these bridges and calculates the maximum interface shear force acting on the shear connectors when used at 6-ft spacing. Nominal shear capacity of the shear connector assembly developed in this project = 295.3 kips, and the design shear capacity = 0.9 × 295.3 = 265.5 kips. Table 3.25 shows that the shear connector assembly can be used at 6-ft spacing for bridge with a span-to-depth ratio up to 27.0. Figure 3.97 gives the interface shear demand per unit length versus the girder span-to-depth ratio. This plot indicates that the girder span-to-depth ratio correlates well with the interface shear demand (R2 = 0.90). 3.3.2.2 Design Example PCI Bridge Design Manual, Chapter 9, Design Example 9.1a: The superstructure consists of six BT-72 beams spaced at 9-ft centers, as shown in Figure 3.94, designed to act compositely with the cast-in-place concrete deck to resist all superimposed dead loads, live loads, and impact. Design live load is HL93. Interface Shear Transfer (LRFD Article 5.7.4) At the Strength Limit State, the horizontal shear at a section on a per unit basis can be taken as:


Vhi = Vu dv

Table 3.25. Interface shear demand in different prestressed concrete I-girder bridges. Bridge Name PCI BDM Example 9.1a Florida Bridge, Florida Oxford South, Nebraska Kearney East, Nebraska Oxford South, Nebraska

SpanGirder toSp. Depth (ft) Ratio

Interface Shear Demand (kips/in.)

Spacing of the Shear Connector Assembly

20.0

2.86

92.8

10

25.0

3.38

78.6

4.42

9

24.9

3.58

74.2

Continuous NU1800

5.92

8.5

28.0

3.70

71.7

Continuous NU1350

4.42

9

31.7

4.67

56.8

Span (ft)

Span Type

Girder Size

Girder Depth (ft)

120

Simple

BT-72

6

9

150

Simple

FL I-72

6

110

Continuous NU1350

166 140

Note: PCI BDM = [Precast/Prestressed Concrete Institute] PCI Bridge Design Manual 2011B.




5.0 4.5 y = 0.15x - 0.18 R² = 0.93

Interface Shear Demand (kip/in.)

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

16

18

20

22

24 26 28 Span-to-Depth Ratio (ft/ft)

30

32

34

Figure 3.97. Interface shear demand versus girder span-to-depth ratio.

where Vhi = horizontal factored shear force per unit length of the beam (kips/in.) Vu = factored shear force at specified section due to superimposed loads after the deck is cast (kips). Shear force due to girder weight and deck weight are excluded. dv = distance between the centroid of the tension steel and the mid-thickness of the slab = (de − ts/2) = 75.78 − 7.5/2 = 72.03 in. The AASHTO LRFD Bridge Design Specifications do not identify the location of the critical section. For convenience, it will be assumed here to be the same location as the critical section for vertical shear, at Point 0.051L. Using load combination Strength I: Vu = 1.25(5.4) + 1.5(10.8) + 1.75(73.8 + 30.6) = 205.7 kips Therefore, the applied factored horizontal shear is Vhi = 205.7 72.03 = 2.86 kips/in. Required Vni = Vhi φ = 2.86 0.9 = 3.17 kips/in.


where Vni is nominal shear resistance. Required nominal shear capacity for 6-ft connector spacing Vni = 3.17 (72) = 228 kips Nominal shear capacity of the CDR shear connector assembly was developed and tested in this project = 310.0 kips OK




3.3.3 Longitudinal Design of Deck–Girder System with Steel Girders 3.3.3.1 Parametric Study The parametric study included a wide range of bridges with the following criteria: Number of spans = 1 and 2 Span length = 100 ft, 125 ft, and 150 ft Girder spacing = 6 ft, 9 ft, and 12 ft Span-to-depth ratio = 21.1 to 27.4 Shear connector groups: Spacing = up to 6 ft Number of studs = nine studs/group Size of studs = 7/8 in., 1 in., and 1¼ in. Minimum spacing between individual studs longitudinally and transversely = 4 times the stud diameter Fatigue capacity: AASHTO LRFD Bridge Design Specifications Strength: 75% of the strength determined by Article 6.10.10.4.3 of the AASHTO LRFD Bridge Design Specifications. Deflection: Use Euler–Bernoulli Beam Analysis with 75% EI of the composite section properties. Concrete deck: 8.5-in.-thick slab, concrete strength = 6 ksi, normal weight concrete Steel beam section: A plate girder I-shape steel section was considered for all cases. The span of each case was made of three segments. Table 3.26 shows the details of all cases and the corresponding spacing between the stud groups and the controlling design criteria: fatigue or strength. This table shows that the spacing between the shear connector clusters—in all cases except Case 18—is controlled by the fatigue design. 3.3.3.2 Design Example The research team selected Case 16 (Table 3.26)—a two-span bridge—to demonstrate the details of the design procedure. Figure 3.98 shows the layout of the three segments of the steel-plate girder. Materials specifications Deck concrete f c′ = 6.0 ksi, modulus of elasticity of the deck Ec = 4,695 ksi Deck reinforcement fy= 60 ksi Structural steel: yield strength Fy = Fyw = Fyt = Fyc = 50 ksi Studs: tensile strength Fu = 72 ksi Modular ratio n = 6.0


Top Flange

Web

Bottom Flange

Top Flange

Web

Bottom Flange

Top Flange

Web

Bottom Flange

Provided Spacing Between Clusters of 7/8-in. studs (in.)

Design Controlled by Fatigue or Strength

Provided Spacing Between Clusters of 1-in. studs (in.)


Provided Spacing Between Clusters of 11/4-in. studs (in.)


52.75

22.7

16x.875

40x0.5

16x0.75

16x.875

40x0.5

16x1.0

16x.875

40x0.5

16x0.75

38

F

50

F

72

F

2

1_100_9_21.9

1

100

9

54.75

21.9

18x1.0

42x0.625

18x0.75

18x1.0

42x0.625

18x1.125

18x1.0

42x0.625

18x0.75

32

F

36

F

58

F

3

1_100_12_21.1

1

100

12

56.75

21.1

20x1.125

44x0.625

20x0.875

20x1.125

44x0.625

20x1.25

20x1.125

44x0.625

20x0.875

28

F

38

F

60

F

4

2_100_6_24.6

2

100

6

48.75

24.6

14x0.875

36x0.5

14x0.75

14x1.25

36x0.5

14x1.25

14x2

36x0.5

14x2.25

34

F

44

F

68

F

5

2_100_9_22.7

2

100

9

52.75

22.7

16x.875

40x0.5

16x0.75

16x1.25

40x0.5

16x1.25

16x2.25

40x0.5

16x2.5

26

F

34

F

54

F

6

2_100_12_21.9

2

100

12

54.75

21.9

18x1.0

42x0.625

18x0.75

18x1.5

42x0.625

18x1.5

18x2.25

42x0.625

18x2.5

20

F

26

F

40

F

7

1_125_6_24.7

1

125

6

60.75

24.7

16x0.875

48x0.5

16x0.75

16x0.875

48x0.5

16x1.25

16x0.875

48x0.5

16x0.75

40

F

54

F

72

F

8

1_125_9_22.5

1

125

9

66.75

22.5

18x1.0

54x0.625

18x0.75

18x1.0

54x0.625

18x1.5

18x1.0

54x0.625

18x0.75

34

F

46

F

72

F

9

1_125_12_21.8

1

125

12

68.75

21.8

20x1.125

56x0.75

20x0.875

20x1.125

56x0.75

20x1.5

20x1.125

56x0.75

20x0.875

28

F

38

F

62

F

10

2_125_6_27.4

2

125

6

54.75

27.4

14x0.875

42x0.5

14x1.0

14x1.25

42x0.5

14x1.5

14x2.5

42x0.5

14x2.75

38

F

50

F

72

F

11

2_125_9_23.2

2

125

9

64.75

23.2

16x0.875

52x0.625

16x.875

16x1.25

52x0.625

16x1.25

16x2.25

52x0.625

16x2.5

28

F

36

F

58

F

12

2_125_12_22.5

2

125

12

66.75

22.5

18x1.0

54x0.625

18x0.875

18x1.5

54x0.625

18x1.625

18x2.5

54x0.625

18x2.75

22

F

30

F

48

F

13

1_150_6_25.4

1

150

6

70.75

25.4

16x1.0

58x0.625

16x1.0

16x1.0

58x0.625

16x1.5

16x1.0

58x0.625

16x1.0

44

F

58

F

72

F

14

1_150_9_24.1

1

150

9

74.75

24.1

18x1.125

62x0.625

18x1.125

18x1.125

62x0.625

18x1.75

18x1.125

62x0.625

18x1.125

36

F

48

F

72

F

15

1_150_12_22.3

1

150

12

80.75

22.3

20x1.125

68x0.75

20x1.0

20x1.125

68x0.75

20x1.875

20x1.125

68x0.75

20x1.0

30

F

38

F

62

F

16

2_150_6_27

2

150

6

66.75

27

16x0.875

54x0.625

16x0.875

16x1.25

54x0.625

16x1.5

16x2.5

54x0.625

16x2.75

38

F

50

F

72

F

17

2_150_9_24.7

2

150

9

72.75

24.7

18x1.0

60x0.625

18x0.875

18x1.75

60x0.625

18x1.875

18x2.625

60x0.625

18x2.875

30

F

40

F

62

F

18

2_150_12_23.5

2

150

12

76.75

23.5

20x1.125

64x0.75

20x0.875

20x1.5

64x0.75

20x1.75

20x2.75

64x0.75

20x3.0

24

S

30

F

48

F

Note: F = fatigue; S = strength.

(ft)

(ft)

(in.)

Span-to-Depth Ratio

6

Total Depth

100

Girder Spacing

1

Span Length

1_100_6_22.7

Title

Number of Spans


1

Case No.

Segment 1 (in.)

Segment 2 (in.)

Segment 3 (in.)


Table 3.26. Results of the parametric study for the precast deck system with steel girders.



Figure 3.98. Layout of the plate girder steel segments.

Bridge criteria Span length: Two equal spans = 150 ft each Number of girder lines = 9 Girder spacing = 6 ft Deck overhang = 2 ft Bridge roadway width: 52 ft, no pedestrian traffic Skew = 0° Slab thickness ts = 8.5 in. Haunch thickness = 3.25 in. from bottom of the deck to the top of the girder web. The haunch thickness is used in the calculation of deck dead load and section properties. Cross-frame spacing = 25 ft Miscellaneous structural steel = 10% of girder weight Superimposed dead load = 215 lb/ft Future wearing surface = 30 psf Composite action is assumed for full length (positive and negative moment regions). Noncomposite section data Positive moment region (abutment segment): Depth of the web D = 54 in. tw = 0.625 in.




Width of the top flange bft = width of the bottom flange bfb = 16 in. Thickness of the bottom flange tfb = 0.875 in. Thickness of the top flange tft = 0.875 in. Negative moment region (intermediate segment): D = 54 in. tw = 0.625 in. bft = bfb = 16 in. tfb = 1.5 in. tft = 1.25 in. Negative moment region (pier segment): D = 54 in. tw = 0.625 in. bft = bfb = 16 in. tfb = 2.75 in. tft = 2.5 in. The point of dead load contraflexure (zero moment) has been determined to be approximately 100 ft. from abutment. Section size changes will occur nearby these points. Girder geometry check btf (positive moment region) = 16 in. > 13.39 in. Thus, the unbraced length of the top flange at the positive moment region is compact at the time when the bridge is open to traffic. LTB of top flange overhang is not critical. t tf ( positive moment region ) = 0.875 in. >

16

12 = 0.874 in. 29000 0.38 50

Thus, the top flange at the positive moment region is compact at the time when the bridge is open to traffic. FLB of top flange overhang is not critical. Geometry of stud clusters Using 6-in. long, 1¼-in. j studs, the ratio of height to diameter is h d = 6 1.25 = 4.8 > 4 OK

( LRFD Article 6.10.10.1.1)




The depth from the top of the top flange to the bottom of the deck does not exceed 2.375 in. Therefore, the stud shear connectors penetrate more than 2 in. into the slab. The flange width is 16 in. Minimum spacing of the studs of four diameters and minimum edge distance of 1 in. allow for placement of three studs per row. Proposed cluster consists of three rows by three columns = nine studs per cluster. Spacing for Fatigue Limit State Assumed average daily truck traffic = 3,000 trucks/day > 960 trucks/day The Fatigue I load combination is used, and the fatigue shear resistance Zr for infinite life is taken as Z r = 5.5 d 2 = 5.5 (1.25)2 = 8.59 kip

( LRFD Article 6.10.10.2-1)

Table 3.27 summarizes the required longitudinal spacing between clusters at tenth points of the first span. The smallest longitudinal spacing between the shear connectors given in the table is 76 in., which is greater than the 72 in. Thus, placing all clusters at a uniform spacing of 6 ft (72 in.) will meet the fatigue capacity requirement over the full length of the bridge. Therefore, use 26 clusters per span at 72-in. spacing. Spacing for Strength Limit State Minimum number of shear connectors n =

P Qr

(LRFD Equation 6.10.10.4.1-2)

1. Required connectors from end support to maximum positive moment (L= 63.21 ft) P = total nominal shear force = the smaller of P1p or P2p


P1p = 0.85 Fc′b s t s = 3121.2 kip

where bs is the effective width of the concrete deck (in.), ts is the thickness of the concrete deck (in.).

Table 3.27. Required longitudinal spacing between clusters of the first span. Location

Shear Range, Vr (kips)

Moment of Inertia, I (in.4)

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00

59 51 45 45 45 47 48 50 51 53 57

76315 76315 76315 76315 76315 76315 76622 100919 100919 146913 146913

Neutral Axis to Bottom Fiber (in.) 49.8 49.8 49.8 49.8 49.8 49.8 50.0 48.1 48.1 45.8 45.8

Moment of Area, Q (in.3)

VrQ/I (kips/in.)

Zr (kips)

Fatigue Spacing (in.)

1327.1 1327.1 1327.1 1327.1 1327.1 1327.1 1308.5 1568.9 1568.9 1913.5 1913.5

1.02 0.89 0.78 0.78 0.78 0.81 0.82 0.77 0.79 0.68 0.74

8.59 8.59 8.59 8.59 8.59 8.59 8.59 8.59 8.59 8.59 8.59

76.0 87.2 98.8 98.8 98.8 95.6 94.4 100.5 97.6 113.1 105.0




P2p = Fyw Dt w + Fyt bft t ft + Fyc b fc t fc = 3087.5 kip

(LRFD Equation 6.10.10.4.2-3)

where Fyw is the yield strength of the web (ksi). P = 3087.5 kips Qr = factored shear resistance of one shear connector Qr = φsc Qn = 0.85 Min.[0.5(π /4)d 2 f c′Ec ,Rg (π /4)d 2 Fu ]

(LRFD Equation 6.10.10.4.3)

where Rg = a group factor = 0.72 (developed in this project based on the experimental investigation).    π 2 0.5  4  (1.25) 14 × 6500 = 185.1 kips   = ( 0.85)( 62.7 ) = 53.3 kips Qr = φsc Qn = (0.85)Min     0.72  π  (1.25)2 (71) = 62.7 kips  4    Number of required studs = 3087.5/53.3 = 57.9 studs (over 63.21 ft) Number of provided clusters at 6 ft = 57.9/6 = 10 clusters Number of provided studs = 10 clusters (nine studs per cluster) = 90 studs

OK

2. Required connectors from maximum positive moment section to the center support (L = 86.79 ft)

( LRFD Equation 6.10.10.4.2-6 )

P= Pp + Pn Pp = smaller of P1p or P2p P1p = 0.85 F′cbsts = 3121.2 kips P2p = FywDtw + Fytbfttft + Fycbfctfc = 3087.5 kips Pp = 3087.5 kips Pn = smaller of P1n or P2n P1n = Fyw Dt w + Fyt bft t ft + Fyc b fc t fc = 5887.5 kip

( LRFD Equation 6.10.10.4.2-7 )

P2n = 0.45 Fc′ bs t s = 1652.4 kip

( LRFD Equation 6.10.10.4.2-8 )

Pn = 1625.4 kips P = 3087.5 + 1625.4 = 4712.9 kips, Qr = 53.3 kips




Number of required studs = 4712.9/53.3 = 88.4 studs (over 86.79 ft) Number of provided clusters over 86.79 ft at 6 ft = 86.79/6 = 14 clusters Number of provided studs = 14 clusters (9 studs per cluster) = 126 studs

OK

Minimum negative moment deck reinforcement This girder was designed as a composite section throughout. To control the deck cracking at the negative moment region, the tensile stresses in the concrete deck caused by applicable load combinations shall be limited to 0.9 fr (where fr is the modulus of rupture of concrete); otherwise, longitudinal reinforcement in accordance with AASHTO LRFD Bridge Design Specifications Article 6.10.1.7 shall be provided. Negative bending moment on composite section MDC2 = 713 kip.ft MDw = 597 kip.ft MLL = 2182 kip.ft Composite section properties Long-term modular ratio, n = 18 Moment of inertia, I = 113,140 in.4 Distance from the centroid to bottom fiber, yb = 37.80 in. Distance from the centroid to top surface of the deck, yd_Top = 56.75 + 3.25 + 8.5 – 37.80 = 30.70 in. Distance from the centroid to bottom surface of the deck, yd_Bottom = 56.75 + 3.25 – 37.80 = 22.20 in. Short-term modular ratio n = 6 I = 146,913 in.4 yb = 45.76 in. yd_Top = 56.75 + 3.25 + 8.5 – 45.76 = 22.74 in. yd_Bottom = 56.75 + 3.25 – 45.76 = 14.24 in. Deck stresses (at Service II Limit State) σ Deck_Top =

( 713 + 597 ) × 12 18 × 113140

× 30.70 + 1.3 ×

( 2182 ) × 12 6 × 146913

× 22.74 = 1.12 ksi




σ Deck_Bottom =

( 713 + 597 ) × 12 18 × 113140

× 22.20 + 1.3 ×

( 2182 ) × 12 6 × 146913

× 14.24 = 0.72 ksi

f r = 0.24 f c′ = 0.59 ksi, σ Deck_Top > 0.9f r where sDeck_Top represents the normal stresses at the top surface of the deck, and s Deck_Bottom represents the normal stresses at the bottom surface of the deck. Thus, the deck is expected to be cracked at service load. Two options may be used: (1) supply adequate crack control and strength passive (rebar) reinforcement, or (2) supply adequate post-tensioning to ensure no flexural cracking at service load. Option 1: Supply adequate crack control and strength passive (rebar) reinforcement. Total tensile force in the deck = 0.5(1.12 + 0.72)(8.5)(6 × 12) = 563.0 kips Section 6.10.1.7 states that the reinforcement used to satisfy this requirement shall have a specified minimum yield strength not less than 60.0 ksi; the size of the reinforcement should not exceed No. 6 bars. The required reinforcement should be placed in two layers distributed uniformly across the deck width, and two-thirds should be placed in the top layer. The individual bars should be spaced at intervals not exceeding 12.0 in. Required area of rebars = 563.0/60 = 9.4 in.2 Area of the top layer = (2/3)(9.4) = 6.3 in.2, provide No. 6 bars at 5 in. Area of the bottom layer = (1/3)(9.4) = 3.1 in.2, provide two No. 6 bars per every longitudinal rib Option 2: Supply adequate post-tensioning to ensure no flexural cracking at service load. Required number of strands: Minimum required compressive stress at mid height of deck = 1.12 – (0.9 × 0.59) = 0.59 ksi Minimum required prestressing force at mid height of deck = 0.59 × 8.5 × (6.0 × 12) = 361.0 kips Effective prestressing in the 0.5-in.-diameter strands = 167.6 ksi (see the deck design in Section 3.3.1 of this report) Minimum required strands per beam spacing = 361.0 / (167.6 × 0.153) = 14 strands

3.4 Design Guidelines This project resulted in development of design and detailing methods for bridges built with either concrete girders or steel girders supporting full-depth precast deck panel systems with shear connection spacing of up to 6 ft. Details of the precast deck panel and the panel-to-panel and panel-to-girder connections are given in Chapter 2.

3.4.1 Precast Deck 1. It is possible to have full-depth deck panels that are 6-ft long (in the direction of traffic) and as wide as allowed for shipping and handling. In this case, the shear connectors will be provided at the transverse edges of the panels.




2. It is possible to have panels that are as long as 12 ft, generally considered the maximum allowed for shipping without a special permit in most of the United States. In this case, an intermediate pocket would be required so that the maximum spacing of 6 ft is not exceeded. 3. Ribbed slab panels have been shown to have adequate resistance while saving weight, which could be advantageous in deck replacement projects that demand increase in live load. Ribbed slab panels are recommended to have longitudinal ribs over the girder lines and transverse ribs along the transverse edges. These ribs would eliminate potential for twisting as the wheel loads travel along the bridge deck. 4. No special design provisions are required for ribbed slabs as given in this project, as the total depth to the steel is maintained as in solid panels. 5. When the slab minimum thickness of 5 in. is used, the capacity of the panels in punching shear is adequate. 6. Only the joints where the interface shear connectors are located are filled with UHPC. The haunch between the girder top face and the deck soffit between the joints may be left unfilled or may be filled as discussed in the following section. 7. For slabs that are supported on discrete joints over the girder lines, a method is presented in the research to allow for more accurate design than currently in the AASHTO LRFD Bridge Design Specifications (Figures 2.2 to 2.7 of this report).

3.4.2 Haunch (Build-Up) Between Girders and Panels 1. Testing was done using a 2.5-in. to 3.5-in. gap (haunch, or build-up) between the top of the girder and the bottom of the deck. In the middle 50% of the span in the actual design, it is recommended that the haunch not exceed 2.5 in. Otherwise, the Vierendeel behavior of the beam–deck connection with tall discrete joints must be properly recognized in structural design. 2. For deflection analysis it is recommended that EI be reduced to 0.75 EI of the full composite section if the shear connection spacing is 6 ft, and the haunches are not filled with concrete. It is further recommended that the reduction factor become 1.0 at a spacing of 4 ft or less. Linear interpolation is to be used between 4 ft and 6 ft. 3. No degree-of-composite-action adjustments for strength analysis are shown by analysis and testing to be required. 4. All analysis and testing were conducted on details that only fill the shear key pocket with concrete grout. In practice, the haunch may be left unfilled, packed with extruded poly styrene, or filled with flowable 4.0-ksi concrete grout. While it helps to improve stiffness, filling the space with concrete was not counted on for interface capacity between the girders and the deck. 5. It is recommended that all shear pockets be filled with UHPC, as defined by FHWA. The transverse joints could also be filled with UHPC if no longitudinal post-tensioning is supplied in the deck. If the deck is longitudinally post-tensioned, the transverse joint material may be compatible with the precast deck concrete rather than the more expensive UHPC. 6. An innovative method is used for post-tensioning whereby all grouting is done in one stage to simplify construction. After the grouting material gains enough strength, the post-tensioning operation commences. This is done using a duct-in-duct system and unbonded, greased, post-tensioning strands. Analysis has shown that the loss of posttensioning—transferred from the deck to the girder because of the full connection before post-tensioning—is insignificant. 7. If post-tensioning is not used, it is recommended to fill the transverse joint with UHPC of enough width to allow splicing and development of projecting bars to achieve




longitudinal deck continuity. The recommended details are given and are consistent with FHWA recommendations.

3.4.3 Concrete Girder-to-Deck Joint 1. Based on numerous trials and iterations, CDR—a new connection hardware—was developed for this research. Note that the CDR is placed in the precast girder during production in the precast plant. The two threaded rods are made extra long to allow for field-cutting to the proper length and for haunch variability. 2. Extensive analysis and testing has been done to establish the minimum ultimate nominal capacity of the connection, using the minimum material properties specified—mainly 8.0-ksi girder and 6.0-ksi deck concrete—and UHPC joint material. 3. It is recommended that 310-kip minimum ultimate nominal capacity be used for the design, with a recommended capacity reduction factor (resistance factor) of 0.9. Therefore, no analysis is required to size the rods, plate, or tube of the connection hardware assembly. Analysis is only done on the demand side.

3.4.4 Steel Girder-to-Deck Joint 1. As a result of this project, the final configuration recommended is a cluster of up to nine studs at 6-ft maximum spacing. 2. Although the testing was performed on 1-in.-diameter studs, ¾-in.-, 7⁄8-in.-, and 1¼-in.diameter studs can be also used as long as no more than nine studs are used without prior experimental assessment of group effect. 3. The fatigue capacity of the studs remains as given in the current AASHTO LRFD Bridge Design Specifications (2017). 4. The nominal strength of the connection is recommended to be limited to 72% of the nominal tensile strength of the studs. Current resistance factors of the AASHTO LRFD Bridge Design Specifications should be used.

3.4.5 Concrete Girder Design 1. For all service loading combinations (excluding deflection), use the full EI value of the composite section. 2. For deflection analysis, it is recommended that EI be reduced to 0.75 EI of the full composite section if the shear connection spacing is 6 ft and the haunches are not filled with concrete. It is further recommended that the reduction factor become 1.0 at a spacing of 4 ft or less. Linear interpolation is to be used between 4 ft and 6 ft. 3. For flexural strength, no changes are proposed. 4. For shear strength, no change is proposed as long as the spacing between connections is less than the total girder depth. In the event that the spacing is greater than the girder depth, it is conceivable that the diagonal shear failure plane may develop from the bottom to the top of the girder without engaging the connection. In this situation, it is recommended that the total depth of the section be taken as the girder depth—excluding the deck and haunch. 5. For horizontal shear demand, it is recommended to use only the forces that are applied after the member becomes composite in calculating the demand.

3.4.6 Steel Girder Design 1. When discrete joints are used, the top flange shall be considered as discretely braced for all superimposed loads after the deck is sufficiently connected. The unbraced length of the top




flange is the lesser of the cluster spacing or the cross-frame spacing. No changes are proposed for FLB or LTB provisions. 2. For constructability, no changes are proposed. 3. For stress checks, no changes are proposed. 4. For deflection analysis, it is recommended that EI be reduced to 0.75 EI of the full composite section if the shear connection spacing is 6 ft and the haunches are not filled with concrete. It is further recommended that the reduction factor become 1.0 at a spacing of 4 ft or less. Linear interpolation is to be used between 4 ft and 6 ft. 5. For Fatigue and Fracture Limit State, no changes are proposed. 6. For Strength Limit State, no changes are proposed. 7. It is recommended to limit the nominal strength of the connection to 72% of the nominal tensile strength of the studs. Current resistance factors of the AASHTO LRFD Bridge Design Specifications should be used. 8. If the girder is designed as a composite section throughout the whole length, AASHTO LRFD Bridge Design Specifications Provision 6.10.1.7 shall be applied. Longitudinal reinforcement meeting that provision should be spliced sufficiently to perform the required continuity and development. The splice connection details and materials were proposed previously in this project. Alternatively, longitudinal post-tensioning should be used to limit these tensile stresses and to control deck cracks.

3.5 Proposed Changes to AASHTO LRFD Bridge Design Specifications This section presents the proposed changes to the AASHTO LRFD Bridge Design Specifications, 8th edition (2017). Proposed changes are underlined. The following list of proposed revisions to the AASHTO LRFD Bridge Design Specifications is currently in the process of being developed in a working agenda item format for easier presentation to the relevant Committees of the AASHTO Committee on Bridges and Structures.

3.5.1 Item 1: Create a New Section 2.5.2.6.4 This item is related to reduction of stiffness for deflection calculations when discrete joints are used. 2.5.2.6.4—Precast Deck Panels Supported by Discrete Joints at a 48- to 72-in.-Wide Spacing

C2.5.2.6.4

For deflection analysis of precast deck panel systems supported by a discrete joint system, the stiffness of the full composite section EI shall be reduced to 0.75 EI if the shear connection spacing is 6 ft. The 0.75 reduction factor shall become 1.0 at a spacing of 4 ft or smaller. Linear interpolation shall be used between 4 and 6 ft.

Research by Badie et al. (2018) has indicated that when the space between shear connectors is increased from 48 to 72 in. and the haunch between the top face of the beam and soffit of the deck is not filled with a cementitious material, it is possible to have a loss of overall stiffness. This loss may be conservatively assumed to equal 25% for live load deflection calculation. This requirement seldom controls design for beams of typical span/depth ratios.

3.5.2 Item 2: Add New Reference to Section 2.8 Badie, S. S., G. Morcous, and M. K. Tadros. NCHRP Research Report 895: Simplified Full-Depth Precast Concrete Deck Panel Systems. Transportation Research Board, Washington, D.C., 2018.




3.5.3 Item 3: Modify Section 5.7.4 This item is related to changing the maximum spacing of shear connectors for concrete girders.

5.7.4—Interface Shear Transfer—Shear Friction C5.7.4.1

5.7.4.1—General Interface shear transfer shall be considered across a given plane at: •

An existing or potential crack,

•

An interface between dissimilar materials,

•

An interface between two concretes cast at different times, or

•

The interface between different elements of the cross section.

Where the required interface shear reinforcement in girder–slab design exceeds the area required to satisfy flexural shear requirements, additional reinforcement shall be provided to satisfy the interface shear requirements. The additional interface shear reinforcement need only extend into the girder a sufficient depth to develop the design yield stress of the reinforcement, rather than extending the full depth of the girder as is required for vertical shear reinforcement.

Shear displacement along an interface plane may be resisted by cohesion, aggregate interlock, and shear friction developed by the force in the reinforcement crossing the plane of the interface. Roughness of the shear plane causes interface separation in a direction perpendicular to the interface plane. This separation induces tension in the reinforcement balanced by compressive stresses on the interface surfaces. Any reinforcement crossing the interface is subject to the same strain as the designed interface reinforcement. Insufficient anchorage of any reinforcement crossing the interface could result in localized fracture of the surrounding concrete.

Reinforcement for interface shear may consist of single bars, multiple leg stirrups, or welded wire reinforcement. All reinforcement present where interface shear transfer is to be considered shall be fully developed on both sides of the interface by embedment, hooks, mechanical methods such as headed studs, or welding to develop the design yield stress.

5.7.4.3—Interface Shear Resistance

C5.7.4.3

Except for specialized connection systems, shear friction theory as given below may be used to determine the reinforcing bars required to connect the two interface concretes. The factored interface shear resistance Vri shall be taken as Vri = φVni

(5.7.4.3-1)

and the design shall satisfy Vri ≥ Vui

For specialized connection systems—such as that developed by Badie et al. (2018) and shown in Figure C5.7.4.3-1—the ultimate shear strength of 310 kips of the connection is already determined in the research and can be directly used in design, as long as the minimum material capacities of the connection as specified in the research are used. For concrete and steel strengths below those specified for the connection in Figure 1, FEA and modified shear friction theory may be used, supplemented with full-scale testing.

(5.7.4.3-2)




where Vni =

nominal interface shear resistance (kip)

Vui =

factored interface shear force due to total load, based on the applicable strength and extreme event load combinations in Table 3.4.1-1 (kip)

φ

resistance factor for shear specified in Article 5.5.4.2. For the extreme limit state event, φ may be taken as 1.0.

=

Figure C5.7.4.3-1 Special connection system developed by Badie et al. (2018) Total load shall include all noncomposite and composite loads appropriate to the interface being investigated. 5.7.4.5—Computation of the Factored Interface Shear Force for Girder–Slab Bridges Based on consideration of a free body diagram and utilizing the conservative envelope value of Vu1, the factored interface shear stress for a concrete girder–slab bridge may be determined as

vui =

Vu1 bvi d v

(5.7.4.5-1)

where dv

=

distance between the centroid of the tension steel and the mid-thickness of the slab to compute a factored interface shear stress

The factored interface shear force in kips/ft for a concrete girder–slab bridge may be determined as

Vui = vui Acv = vui 12bvi

(5.7.4.5-2)

If the net force Pc across the interface shear plane is tensile, additional reinforcement Avpc shall be provided as

Avpc =

Pc φf y

(5.7.4.5-3)

C5.7.4.5 The following illustrates a free body diagram approach to computation of interface shear in a girder– slab bridge. In reinforced concrete, or prestressed concrete, girder bridges, with a cast-in-place slab, horizontal shear forces develop along the interface between the girders and the slab. The classical strength of materials approach, which is based on elastic behavior of the section, has been used successfully in the past to determine the design interface shear force. As an alternative to the classical elastic strength of materials approach, a reasonable approximation of the factored interface shear force at the strength or extreme event limit state for either elastic or inelastic behavior and cracked or uncracked sections can be derived with the defined notation and the free body diagram shown in Figure C5.7.4.5-1 as follows: Mu2 =

maximum factored moment at Section 2 (kip-in.)

V1 =

factored vertical shear at Section 1 concurrent with Mu2 (kip)

M1 =

factored moment at Section 1 concurrent with Mu2 (kip-in.)

∆ℓ =

unit length segment of girder (in.)

C1 =

compression force above the shear plane associated with M1 (kip)

Cu2 =

compression force above the shear plane associated with Mu2 (kip)

Mu2 = M1 + V1 ∆

Cu 2 = Cu 2 = C1 =

Mu2

(C5.7.4.5-2)

dv M1 dv

+

(C5.7.4.5-1)

V1 ∆ dv

M1 dv


(C5.7.4.5-3)

(C5.7.4.5-4)



Figure C5.7.4.5-1—Free Body Diagrams

Vh = Cu2 – C1

Vh =

V1 dv

(C5.7.4.5-5) (C5.7.4.5-6)

Such that for a unit length segment:

Vhi =

V1 dv

(C5.7.4.5-7)

where Vhi =

factored interface shear force per unit length (kips/length)

The variation of V1 over the length of any girder segment reflects the shear flow embodied in the classical strength of materials approach. For simplicity of design, V1 can be conservatively taken as Vu1 (since Vu1, the maximum factored vertical shear at Section 1, is not likely to act concurrently with the factored moment at Section 2); and further, the depth, dv, can be taken as the distance between the centroid of the tension steel and the midthickness of the slab to compute a factored interface shear stress. For design purposes, the computed factored interface shear stress of Equation 5.7.4.5-1 is converted to a resultant interface shear force computed with Equation 5.7.4.5-2 acting over an area, Acv, within which the computed area of reinforcement, Avf, shall be located. The resulting area of reinforcement, Avf, then defines the area of interface reinforcement required per foot of girder for direct comparison with vertical shear reinforcement requirements. For beams or girders, the longitudinal center-tocenter spacing of nonwelded interface shear connectors shall not exceed 72.0 in. For cast-in-place box girders, the longitudinal center-to-center spacing of nonwelded interface shear connectors shall not exceed 24.0 in.

Recent research (Markowski et al. 2005, Tadros and Girgis 2006, Badie and Tadros 2008, Sullivan et al. 2011) has demonstrated that increasing interface shear connector spacing from 24.0 to 48.0 in. has resulted in no deficiency in composite action for the same resistance of shear connectors per foot and for girder and deck configurations. These research projects have independently demonstrated no vertical separation between the girder top and the deck under cyclic or ultimate loads. However, the research did not investigate relatively shallow members; hence, the additional limitation related to the member depth is provided. Research by Badie et al. (2018) has demonstrated that spacing between shear connectors can be extended to 72 in. If the connector spacing is greater than the girder depth, then it is recommended that vertical shear reinforcement be determined, based on girder depth rather than composite member depth. As the spacing of connector groups increases, the capacities of the concrete and grout in their vicinity become more critical and need to be carefully verified. This applies to all connected elements at the interface. Equations 5.7.4.3-2 and 5.7.4.3-3 are intended to ensure that the capacity of the concrete component of the interface is adequate. Methods to enhance that capacity, if needed, include use of high-strength materials and of localized confinement reinforcement.




3.5.4 Item 4: Add a New Reference to Section 5.15 Badie, S. S., G. Morcous, and M. K. Tadros. NCHRP Research Report 895: Simplified Full-Depth Precast Concrete Deck Panel Systems. Transportation Research Board, Washington, D.C., 2018.

3.5.5 Item 5: Modify Section 6.10.10.1.2 This item is related to changing the maximum spacing of shear connectors for steel girders. C6.10.10.1.2

6.10.10.1.2—Pitch The pitch of the shear connectors shall be determined to satisfy the fatigue limit state, as specified in Article 6.10.10.2 and 6.10.10.3. The resulting number of shear connectors shall not be less than the number required to satisfy the strength limit state as specified in Article 6.10.10.4. The pitch, p, of shear connectors shall satisfy

p≤

nZ r Vsr

(6.10.10.1.2-1)

in which Vsr =

=

horizontal fatigue shear range per unit length (kip/in.)

V fat

Vfat =

2

+ Ffat

2

(6.10.10.1.2-2)

longitudinal fatigue shear range per unit length (kip/in.)

=

Vf Q

Ffat =

Ffat1 =

I

(6.10.10.1.2-3)

radial fatigue shear range per unit length (kip/in.) taken as the larger of either:

Abot σ flg wR

(6.10.10.1.2-4)

or

Ffat 2 =

Frc w

(6.10.10.1.2-5)

At the fatigue limit state, shear connectors are designed for the range of live load shear between the deck and top flange of the girder. In straight girders, the shear range normally is due to only major-axis bending if torsion is ignored. Curvature, skew, and other conditions may cause torsion, which introduces a radial component of the horizontal shear. These provisions provide for consideration of both of the components of the shear to be added vectorially, according to Equation 6.10.10.1.2-2. The parameters I and Q should be determined using the deck within the effective flange width. However, in negative flexure regions of straight girders only, the parameters I and Q may be determined using the longitudinal reinforcement within the effective flange width for negative moment, unless the concrete deck is considered to be effective in tension for negative moment in computing the range of the longitudinal stress, as permitted in Article 6.6.1.2.1. The maximum longitudinal fatigue shear range, Vfat, is produced by placing the fatigue live load immediately to the left and to the right of the point under consideration. For the load in these positions, positive moments are produced over significant portions of the girder length. Thus, the use of the full composite section, including the concrete deck, is reasonable for determining the stiffness used to determine the shear range along the entire span. Also, the horizontal shear force in the deck is most often considered to be effective along the entire span in the analysis. To satisfy this assumption, the shear force in the deck should be developed along the entire span. For straight girders, an option is permitted to ignore the concrete deck in computing the shear range in regions of negative flexure, unless the concrete is considered to be effective in tension in computing the range of the longitudinal stress, in which case the shear force in the deck must be developed. If the concrete is ignored in these regions, the maximum pitch specified at the end of this Article must not be exceeded. The radial shear range, Ffat, typically is determined for the fatigue live load positioned to produce the largest positive and negative major-axis bending moments in the span. Therefore, vectorial addition of the longitudinal and radial components of the shear range is conservative because the longitudinal and radial shears are not produced by concurrent loads.




where σflg =

range of longitudinal fatigue stress in the bottom flange without consideration of flange lateral bending (ksi)

Abot =

area of the bottom flange (in. 2)

Frc =

net range of cross frame or diaphragm force at the top flange (kip)

=

moment of inertia of the short-term composite section (in.4)

=

distance between brace points (ft)

n

=

number of shear connectors in a cross section

p

=

pitch of shear connectors along the longitudinal axis (in.)

Q

=

first moment of the transformed short-term area of the concrete deck about the neutral axis of the short-term composite section (in.3)

I

R

=

minimum girder radius within the panel (ft)

Vf

=

vertical shear force range under the applicable fatigue load combination specified in Table 3.4.1-1 with the fatigue live load taken as specified in Article 3.6.1.4 (kip)

w

=

effective length of deck (in.) taken as 48.0 in., except at end supports where w may be taken as 24.0 in.

Zr =

shear fatigue resistance of an individual shear connector determined as specified in Article 6.10.10.2 (kip)

For straight spans or segments, the radial fatigue shear range from Equation 6.10.10.1.2-4 may be taken equal to zero. For straight or horizontally curved bridges with skews not exceeding 20 degrees, the radial fatigue shear range from Equation 6.10.10.1.2-5 may be taken equal to zero.

The center-to-center pitch of shear connectors shall not exceed 72 in. for members having a web depth greater than or equal to 24.0 in. For members with a web depth less than 24.0 in., the center-to-center pitch of shear connectors shall not exceed 24.0 in. The center-tocenter pitch of shear connectors also shall not be less than six stud diameters.

Equation 6.10.10.1.2-4 may be used to determine the radial fatigue shear range resulting from the effect of any curvature between brace points. The shear range is taken as the radial component of the maximum longitudinal range of force in the bottom flange between brace points, which is used as a measure of the majoraxis bending moment. The radial shear range is distributed over an effective length of girder flange, w. At end supports, w is halved. Equation 6.10.10.1.2-4 gives the same units as Vfat. Equation 6.10.10.1.2-5 will typically govern the radial fatigue shear range where torsion is caused by effects other than curvature, such as skew. Equation 6.10.10.1.2-5 is most likely to control when discontinuous cross frame or diaphragm lines are used in conjunction with skew angles exceeding 20 degrees in either a straight or horizontally curved bridge. For all other cases, Frc can be taken equal to zero. Equations 6.10.10.1.2-4 and 6.10.10.1.2-5 yield approximately the same value if the span or segment is curved and there are no other sources of torsion in the region under consideration. Note that Frc represents the resultant range of horizontal force from all cross frames or diaphragms at the point under consideration due to the factored fatigue load plus impact that is resisted by the shear connectors. In lieu of a refined analysis, Frc may be taken as 25.0 kips for an exterior girder, which is typically the critical girder. Frc should not be multiplied by the factor 0.75 discussed in Article C6.6.1.2.1. Equations 6.10.10.1.2-4 and 6.10.10.1.2-5 are presented to ensure that a load path is provided through the shear connectors to satisfy equilibrium at a transverse section through the girders, deck, and cross frame or diaphragm. The basis for the previous 24.0 in. maximum center-to-center spacing for all web depths was based on scaled experiments in the 1940s that recommended a maximum pitch of three-to-four slab thicknesses, as described further in Yura et al. (2008). More recent test results (Badie and Tadros 2008, Provines and Ocel 2014A and 2014B) have shown that placing shear connectors at a pitch of up to 48.0 in. has no negative effect on the global flexural resistance of composite steel members. The research did not test very shallow web depths with long pitches, and limiting the pitch to 24.0 in. for a web depth less than 24.0 in. was to ensure that designs stay within the bounds that have proven satisfactory in experiments. Recent research by Badie et al. (2018) has demonstrated that clusters of nine studs each may be used to effectively increase the spacing between clusters up to 72 in. The minimum compressive strength of the grout recommended for this spacing of 72 in. is 14 ksi. The minimum flexural strength, with utilization of steel fibers, is 1.5 ksi. There are prebagged UHPC materials on the market to satisfy this requirement.




3.5.6 Item 6: Modify Section 6.10.10.4.3 This item is related to changing the nominal shear resistance of steel studs. 6.10.10.4.3—Nominal Shear Resistance The nominal shear resistance of one stud shear connector embedded in a concrete deck shall be taken as Qn = 0.5 Asc

fc Ec ≤ Rg Asc Fu

(6.10.10.4.3-1)

where Asc =

cross-sectional area of a stud shear connector (in.2 )

Ec =

modulus of elasticity of the deck concrete determined as specified in Article 5.4.2.4 (ksi)

Fu =

specified minimum tensile strength of a stud shear connector determined as specified in Article 6.4.4 (ksi)

Rg =

Group reduction factor

=

0.72 for clusters of nine studs, where the spacing between clusters is 72 in.

C6.10.10.4.3 Studies have defined stud shear connector strength as a function of both the concrete modulus of elasticity and concrete strength (Ollgaard et al. 1971). Note that an upper bound on stud shear strength is the product of the cross-sectional area of the stud times its ultimate tensile strength. Equation 6.10.10.4.3-2 is a modified form of the formula for the resistance of channel shear connectors developed in Slutter and Driscoll (1965) that extended its use to lightweight—as well as normalweight—concrete. Studies by Badie et al. (2018) have demonstrated that the resistance when a group of studs is used in a cluster may be less than distributed studs by as much as 28%. If more than nine studs are required to be used, additional experimental research should be conducted. The minimum compressive strength of the grout recommended for this spacing of 72 in. is 14 ksi. The minimum flexural strength, with utilization of steel fibers, is 1.5 ksi. There are prebagged UHPC materials on the market to satisfy this requirement.


3.5.8 Item 8: Add New Paragraphs to Section 9.7.5.3 This item is related to filling the shear pockets and the transverse joints in a single operation. 9.7.5.3—Longitudinally Post-Tensioned Precast Decks

C9.7.5.3 Construction can be significantly accelerated when all grouting of pockets and of transverse joints in precast deck panels is done in a single operation. This would make the deck and the beam share in the posttensioning force applied after grouting. Such construction shall be used for simple span bridges. However, for continuous spans, secondary effects of post-tensioning may not allow for the deck to be composite with the beam without significant loss of the deck prestress to the beam. Analysis in Badie et al. (2018) has indicated that the average loss of prestress (from the deck to the beam) is in the range of 2% to 20% for simple span bridges. However, this significant construction acceleration may not be feasible for continuous spans, as the post-tensioning secondary moments may be large enough to offset or even reverse the effect of the primary moments. It is possible, however, to have creative design solutions that would allow for posttensioning after full grouting for continuous spans. However, the solutions are not direct solutions and cannot be generalized at this time for all practical cases.





3.6 Economical Impact of Proposed Guidelines and Specifications 1. Using ribbed slab deck panels reduces the weight of the deck by about 10% to 20%, compared to constant-thickness slabs. This helps when a deck replacement project requires that live load capacity be increased. This solution would be less time-consuming and less expensive than girder strengthening. 2. Using the proposed optimized transverse joint details and the discrete interface shear joint system reduces the amount of grouting materials and labor costs, as well as the associated labor. 3. If the option of eliminating grouting of the haunch is exercised, the high volume of haunch grouting materials and the associated labor are eliminated. Further, the complication of blind grouting and the difficulty of pre-wetting the top face of the concrete girder are avoided. 4. Increasing the shear connector spacing up to 6 ft eliminates the need for creating shear pockets in 6-ft-long precast panels and requires only one pocket per girder line for 12-ft-long panels. Blind intermediate pockets in current systems and the difficulties in fitting up the hardware projecting from the girders with the pockets in the panels have been a constant challenge for precasters and contractors and have caused increased cost to match the risk of relatively low tolerances. 5. Although the UHPC proposed for the shear pockets is more expensive than conventional concrete and some other grouting materials, it has far superior strength and toughness. In addition, it enhances durability of the system. The proposed details attempt to minimize the UHPC volume and the associated costs. 6. When longitudinal post-tensioning is desired to keep the deck from experiencing transverse cracks, several simplifying measures are proposed in this project. A novel duct-in-duct, unbonded, post-tensioning system is proposed. Thus, the difficult and time-consuming field grouting of the post-tensioned ducts is eliminated. Single-stage grouting of all field-grouting joints saves considerable construction time. When post-tensioning is applied after all joint grouting is completed, the beam shares a part of the prestress. The prestress loss to the beam has been found to be small for simple span bridges. Single-stage grouting, with later post-tensioning of the composite deck beam, is recommended. For continuous spans, single-stage post-tensioning is possible. However, it must be carefully studied on a projectby-project basis, and the post-tensioning profile must be adjusted to account for secondary post-tensioning.



CHAPTER 4

Conclusions and Recommendations for Future Research 4.1 Conclusions A full-depth precast concrete deck panel system was developed. The system includes an innovative girder–deck connection spaced up to 6 ft, compared to the current limit of 4 ft. It also includes other innovative features, such as the use of UHPC for the joint between the girder and the deck. UHPC is used for the transverse joint between panels if no longitudinal post-tensioning is provided. If post-tensioning is provided, a simplified duct-in-duct posttensioning is proposed to eliminate the difficult field-splicing of the ducts. The shear pockets exist only in the transverse joints between the panels if the panels are made 6-ft long. If the panels are 12-ft long, only one intermediate pocket would be required at each girder line. The deck slab can be solid, or it can be ribbed to reduce its weight and, thus, increase allowance for additional loads in situations where such an upgrade is desirable. The interface shear joints (i.e., pockets) are filled with UHPC grout, while the haunches between the shear joints in the space between the beam top face and the deck soffit may be left ungrouted. This is called a “discrete joint” system, which would reduce the labor and materials needed to fill the haunch. Also, blind grouting of the haunch—and associated questionable quality—would be eliminated. All analysis and testing are performed on the option with discrete joints. Owners who choose to grout the haunches would thus have a more conservative system, as filled haunches increase the system’s stiffness. Because the haunches are not counted on for structural loading, a secondary but important conclusion is to convince designers that a simple, relatively low-strength, flowable fill would be adequate for the haunches. UHPC was selected as the recommended material for filling the shear connection joints and the transverse joints if no post-tensioning is used. The size of the shear pockets, as well as the shear key at the transverse joints between panels, were optimized to minimize the volume of the UHPC used to fill these spaces. The analytical investigation conducted in the project has demonstrated the viability of increasing the shear connection spacing up to 6 ft without significant change in behavior. For two-way decks that are only supported at discrete joints along the girder lines, design aids are developed in this report to facilitate design of the reinforcement—especially in the longitudinal direction. In addition, the analytical investigation has shown that behavior of the beam in the longitudinal direction can be reasonably predicted using the conventional Euler–Bernoulli Beam Theory. Three-dimensional nonlinear finite element analysis has proved to be a valuable tool for investigating the stress concentration around the shear connectors. In addition, it provides insights into how forces are distributed among the shear connectors in the joint. In this project, the finite element analysis indicates that the quality of the grouting material of the shear 142 Copyright National Academy of Sciences. All rights reserved.


Conclusions and Recommendations for Future Research 143

connection joints is the most critical factor in ensuring adequate structural capacity. Therefore, the research team concluded that UHPC is the best available joint material. The experimental investigation conducted with concrete girders in the project has shown that full composite action is expected in flexure design at all Service and Strength Limit States. In addition, full composite action is expected in vertical shear design even when the spacing between the shear connectors exceeds the girder depth. The horizontal shear nominal capacity of the proposed novel connection for concrete girder to concrete deck, shown in Figure 4.1, at a spacing up to 6 ft is 310 kip. This capacity is higher than the demand for most prestressed concrete girder bridges, as shown in the design examples. This capacity is proposed for the unique connection being proposed in this research, as demonstrated in the examples. The experimental investigation conducted with steel girders in the project has shown that fatigue load has no detrimental effect on the composite action of the slab–beam system made with joints spaced at 6 ft. Therefore, no changes are proposed for the fatigue design of the shear connectors given in Article 6.10.10.2 of the AASHTO LRFD Bridge Design Specifications. Full composite action is expected at all Service and Strength Limit States. No reduction of the full composite beam stiffness is warranted, except for deflection calculation where a 75% reduction factor should be applied to the full composite beam stiffness. The strength tests on the push-off specimens and large-scale beam have shown that a 0.72 group reduction factor is proposed to be applied to the stud strength (i.e., Equation 6.10.10.4.3-1 of the AASHTO LRFD Bridge Design Specifications). This group reduction factor is considered conservative because failure in these tests was observed in the deck panels, rather than in the UHPC joints. Future testing may provide a more accurate estimate of this factor. The research team has determined that construction can be significantly accelerated when all grouting of pockets, as well as transverse joints, is done in a single operation. This would imply that both the deck and the beam share in the post-tensioning force applied after grouting.

Figure 4.1. Novel connection for concrete girder to concrete deck.




Analysis has indicated that the average loss of prestress (from the deck to the beam) is in the range of 2% to 20% for simple span bridges. However, this significant improvement was not found to be true for continuous spans, as the post-tensioning secondary moments may be large—or even larger—than the primary moments. It is possible to have solutions that allow post-tensioning after grouting, even for continuous spans. However, the solutions are not direct and cannot be generalized at this time for all practical cases. Guidelines are provided to help engineers in implementing this system for highway bridges. A draft of proposed revisions to the AASHTO LRFD Bridge Design Specifications provisions is also presented.

4.2 Recommendations for Future Research The recommendation of introducing a 0.72 group reduction factor to Equation 6.10.10.4.3-1 of the AASHTO LRFD Bridge Design Specifications is conservative and can be used in practice at this time until further research justifies raising this factor. The 0.72 proposed factor was influenced by the relatively low capacity observed in the push-off specimens. However, it is well known that push-off specimens almost always yield low capacity, compared to full beams. It is recommended that this factor be reevaluated using large-scale composite beam specimens. The research team recommends that a parametric study be performed to find practical solutions for application of post-tensioning in continuous span bridges. Such study could propose a new way of determining tendon profiles that pass through the beams, instead of the conventional method of placing the post-tensioned tendons at mid thickness of the deck. These design complications may be justified by the significant shortening of construction time when one stage of grouting in the field is eliminated.



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Oesterle, R. G., A. F., Elremaily, Z. J., Ma, R. Eriksson, and C. Prussack. NCHRP Project 12-69 “Design and Construction Guidelines for Long-Span Decked Precast, Prestressed Concrete Girder Bridges.” Contractor’s Final Report. Transportation Research Board, Washington, D.C., 2009. http://onlinepubs.trb.org/onlinepubs/ nchrp/docs/NCHRP12-69_FR.pdf. Oliva, M., and P. Okumus. Composite Girder Connections for Precast Concrete Decks. Aspire Magazine, Summer 2013, pp. 44–45. Ollgaard, J. G., R. G. Slutter, and J. W. Fisher. Shear Strength of Stud Connectors in Lightweight and Normal Weight Concrete. Engineering Journal, Vol. 8, No. 2, 1971, p. 55. Popovics, S. Strength and Related Properties of Concrete: A Quantitative Approach. John Wiley & Sons, Inc., New York, 1998. Precast/Prestressed Concrete Institute. State-of-the-Art Report on Full-Depth Precast Concrete Bridge Deck Panels. Chicago, Ill., 2011A. Precast/Prestressed Concrete Institute. PCI Bridge Design Manual. 3rd ed., Chicago, Ill., 2011B. Precast/Prestressed Concrete Institute. Full Depth Deck Panels Guidelines for Accelerated Bridge Deck Replacement or Construction. 2nd edition, Chicago, Ill., 2011C. Provines, J., and J. Ocel. Strength and Fatigue Resistance of Clustered Shear Studs. In Proceedings of the World Steel Bridge Symposium, Toronto, Ontario, Canada, 2014A. Provines, J., and J. Ocel. Strength and Fatigue Resistance of Shear Stud Connectors. In Proceedings of the National Accelerated Bridge Construction Conference, Miami, Fla., 2014B. Ralls, M. L., B. Tang, S. Bhidé, B. Brecto, E. Calvert, H. Capers, D. Dorgan, E. Matsumoto, C. Napier, W. Nickas, and H. Russell. Prefabricated Bridge Elements and Systems in Japan and Europe. Report FHWA-PL-05-003. FHWA, U.S. Department of Transportation, 2005. Scholz, D. P., J. A. Wallenfelsz, C. Lijeron, and C. L. Roberts-Wollmann. Recommendations for the Connection Between Full-Depth Precast Bridge Deck Panel Systems and Precast I-Beams. Report FHWA/VTRC 07-CR17. Virginia Transportation Research Council and FHWA, U.S. Department of Transportation, 2007. Slutter, R. G., and G. C. Driscoll, Jr. Flexural Strength of Steel–Concrete Composite Beams. Journal of the Structural Division, Vol. 91, No. ST2, 1965, pp. 71–99. Special Report 249: Building Momentum for Change: Creating a Strategic Forum for Innovation in Highway Infrastructure. Transportation Research Board, Washington, D.C., 1996. http://www.trb.org/Publications/ Blurbs/153303.aspx. Stephen, E. Simulation of the Long-Term Behavior of Precast/Prestressed Concrete Bridges. MA thesis. University of Cincinnati, Ohio, 2006. Sullivan, S. R., C. L. R. Wollmann, and M. K. Swenty. Composite Behavior of Precast Concrete Bridge Deck–Panel Systems. PCI Journal, Vol. 56, No. 3, 2011, pp. 43–59. Sun, C. S., M. K. Tadros, K. C. Kopper, and T. N. Belill. Innovative Precast Concrete Adjacent-Box-Beam System Implemented in the St. Clair Road Bridge in Michigan. PCI Journal, Vol. 63, No. 3, 2018, pp. 41–50. Tadros, M. K., and M. C. Baishya. NCHRP Report 407: Rapid Replacement of Bridge Decks. TRB, National Research Council, Washington, D.C., 1998. Tadros, M. K., S. S. Badie, and M. R. Kamel. Girder/Deck Connection for Rapid Removal of Bridge Decks. PCI Journal, Vol. 47, No. 3, 2002, pp. 2–12. Tadros, M. K., and A. F. Girgis. Concrete Filled Steel Tube Arch. Nebraska Department of Roads, 2006. Timoshenko, S. Theory of Elastic Stability. McGraw–Hill Book Company, Inc., New York, 1936. Wells, Z. G., P. J. Barr, and P. H. James. Performance of Post-Tensioned Curved-Strand Connections in Transverse Joints of Precast Deck Panels. Journal of Bridge Engineering, Vol. 18, No. 10, 2013, pp. 1062–1073. Wipf, T., S. Sritharan, A. Abu-Hawash, B. Phares, and D. Bierwagen. Iowa’s Ultra-High Performance Concrete Implementation: Bridging Gaps in Structural Materials and Design. Research News, April 2011, pp. 1–12. Yamane, T., M. K. Tadros, S. S. Badie, and M. C. Baishya. Full-Depth Precast Prestressed Concrete Bridge Deck System. PCI Journal, Vol. 43, No. 3, 1998, pp. 50–66. Yura, J., T. Helwig, R. Herman, and C. Zhou. Global Lateral Buckling of I-Shaped Girder Systems. Journal of Structural Engineering, Vol. 134, No. 9, 2008, pp. 1487–1494. Zaki, A. R., and A. F. Girgis. Princess Margaret Bridge Rehabilitation. In Proceedings of the 6th International IABMAS Conference: Bridge Maintenance, Safety, Management, Resilience, and Sustainability (F. Biondini, and D. M. Frangopol, eds.). CRC Press, London, 2012. Zienkiewicz, O. C., R. L. Taylor, and J. Z. Zhu. The Finite Element Method: Its Basis and Fundamentals, 6th edition. Butterworth–Heinemann, UK, 2005. Zokaie, T., T. A. Osterkamp, and R. A. Imbsen. NCHRP Project 12-26 “Distribution of Wheel Loads on Highway Bridges.” NCHRP Research Results Digest, No. 187, Transportation Research Board, National Research Council, Washington, D.C., 1991.



Appendices A–C

Appendices A through C are not printed herein but are available for download from the TRB website (trb.org) by searching for “NCHRP Research Report 895.” The appendices include the following: Appendix A: Literature Review Appendix B: Analytical Program Appendix C: Shop Drawings

148 Copyright National Academy of Sciences. All rights reserved.


Abbreviations and acronyms used without definitions in TRB publications: A4A AAAE AASHO AASHTO ACI–NA ACRP ADA APTA ASCE ASME ASTM ATA CTAA CTBSSP DHS DOE EPA FAA FAST FHWA FMCSA FRA FTA HMCRP IEEE ISTEA ITE MAP-21 NASA NASAO NCFRP NCHRP NHTSA NTSB PHMSA RITA SAE SAFETEA-LU TCRP TDC TEA-21 TRB TSA U.S. DOT

Airlines for America American Association of Airport Executives American Association of State Highway Officials American Association of State Highway and Transportation Officials Airports Council International–North America Airport Cooperative Research Program Americans with Disabilities Act American Public Transportation Association American Society of Civil Engineers American Society of Mechanical Engineers American Society for Testing and Materials American Trucking Associations Community Transportation Association of America Commercial Truck and Bus Safety Synthesis Program Department of Homeland Security Department of Energy Environmental Protection Agency Federal Aviation Administration Fixing America’s Surface Transportation Act (2015) Federal Highway Administration Federal Motor Carrier Safety Administration Federal Railroad Administration Federal Transit Administration Hazardous Materials Cooperative Research Program Institute of Electrical and Electronics Engineers Intermodal Surface Transportation Efficiency Act of 1991 Institute of Transportation Engineers Moving Ahead for Progress in the 21st Century Act (2012) National Aeronautics and Space Administration National Association of State Aviation Officials National Cooperative Freight Research Program National Cooperative Highway Research Program National Highway Traffic Safety Administration National Transportation Safety Board Pipeline and Hazardous Materials Safety Administration Research and Innovative Technology Administration Society of Automotive Engineers Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) Transit Cooperative Research Program Transit Development Corporation Transportation Equity Act for the 21st Century (1998) Transportation Research Board Transportation Security Administration United States Department of Transportation




TRANSPORTATION RESEARCH BOARD

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9 780309 479967

NON-PROFIT ORG. U.S. POSTAGE

COLUMBIA, MD PERMIT NO. 88

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500 Fifth Street, NW

Washington, DC 20001

ADDRESS SERVICE REQUESTED

ISBN 978-0-309-47996-7

APPENDIX A: LITERATURE REVIEW A1.1

General ............................................................................................................................ A-2

A1.2

Examples of innovative connection details and full depth precast deck panel systems developed in the past 25 years........................................................................... A-3 A1.2.1

NCHRP 12-41: University of Nebraska-Lincoln (1994-1998)........................ A-3

A1.2.2

University of Illinois at Chicago (1998-2006) ................................................. A-5

A1.2.3

NCHRP 12-65: George Washington University/University of NebraskaLincoln (2003-2008) ........................................................................................ A-6

A1.2.4

PCI Northeast Chapter ................................................................................... A-10

A1.2.5

Virginia Polytechnic Institute and State University (2007-2011).................. A-11

A1.2.6

Purdue University (2008- 2010) .................................................................... A-12

A1.2.7

Utah State University (2010-2012) ................................................................ A-13

A1.2.8

Nebraska Department of Roads/University of Nebraska-Lincoln (2013) ..... A-14

A1.2.9

Princess Margaret Bridge Rehabilitation (2012) ........................................... A-18

A1.2.10 NCHRP 12-69: Longitudinal Joints of Integral Deck Bulb Tees (2009)....... A-20 A1.2.11 FHWA: UHPFRC for Prefabricated Bridge Component Connections.......... A-21 A1.2.11.1 Panel-to-Girder Composite Connection Detail ............................ A-22 A1.2.11.2 Panel-to-Panel Connection Detail ............................................... A-27 A1.3 Shear Connector Spacing ................................................................................................. A-28 A1.4 Suehiro Viaduct, Kansai International Airport Line, Japan ............................................ A-29 A1.5 FHWA Experimental Program ........................................................................................ A-32

NCHRP 12-96, Final Report

A-1

A1.1 General Public inconvenience and loss of income during bridge construction and rehabilitation have prompted exploration of rapid construction methods. In 2001, Federal Highway Administration (FHWA) launched the Accelerated Bridge Construction (ABC) initiative (Accelerated Bridge Construction Manual, FHWA 2011). ABC is bridge construction that uses innovative planning, design, materials, and construction methods in a safe and cost-effective manner to reduce the construction time associated with maintenance of traffic when building new bridges or replacing and rehabilitating existing bridges. Cast-in-place (CIP) bridge deck slab represents a significant part of construction of stringer-type bridge superstructures as much of the construction time is consumed in deck forming, placement and tying of steel bars, and placement and curing of CIP deck concrete. Also, studies conducted by bridge owners, such as Oregon DOT (Johnson 2012), have shown that CIP deck is considered one of the major elements of highway bridges that require continuous maintenance, i.e. patching, sealing, and overlays. This is because CIP deck poses low durability performance due to shrinkage cracking and high permeability. As a result, full-depth precast concrete deck panel systems have been increasingly used to replace CIP decks to enhance speed of deck construction. In addition to high construction speed, full-depth precast concrete deck panel systems have many advantages such as high quality plant production under tight tolerances, low permeability, and much reduced volume changes cracking due to shrinkage and temperature effects during initial curing. High quality precast concrete decks, often two-way prestressed, have a lower life-cycle cost even though they may have higher costs in some US market. As a result, use of full-depth precast concrete deck panel systems have been steadily increasing, specially, over the past 10 years. Development of the full-depth, precast concrete deck panel systems has been made in three distinct periods. The first period was from early 1960s to early 1980s, where no standard geometry, connection details or specifications were used. The second stage was from early 1980s to the end of the second millennium, where more experimental efforts were set towards studying the structural behavior of full-depth precast concrete deck panel systems made composite with the supporting girders (Issa et al. PCI J. 1995, Issa et al. PCI J. 1998). Towards the end of the second stage, new innovative ideas of connecting the precast panels with the supporting girders were developed, such as the development of the large size 1.25 in. diameter steel studs (Badie et al. ASCE BJ 2002), the dovetail steel connection (Tadros & Baishya NCHRP 407, 1998) and the debonded shear key detail for concrete I-girders (Tadros et al. PCI J. 2002). Also, during this era new full-depth precast concrete deck panel systems that have high construction speed were developed and tested (Yamane et al. PCI J. 1998, Badie et al. PCI J. 1998, Badie et al. ACI CI 1999). The third period started in 2000 and has continued since then. Most of the research activities in this period have been focused on developing standard geometry and connection details that ensure high construction speed (overnight construction) and reduced future maintenance. Among these efforts were research conducted at the University of Wisconsin Madison (Carter III et al. PCI J. 2007), research conducted jointly by the George Washington University and University of Nebraska-Lincoln (Badie & Tadros, NCHRP 584, 2008), research conducted at Purdue University (Frosch et al. 2010), research conducted at Virginia Tech. (Scholz et al. VTRC 2007, Sullivan et al. PCI J. 2011), research conducted at Utah State University (Wells et al. 2012),


A-2

and the in-progress research being conducted at University of Nebraska-Lincoln. The goals of these research projects can be summarized as follows: (1) examine the possibility of extending the spacing of the shear pockets, (2) simplify panel-to-panel and panel-to-girder connection details, and (3) develop recommended guidelines for design, detailing, fabrication, installation, and construction for the AASHTO LRFD Bridge Design Specifications (ASSHTO LRFD 2017). A summary of the notable relevant connection details for full-depth precast concrete deck panel systems developed in the past 25 years is given in the following sections. More information can be found in the following references (Issa et al. PCI J. 1995, Tadros & Baishya NCHRP 407 1998, Markowski et al. 2005, Carter III et al. PCI J. 2007, Scholz et al. VTRC 2007, Badie & Tadros, NCHRP 584- 2008, Sullivan et al. PCI J. 2011, Frosch et al. 2010, Wells et al. 2012). A summary of these details and systems can be found in the state-of-the-art repot on full-depth precast concrete deck panels (PCI SOA -01-1911, 2011). Also, useful cast-in-place connection details can be found in NCHRP 10-71 (French et al. 2011). Although the research conducted in the NCHRP 10-71 was for precast/pretensioned members connected longitudinally, some of the developed connection details can be used for full depth precast concrete deck panels supported by concrete/steel girders. A1.2

Examples of innovative connection details and full depth precast deck panel systems developed in the past 25 years

A1.2.1 NCHRP 12-41: University of Nebraska-Lincoln (1994-1998) The major goal of the NCHRP 12-41 project was to develop precast deck panel systems with connection details that provide for rapid replacement of bridge decks (Tadros & Baishya NCHRP 407 1998). The following products were developed and experimentally validated. (1) Debonded shear key system for prestressed concrete bridge girders made composite with the concrete deck (Tadros et al. PCI J 2002): The system utilizes the mechanical anchorage of concrete shear keys created on the top flange of a concrete girder combined with shear reinforcement crossing the interface, as shown in Figure 1. Sealant is applied to the top surface of the girder to break the bond between the top flange and the concrete deck. The system has the advantage of facilitating future deck removal, while protecting the top flange of the girder from damage. Although this system was developed for CIP deck slabs, it can be used also with full depth precast deck panel systems. (2) Large size 1.25 inch diameter shear studs for composite action in steel girders (Badie et al. ASCE BJ 2002, Badie et al. AISC J. 2007): Shear studs used in composite steel bridge construction are typically 3/4 in. or 7/8 in. in diameter. This researcher developed the 1.25 in. diameter stud, as shown in Figure 2, because it has about twice the strength and a higher fatigue capacity than the 7/8 in. diameter stud. Thus, fewer studs are required along the length of the steel girder. This would increase bridge construction speed in future deck replacement, and reduce the possibility of damage to the studs and girder top flange during deck removal. The idea of using large size bars as shear connectors was extended to concrete girders in NCHRP 12-65 (Badie & Tadros NCHRP 584) as will be discussed later in this section. (3) NUDECK System: The system was originally a continuous partial depth system (Badie et al. PCI J 1998), but quickly evolved into a full-depth system (Fallaha et al. PCI J 2004). The deck panels are typically 8 in. thick and use a female-to-female transverse joint, as shown in Figure 3. The connection to the supporting structure is accomplished through an 8 in. wide gap over the girder that runs the length of the panel where shear connectors are extended in the gap, as shown in Figure 2. The system is pretensioned transversely.


A-3

(4) In the longitudinal direction, the system can be post-tensioned where the post-tensioning tendons are provided in the 8-in. gap over the girder lines as shown in Figure 2, or it can be conventionally reinforced by splicing the longitudinal bars utilizing high strength spirals as shown in Figure 4 (Badie 1997). (5) Full depth precast deck panel system (Yamane et al. PCI J 1998): This system provides a stemmed precast panel provided with blind shear pockets. The shear connectors and pockets were designed to create full composite action with the supporting girders utilizing a mix of headed and headless studs to facilitate deck removal. The system is transversely pretensioned and longitudinally post-tensioned.

Figure 1. Debonded shear key system (Tadros et al. PCI J 2002)

Figure 2. 1.25 inch studs used on the Skyline Bridge, Omaha, NE (Fallaha et al. PCI J 2004)

Figure 3. Full-depth NUDECK System

Figure 4. Splicing longitudinal bars using high strength spirals (Badie 1997)


A-4

A1.2.2 University of Illinois at Chicago (1998-2006) Issa et al. (PCI J. 1998) performed finite element modeling of both simply supported and continuous bridge spans. The purpose was to determine the amount of longitudinal post-tensioning required to keep the transverse joints of precast bridge deck panels in compression. The modeled simple span bridge was the Culpeper Bridge in VA, which spans 54.5 ft and is 30 ft wide. The modeled continuous span bridge was the Well and River Bridge, located near the city of Niagara Falls. Both modeled bridges had steel girders as the deck support structure. Based on the finite element models, it was determined that a minimum compressive stress in the deck of 200 psi is required for simply supported spans and 450 psi for the interior supports of continuous spans. The design recommendations have been used by the Illinois Department of Transportation in at least five bridge deck replacement projects. Issa et al. (PCI J. 2003) conducted 28 push-out tests consisting of 14 full scale and 14 quarter scale specimens. The precast panels were connected to each flange of an A36 steel beam using welded shear studs, as shown in Figure 5. The variables tested include the number of shear studs in each pocket and also the number of pockets present on the specimen. The pocket spacing was kept consistent at 2 ft. Therefore, as the number of pockets increased, so did the length of the specimen. The study provided several findings. First, the number of shear studs in each pocket does not proportionally increase the load capacity. Second, the load necessary to induce slippage is affected by the configuration and number of studs in the pocket. Third, the ultimate strength increases with an increase in the number of shear pockets. However, the rate of increase is dependent on the number of shear studs per pocket. Finally, the AASHTO LRFD specifications are conservative in determining horizontal shear resistance of shear connectors. The authors also stated that push-off specimens with up to two grout pockets are reliable in evaluating composite behavior. Issa et al. (PCI J. 2006) conducted 11 small scale tests on a panel-to-concrete girder connection. The specimens consisted of a concrete girder section with a precast panel attached to either side, as shown in Figure 6. The tests evaluated the effect of the number and configuration of shear studs per pocket on the shear strength of the connection, as well as embedment depth of the shear stud in the panel. The test results showed that: (1) the shear strength of the connection increased proportionally with the number of studs, (2) the configuration of shear studs in the pocket affected the load at which slippage was induced, (3) the embedment depth of the shear stud in the panel affected the amount of slippage the specimen could undergo before failure, and (4) threaded bolts could be used as a shear stud for use with concrete girders.

Figure 5. Push-out specimen used by Issa et al. (PCI J. 2003)


A-5

Figure 6. Push-out specimen used by Issa et al. (PCI J. 2006) A1.2.3 NCHRP 12-65: George Washington University/University of Nebraska-Lincoln (2003-2008) The objectives of the NCHRP 12-65 project (Badie & Tadros, NCHRP 584, 2008) were to develop: (a) recommended guidelines and LRFD specifications language for design, fabrication and construction of full-depth, precast-concrete bridge deck panel systems without the use of posttensioning or overlays, and (b) connection details for new deck panels systems that can be summarized as follow:. (1) Panel-to-panel connection details: Two panel-to-panel connection details were developed. The connection details were developed to splice the longitudinal reinforcing bars to fully develop their yield strength while minimizing the required development length utilizing steel tubes to confine the spliced bars, as shown in Figure 7. Detail #1 uses a hidden steel tube on one edge of the panel and the longitudinal bars extend outside the panel on the other edge. Detail #2 uses a hidden steel tube, on both edges that are provided with a top surface slot where the splice bar can be inserted. This detail has been used successfully on implementation bridges by TX DOT and Utah DOT, as shown in Figure 8. These details provide minimum exposure of the grouted area to the environment and full longitudinal continuity of the panels without using longitudinal post-tensioning.


A-6

1"  grouting pipe 1'-2"

2'-0" 9 1/2"

9 1/2"

5"

5"

2'-0"

9"

5"

5"

1'-2"

9 1/2"

9 1/2"

7 1/2"

3 3/4"

4 1/4"

3/4"

1'-7"

6 3/4"

HSS 4x12x3/8", 4" long

1'-2" 1'-0"

1/2" strand

2'-0"

#6 bar

1'-7"

9 1/2"

1 1/4" 9 1/2"

#5 bar

5"

5"

2'-0"

9"

5"

5"

1'-2"

9 1/2"

9 1/2"

3/4"

3 3/4"

4 1/4"

3/4"

#6 bar @ 13.33 in.

Detail 1: using hidden steel tube

HSS 4x12x3/8", 4" long with top slot

Detail 2: using hidden steel tube with a top slot 1/2" strand

#5 bar

#6 bar 2'-0"

#6, 24.5" long splic e bar 3/4"

11 1/2"

1"

3 3/4"

#6

4 1/4"+1/4"*

1'-0"

7 1/2"

11 1/2" X2

#6

#6

11" 1'-0"

Detail 1: using hidden steel tube

1"

X2 11" Deta il D 2

Detail 2: using hidden steel tube with a top slot

Figure 7. Panel-to-panel connection details developed in NCHRP 584 (Badie & Tadros 2008)

Figure 8. NCHRP 584 panel-to-panel connection Detail #2 used on Live Oak Bridge, TX (2) Panel-to-girder connection details: New connection details were developed based on extending the spacing between shear pockets to 48 inches that exceeds the 24 inch LRFD specification limit (Badie et al. ASCE BJ 2010, Badie et al. ASCE BJ 2011). The analytical and experimental programs conducted using these details with the extended spacing showed that full composite action can be achieved. The panel-to-concrete girder connection detail was developed using a cluster of three 1¼ in. double headed studs embedded in the top flange of the concrete girder, as shown in Figure 9. This detail solves the mismatching problem currently encountered between the vertical shear reinforcement of the girder and the shear pockets of the precast panels. NCHRP 12-96, Final Report

A-7

The panel-to-steel girder connection detail was developed using 1¼ in. (31.8 mm) studs clustered in group 48 in. apart, as shown in Figure 9. This detail was used by some state DOTs such Utah DOT and TX DOT. 2'-0"

3"+1/4"*

1'-7"

9 1/2"

9 1/2"

7"

5"

5"

2'-0"

9"

5"

9 1/2"

2" grouting pipe

7"

7"

HSS 14x10x1/4", 6" high piece

1"

5"

5"

3/4"  vent

1'-2"

9 1/2"

5"

3"+1/4"*

1'-2" 7"

9"

2 1/2"

1'-4 1/2"

8- 1 1/4" studs

2 1/2"

Top sur face of the steel girder flange

1'-2"

2'-10"

1'-2"

1'-4 1/2"

9 1/2"

9 1/2"

7"

1'-7" 5"

5"

9"

2'-0" 5"

9 1/2"

5"

2" grouting pipe

3/4"  vent

1'-2" 9 1/2"

7"

7" 3"+1/4"*

7"

2'-0"

HSS 14x10x1/4", 6" high piece

1"

5"

5"

3"+1/4"*

Pa ne l- to-steel girder connetion 1'-2"

3"

1'-4 1/2"

4"

4"

3"

1'-2"

Top sur face of the conc rete girder flange

3- 1 1/4" double headed studs

2'-10"

1'-0"

1'-2"

1'-4 1/2"

Pa ne l- to-concr ete girder c onnetion

2"  grouting pipe

1'-0" 2"  grouting pipe

1 1/4" double hea de d stud

3" + 1/4" **

1"

4 1/2"

5"

3"+1/4"*

1 1/4" studs

5"

3 1/2"

5"

9 1/2"

1" 3 1/2" Light weight angle s used as grout barrier and to adjust f or the panel e le va tion Se ction E-E

1"  bac ker r od Se ction E-E

Pa ne l- to-concr ete girder c onnetion

Re ctangular bar Pa ne l- to-steel girder connetion

Figure 9. NCHRP 584 panel-to-girder connection for steel & concrete girders (Badie & Tadros 2008) (3) Full depth panel systems: Two systems were developed. Both systems do not use longitudinal post-tensioning. The first system is transversely pretensioned with discrete shear pockets at 48 inch spacing and uses the connection details shown in Figures 5 to 7. The second system is conventionally reinforced in both directions. The precast panel has a hidden (blind) continuous channel at the girder lines to house the shear connectors extending from the girder top flange into the deck. After the precast panels are installed and their elevation is adjusted using leveling screws, the continuous channels are filled with non-shrink grout through grouting pipes. The panel has three layers of reinforcement, two transverse layers (top & bottom) for the flexural design of the deck, and one longitudinal layer provided at the middle.


A-8

The longitudinal reinforcement is spliced at the transverse edges of the panel using a mechanical coupling system that utilizes a steel tube and heavy duty nuts. Details of this system are provided in Figures 10 and 11. 9'-0"

5"

5 1/2"

3"

K

Top surface of the flange of the steel girder

K

9'-0" K

#5 bar

5"

3"

1/2" strand

Top surface of the flange of the concrete girder K

Steel studs

1" 5" 3" + 1/4" *

2" grouting pipe

2" grouting pipe

Shear connector

1" 5" 3" + 1/4" *

1'-0"

1'-0"

2"

Section K-K

Figure 10. NCHRP 584 panel-to-girder connection of the second system (Badie & Tadros 2008)


A-9

9'-0" 1/2"

1/2"

8'-11"

4"

9"

HSS 8x4x3/16"

4"

3 5/8"

? ? = 1 1/4"

4"

1"? ? Hex nut with 1/4" thick washer

2"

Section G-G

? = 2"

1/4"

3"

3 1/2"

8 5/8"

F

4"

8"

2" 6" + 1/4" *

1/2" 1/2" 3/4"

5"

1"

2 1/4"

6"

G 1/2" 5" 1/2"

G

4"

4"

1"

2"

1" ? ? all thread bar, 150 ksi F

#8 bar with 5" long thread ends

3/4"

4" 2"

6"+ 1/4" *

6"

3/4"

10"

1/4"

2"

2"

2 5/8" 1/4"

1/4"

HSS 8x4x3/16", A36

1/4"

Section F-F

Figure 11. NCHRP 584 panel-to-panel connection of the second system (Badie & Tadros 2008) A1.2.4 PCI Northeast Chapter In 2001, the Northeast chapter of PCI published the first edition of “Full Depth Deck Panels Guidelines for Accelerated Bridge Deck Replacement or Construction” (PCINER-11-FDDP 2011). The second edition of this publication was released in 2011. Appendix A of this publication provides details for various components of full depth precast deck panel systems. Among them is the following panel-to-girder connection for concrete girders, where a steel plate is installed on the top surface of the concrete girder, as shown in Figure 12. The steel plate is anchored to the top flange using headed steel studs. The shear connection between the precast deck and the concrete girder is established using headed steel studs welded to the steel plate and embedded in the precast panel shear pockets. These studs can be welded to the steel plate before the precast panels are installed, if hidden (blind) shear pockets are used, or after the panels are installed, if open shear pockets are used.

Figure 12. Panel-to-girder connection details provided in PCINER-11-FDDP 2011


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A1.2.5 Virginia Polytechnic Institute and State University (2007-2011) The goals of the study conducted at Virginia Tech. (Scholz et al. FHWA/VTRC 2007 ,Sullivan et al. PCI J 2011) were to: (1) examine the possibility of extending the spacing between the shear pockets beyond the 24 inch limit mandated by the LRFD Specifications, (2) study the structural behavior of the shear connection developed by the PCI Northeast region (shown in Figure 10), (3) compare the structural behavior of a match cast panel-to-panel connection detail with that of a male-female grouted connection. A full scale mockup was built and tested in the lab, as shown in Figure 13. The panels were post-tensioned longitudinally. Test results showed that: (1) full composite action is achievable using either hooked reinforcing bars or shear studs as shear connectors in both 2 ft pocket spacing and 4 ft pocket spacing, (2) although the match cast and male-female panel-to-panel connection details showed almost similar performance, the researchers recommends using the female-female connection detail as it provides high fabrication and construction tolerances. The research also recommended new formulas to design for the horizontal shear connection between the steel plane and the supporting girder and between the steel plane and the precast panel.

Figure 13. Full scale mock up used by Sullivan et al. (PCI J 2011)


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A1.2.6 Purdue University (2008- 2010) The researcher in this project (Frosch et al. 2010) tried to overcome some of the fabrication, construction and durability issues exist with the details developed by other research projects. One of these issues is penetration of the shear pockets and transverse panel-to-panel connection to the top surface of the deck that may affect the long term durability of the finished product. Although hidden (blind) shear pockets, as those developed in NCHRP 584 can be used to reduce the scale of the problem, they complicate fabrication of the panels and block visual inspection of the grout. The research program was conducted in four phases. First, the New England Region (NER) system was evaluated in a series of large scale tests in which the panels were placed on a 40 ft prestressed concrete girder and subjected to three-point loading to evaluate its constructability and composite behavior. Second, the strength and geometry of the current and a new panel to girder joint detail were evaluated and compared in a series of direct shear tests. Third, the strength and geometry of both the current and a new panel-to-panel joint detail were evaluated and compared in a series of direct shear tests. Finally, a large scale specimen was designed, constructed, and evaluated to fully evaluate the new system. In summary, the research project focused on: (1) Developing new details for the panel-to-girder connection, where the shear pockets for the shear connectors are created in a trough formed in the girder top flange and the shear connectors were built integrally with the precast panels during fabrication, as shown in Figure 14 and 15.

Figure 14. Modified New England Region girder with the continuous keyed-trough created in the top flange (Frosch et al. 2010)


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(a) Precast panel with a match-cast, circular, malefemale panel-to-panel connection

(b) double headed shear connectors used with the proposed system

Figure 15. Details of the precast panels (Frosch et al. 2010) Validation of the new connection details was confirmed through direct push-off shear specimen and a full scale mock-up. The following are the findings of the experimental program: (a) use keyed trough surface, (b) minimum stud embedment is 6 in. for #4 - #6 studs, (c) provide minimum 4,000 psi concrete strength in trough, (d) detail girder to resist outward thrust, and (e) the horizontal strength of the joint can be estimated based on the shear stud strength provided by V n = A s f u . (2) Developing new details for the panel-to-panel connection, where match cast circular malefemale joints were used, as shown In Figure 15. Experimental results showed that: (a) checking the shear strength of the joint is not required, (b) either the 6 in. or 8 in. radius joint is recommended, however, the 8 in. radius joint may be preferable for constructability, and (c) commercial cementitious or epoxy based grout can be used to join the precast panels. A1.2.7 Utah State University (2010-2012) Researchers at the Utah State University developed a grouted post-tensioned, curved-strand connection that allows for a single panel replacement (Wells et al. 2012). Figure 16 shows the details of the proposed connection. Curved longitudinal PT tendons are used to compress only the transverse panel-to-panel connection to protect it against leakage. The tendons extend about 3 ft at each edge of the precast panel. Blockouts, provided with a single-strand anchorage device, are created on the top surface of the precast panels to install tendons. Stress analysis conducted using the finite element method showed high stress concentration in the vicinity of the blockouts generated by the applied PT force. Therefore, additional top and bottom transverse steel bars at 3-inch spacing were provided at the edges to protect the panel from cracking. The proposed connection detail was tested for flexure and vertical shear. Also, a full-scale, composite section was constructed using precast panels on steel I-girders to investigate the behavior of the proposed connection due to negative moment, as shown in Figure 17. The test results have shown satisfactory performance in positive moment and vertical shear. However, the full-scale composite test showed that the connection could not deliver the required flexural capacity (i.e. the failure load was about 75 percent of the load calculated using the method of transformed sections).


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Figure 16. Details of the curved-strand connection developed by the Utah State University (Wells et al. 2012)

Figure 17. The full-scale, composite section test conducted at the Utah State University (Wells et al. 2012) A1.2.8 Nebraska Department of Roads/University of Nebraska-Lincoln (2013) Nebraska Department of Roads is in its way to use a full precast deck panel system on Kearney East Bypass, Kearney, NE (Morcous et al. NDOR SPR-P1 (13) M323, 2013). The bridge has two equal 160 ft long spans. The precast panels are pretensioned transversely and post-tensioned longitudinally. The precast panels cover the full width of the bridge and are made skew to match the geometry of the bridge. The cross section of the bridge has a 2 percent slope. Features of the project include: 1. The precast panels are 12 ft long instead of the common 8 ft long panel to minimize the number of transverse joints by 33 percent. 2. The precast panels are provided with blind (hidden) shear pockets at 48 inch spacing similar to the blind shear pockets developed in NCHRP 485 to eliminate the need for deck overlay, as shown in Figure 18. 3. Each shear pocket accommodates 2 – 1.25 inch diameter 120 ksi threaded rods. The threaded rods are anchored in the girder web and in the precast panels using a heavy duty nut and an oversize washer.


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4. In order to accommodate the camber of the girder and maintain a uniform embedment of the shear connectors in the shear pockets, the threaded rods are covered with grease to break the bond between them and the concrete girder. After the girders are installed on the bridge, the threaded rods elevation will be adjusted by turning them up or down. 5. The longitudinal post-tensioned tendons (12 – 0.6 in. strands per girder line) are provided in the haunch between the precast panels and the girder, as shown in Figure 18. The minimum height of the haunch at the tip of the girder is adjusted to 2 inches to provide adequate space for the post-tensioned tendons. The longitudinal post-tensioning force is designed to provide for a full continuity over the intermediate pier for superimposed dead and live loads. 6. A harping device is anchored to the top flange at each end of the bridge. This device is used to harp the strands into the first and last panel on the bridge, as shown in Figure 19. 7. A special end panel is required at each end of the bridge to accommodate the anchorage device of the longitudinal post-tensioned tendons. 8. Two continuous bent plates, welded to metal tabs embedded in the girder top flange, are used to form for the haunch. Construction steps are follows: 1. The girders are installed and the haunch barrier forms are set of the girder top flange. Elevation of the side bent plates is surveyed to adjust for the elevation of the finished deck. 2. The elevation of the shear connectors (threaded rods) is surveyed to guarantee full penetration in the shear pockets. 3. The tendons are laid on the top flange and through the harping devices at each end of the bridge. 4. Deck panels are installed using the special lifting inserts provided at the shear pocket locations to minimize deck penetrations. 5. All transverse joints are filled with non-shrink grout and cured. When the grout reaches 3.5-ksi compressive strength, the longitudinal strands are post-tensioned and anchored at the end special panels. 6. Finally, the haunches are filled with flowable concrete/grout poured from the 4-inch diameter sleeves provided at the pocket locations.


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Figure 18. Details of the shear pockets and the shear connectors (Morcous et al. NDOR SPR-P1 (13) M323, 2013)


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Figure 19. Details of the anchorage and harping devices of the longitudinal post-tensioning reinforcement (Morcous et al. NDOR SPR-P1 (13) M323, 2013) NCHRP 12-96, Final Report

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A1.2.9 Princess Margaret Bridge Rehabilitation (2012) Rehabilitation of the Princess Margaret Bridge, New Brunswick, Canada, required using a full depth precast deck panel system to minimize the construction time and closure period (Zaki & Girgis 2012). The old superstructure consisted of a cast-in-place concrete deck slab supported on traverse floor beams at 9 ft - 2 in. spacing. The floor beams were supported on two longitudinal deck trusses at 31 ft - 6 in. spacing in one stretch of the bridge and two plate girders at 31 ft - 6 in. spacing in another stretch. The new precast deck system used at the deck trusses and plate girders area consisted of precast double tee panels with the pretensioned ribs oriented transverse to the direction of traffic. A typical double tee was 14 ft - 9 in. wide and 31 ft - 6 in. long as shown in Figure 20. The ribs were orientated in the transverse direction to comprise the floor beams and to span between the two main girder lines as shown in Figure 21. The double tees were longitudinally post-tensioned, which totally eliminated coupling of the longitudinal reinforcement. The longitudinal post-tensioned tendons were installed in two ducts located just below the deck slab of the double tee and directly above the longitudinal supporting deck trusses and plate girders, as shown in Figure 22.

Figure 20. The precast double tee system used on the Princess Margaret Bridge, New Brunswick, Canada (Courtesy of SNC Lavalin and eConstruct USA LLc)


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Figure 21. Cross section of the precast double tee system used on the Princess Margaret Bridge, New Brunswick, Canada (1 in. = 25.4 mm) (Courtesy of SNC Lavalin and eConstruct USA LLc)

Figure 22. Cross section of the precast double tee system used on the Princess Margaret Bridge, New Brunswick, Canada (1 in. = 25.4 mm) (Courtesy of SNC Lavalin and eConstruct USA LLc) The double tees were made composite with the longitudinal supporting deck trusses/plate girders through a cast in place concrete spine beams located directly above the deck trusses and plate girders, as shown in Figure 22. Steel studs welded to the top flange of deck trusses/plate girders and embedded in the spine beams were used to create the composite action between the deck trusses/plate girders and the spine beams. The spine beams were made composite with the double tees by creating eight shear pockets per every double tee (four shear pockets over every longitudinal deck truss/plate girder. U-shape reinforcing bars embedded in the spine beams and extended through the shear pockets provided for the required horizontal shear reinforcement, as shown in Figure 23. Concrete of the spine beams was cast through the shear pockets.


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Figure 23. Details of the spine beam used on the Princess Margaret Bridge, New Brunswick, Canada to create the composite action (1 in. = 25.4 mm) (Courtesy of SNC Lavalin and eConstruct USA LLc) A1.2.10 NCHRP 12-69: Longitudinal Joints of Integral Deck Bulb Tees (2009) Integral deck bulb-tees are precast, prestressed concrete I-beams, bulb-tees, or multi-stemmed girders with an integral deck that is cast monolithically and prestressed with the girder (Oesterle et al. 2009). These girders are manufactured in precast concrete plants under closely controlled and monitored conditions, transported to the construction site, and placed side by side in the bridge. Load transfer between adjacent units is accomplished using specially designed longitudinal connections along with a grouted shear key. The most widely used longitudinal connection between deck bulb-tees is a combination of a continuously grouted shear key and welded transverse ties, as shown in Figure 24. This type of connection is intended to transfer shear and prevent relative vertical displacements across the longitudinal joints. The survey conducted in NCHRP 12-69 (Oesterle et al. 2009) has shown that this connection detail is susceptible to cracking due to shrinkage of the grout filling the shear key, temperature change effects and twisting of the individual girders about their shear center, which is above the flange.


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Figure 24. Typical connection detail using grouted shear key and welded steel plates (Oesterle et al. 2009) NCHRP 12-69 (Oesterle et al. 2009, Li et al. 2010) has developed a longitudinal joint detail that includes headed reinforcement bars lap spliced and grouted within a narrow joint formed at the longitudinal edges of the precast deck portion of the precast girders. The geometry and the reinforcement for the alternate joint are shown in Figure 25. The headed steel bars are staggered at 6 in. spacing and extended outside the longitudinal edge of the integral deck. The headed bars help in developing the yield strength of the spliced bars in a short distance, about 6 in. of lap splice. Two No. 5 longitudinal bars are set in the grouted shear key to help in confining the headed studs and develop their yield strength. Laboratory testing indicated that the joint detail has sufficient strength, fatigue characteristics, and crack control for the maximum loads determined from the analytical studies for all combinations of span length, girder spacing, girder depth, and bridge skew used in the analytical studies of NCHRP 12-69.

Figure 25. New connection detail (Li et al. 2010) A1.2.11 FHWA: UHPFRC for Prefabricated Bridge Component Connections Advanced cementitious composite materials, whose mechanical and durability properties far exceed those of conventional concretes, present an opportunity to significantly enhance the performance of field-cast connections, thus facilitating the wider use of modular prefabricated systems.


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Ultra high performance fiber reinforced concrete (UHPFRC) represents a class of such advanced cementitious composite materials. Of particular interest for full depth precast concrete deck panel systems, UHPFRCs can significantly shorten the development length of embedded discrete steel reinforcement and can exhibit exceptional bond when cast against previously cast concrete. These properties allow for a redesign of the modular component connection to facilitate accelerated construction and enhanced long-term system performance. A research, development, and deployment effort focused on UHPFRC connections has been conducted by the U.S. Federal Highway Administration (Graybeal & Swenty 2012). This program is building on a decade of experience with UHPFRC applications (Graybeal 2011) along with past efforts specifically focused on UHPFRC connections (Aarup et al. 2000, Hansen & Jensen 1999) to create practical solutions which address clear needs within the American highway transportation system. More recently, the concept of using UHPC properties to redesign connections between modular bridge components has been recognized in North America. As of early 2012, field-cast UHPC connections between prefabricated bridge components were implemented in 18 bridges in the United States and Canada. These bridges use a range of details to connect different precast concrete modular bridge components, including adjacent box beams, full-depth precast deck panels, and deck-bulb-tee girders. Two fundamental differences between the field-cast UHPFRC connection concept and conventional modular component connection concept are simplicity and performance. The UHPFRC connection concept allows for small, simple connections while delivering better overall performance. The exceptional durability of UHPFRC has been well documented. Of particular importance, UHPFRC contains no coarse aggregate, so it does not exhibit early-age micro cracking common to conventional concrete. This feature, combined with the discontinuous pore structure in the homogeneous cementitious matrix, results in concrete with an extremely low permeability. Table 1 presents a select set of material properties for the UHPC investigated in the study conducted by FHWA. Table 1. Material properties for the UHPFRC investigated in the study conducted by FHWA

The FHWA study developed design details for the: (1) Panel-to-girder composite connection, and (2) panel-to-panel connection. The connection designs deployed have tended to mimic non-contact lap splice connections with a female-female shear key profile. A1.2.11.1 Panel-to-Girder Composite Connection Detail (Graybeal FHWA-HRT-12-041) Figures 26 and 27 provide schematic illustrations of this connection for precast concrete deck panels supported by steel and concrete girders, respectively. The connection detail consists of a hidden continuous open channel provided at every girder line on the underside of the precast deck panel through, which the bottom mat of transverse deck reinforcement passes.


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The continuous channel accommodates the shear connectors, which are steel studs welded to the top flange of the steel girders or reinforcing bars embedded in the web of the concrete girders and extended outside the top flange. The channel is provided with grouting holes that provide access to fill the channel with grout. The concept of the continuous open channel was originally developed in the NCHRP 12-65 (Badie & Tadros NCHRP 584 2007). However, the primary difference is that the extension height of the shear connectors is reduced so as to not interfere with the precast deck.

Figure 26. Schematic illustrations of the composite connection for precast concrete deck panels supported by steel girders (Graybeal FHWA-HRT-12-041)

Figure 27. Schematic illustrations of the composite connection for precast concrete deck panels supported by concrete girders (Graybeal FHWA-HRT-12-041) The connection detail was tested using two 39-ft long concrete beam/deck specimens. The two test specimens had the same basic precast panel and girder designs, but one beam (Beam 1) was built as a conventional specimen with conventional composite connection details, and the other beam (Beam 2) was built as a UHPFRC specimen with the new connection detail. For each beam, one half of the beam simulated a steel girder connection and the other half simulated a concrete girder connection. Figures 28 to 31 show the connection details used on these beams. The field-cast panel-to-girder connection of Beam 1 used Harris Construction Grout, a pre-bagged, non-shrink construction grout, which yielded 7.95 and 7.99 ksi compressive strength at 28 and 106 days respectively. The first batch of conventional grout placed into the connection had an inappropriate rheology and thus was not able to be fully consolidated to fill all of the void space. The grout was too stiff, and thus it filled the blockouts in the deck panels and the areas immediately around the stud clusters, but left some voids in areas farther away from the stud clusters. This issue was encountered on the easternmost 8 ft of the test specimen, with the grout for the remainder of the specimen being of appropriate consistency. After the initial placement had set, void spaces were filled by placing fluid grout into the void spaces laterally via accessible areas on the sides and ends of the haunch. The inappropriate consistency and the secondary grout casting both resulted in greater than anticipated shrinkage cracking of the grout in the haunch connection within the easternmost 8 ft of the test specimen. Figures 32 & 33 provide representative examples of the cracking observed in the haunch connection grout near the east end of the specimen.


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Figure 28. Beam 1 (Conventional composite connection): Transverse cross section of emulative steel girder connection (Graybeal FHWA-HRT-12-041)

Figure 29. Beam 1 (Conventional composite connection): Transverse cross section of emulative concrete girder connection (Graybeal FHWA-HRT-12-041)


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Figure 30. Beam 2 (UHPC composite connection): Transverse cross section of emulative steel girder connection (Graybeal FHWA-HRT-12-041)

Figure 31. Beam 2 (UHPC composite connection): Transverse cross section of emulative concrete girder connection (Graybeal FHWA-HRT-12-041) The field-cast panel-to-girder connection of Beam 2 used a UHPFRC mix, which yielded 22.1, 27.0, 27.7 and 29.7 ksi compressive strength at 21, 97, 180 and 270 days respectively. The UHPFRC mix design included 317.5 kg (700 lbs) of Ductal Premix, 20.3 kg (44.8 lbs) of water, 4.3 kg (9.5 lbs) of Chryso Premia 150 superplasticizer, and 22.6 kg (50 lbs) of 12.7 mm long by 0.2 mm diameter (0.5 in. long by 0.008 in. diameter) straight steel fibers. NCHRP 12-96, Final Report

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Figure 32. Cracking apparent on north face of haunch near east end of the Beam 1 prior to start of structural loading (Graybeal FHWA-HRT-12-041)

Figure 33. Cracking apparent on top of deck at grout pocket near east end of Beam 1 prior to start of structural loading (Graybeal FHWA-HRT-12-041) The test program for each specimen included two phases. First, each test specimen was subjected to cyclic loads in order to simulate the type of service-level fatigue loadings commonly applied to highway bridge structures. A four-stage loading program was used, where the first three stages each subjected the test specimen to more than 2 million cycles of structural loading. The final stage subjected the test specimen to more than 5 million additional cycles of structural loading. The vertical shear force range was increased by approximately one-third at each successive stage, resulting in the final stage applying twice the vertical shear force range as the initial stage. The results of the cyclic load test clearly demonstrate that the horizontal shear interface of Beam 1 remained intact throughout the entirely of the cyclic loading. No differential movement was observed electronically or visually at various levels of the cyclic load. The conventional grout remained well bonded to the precast surfaces with no indication of cracking, delamination, or debonding. The new connection detail of Beam 2 succeeded in resisting all cyclic structural loads to which they were subjected throughout the testing program. No damage was observed within the UHPFRC composite connection or in the adjoining steel connectors throughout the duration of this testing. After the completion of the cyclic loading program, each specimen was subjected to static loading. During the static testing to failure, the UHPFRC test specimen carried a peak applied shear load of 498 kips (2215 kN), which corresponds to a horizontal shear per unit length of 12.0 kips/inch (2.1 kN/mm).


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At this load, the prestressed girder began to fail in a combination of horizontal and vertical shear in the web and top flange of the girder. Horizontal shear distress was also observed in the precast deck elements adjacent to the haunch. The conventional test specimen carried a peak applied shear load of 445 kips (1980 kN), which corresponds to a horizontal shear per unit length of 10.45 kips/inch (1.83 kN/mm). More details of the cyclic and static tests can be found in the following reference: Graybeal FHWA-HRT-12-041. A1.2.11.2 Panel-to-Panel Connection Detail (Graybeal, FHWA-HRT-11-023) The connection detail is made of a female-female cast-in-place as shown in Figure 34. No. 5 bars, which represent the deck reinforcement, extend inside the connection.

Figure 34. UHPC longitudinal connection specimen with non-contact, lap-splice detail (Graybeal, FHWA-HRT-11-023) The No. 5 bars of adjacent panels are staggered in order to avoid interference inside the connection. Two No. 5 bars are set in the connection parallel to the transverse edge of the panel to provide confinement that helps in reducing the development length of the spliced bars. UHPC mix is used to fill the connection. The connection detail was tested for fatigue and ultimate. The tested components simulated a 94.5 by 84.7-inch portion of a bridge deck that included a 6 inch (152 mm) wide field-cast UHPC connection.


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The specimens were loaded on a simple span, with the load applied through a simulated wheel patch placed adjacent to the connection near midspan. Cyclic loads were applied first, with the test program including at least 2 million cycles to a load just below the cracking strength of the specimen followed by at least 5 million cycles to a load larger than the cracking strength of the specimen. After the completion of the cyclic testing, each test specimen was statically loaded to failure. The tests showed satisfactory behavior of the connection detail. A1.3 Shear Connector Spacing The AASHTO LRFD Specifications (AASHTO LRFD 2012) state that spacing between the shear connectors for steel or concrete girders should not exceed 24 in. The original sources of the current maximum connector spacing of 24 in. are unclear. An investigation described in NCHRP Report 584 (Badie & Tadros 2008) on full-depth precast concrete deck panels, attributes that limit to a “rule of thumb” in design suggested in 1943 (Newmark & Siess 1943). The 24-in. limit first appeared in the 4th edition of the AASHTO Standard Specifications for Highway Bridges in 1944 and was kept without any changes in the following editions until the latest edition of the AASHTO Standard Specifications (AASHTO Standard 2002). When the first edition of the AASHTO LRFD Specifications appeared in 1994, the 24 in. limit was adopted and it was kept without any changes in the following editions until the 6th edition (AASHTO LRFD 2012). It is very important to remember that the 24. in. recommended by Newmark & Siess (1943) was developed for shear connectors uniformly distributed along the length of the supporting girders, which is the common case when cast-in-place decks are used, and not for clusters of studs, which is the case for when full depth precast concrete deck panels are used. During the last 15 years, extending the spacing between the shear connection clusters of precast composite concrete bridge decks and girders has received great interests. There are two important reasons why closely spaced blockouts are undesirable in precast concrete deck panels. First, each blockout requires special labor for fabrication and grouting. Second, a precast concrete deck panel manufactured with blockouts spaced at 24 in. may have a definite plane of weakness through the blockout openings. Special care must be taken to reinforce this weak section, particularly for effects of moving and handling to avoid cracking. In both cases, minimizing the number of connectors and blockouts is preferred (Oliva & Okumus 2013). These connections using steel studs were the focus of a push-off investigation by Issa et al. (2003) in which clusters of studs in a pocket were found to have less capacity than the sum of individual studs. The AASHTO “Q n ” capacity value for studs in Article 6.10.10.4 of the 2012 AASHTO LRFD Specifications, however, matched Issa’s measured capacity for two stud clusters in a single pocket. The test data showed a 15 to 25% capacity reduction when the number of studs was increased or the number of pockets increased. AASHTO does not specifically change capacity with the number of studs in a cluster, but taking the capacity as 85% or less of AASHTO’s value when more than two studs are clustered in a pocket is recommended based on Issa’s work. Since push-off specimens do not provide accurate representation of the composite deck/girder behavior due to their limited size and lack of stability of the specimens during testing, a series of recent research activities has re-examined the needs of composite deck connections through testing of full scale composite beams. Testing of panels connected to 84-ft-long steel girders with both 24-in. and 48-in. connector spacing was conducted at the University of Wisconsin (Markowski et al. 2005) and found no reduction in composite action stiffness or strength with the wider spacing, even after 2 million cycles of repeated service loading.


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On testing to the theoretical ultimate capacity, no deck uplift was detected and the 48-in. connector spacing provided an actual ultimate load capacity higher than predicted using AASHTO procedures, even though no capacity reduction was taken for multiple studs per pocket. In NCHRP 12-65, Badie & Tadros (NCHRP 584, 2008) tested two composite beams where spacing between the shear connectors clusters was set at 24 and 48 in. The beams consisted of a full depth precast deck panels supported on steel girders. The composite beams were exposed to two million cycles of fatigue load and then tested to failure. The test results have shown that extending the stud spacing from 24 to 48 in. has no detrimental effect either on the composite beam stiffness or the ultimate flexural capacity. The study recommended providing special confinement of the shear connector individual clusters in order to guarantee full development of the steel studs. Another study was conducted at Virginia Tech. (Scholz et al. 2007 ,Sullivan et al. 2011) were to examine the possibility of extending the spacing between the shear pockets beyond the 24 inch limit mandated by the LRFD Specifications. A full scale mockup was built and tested in the lab, where the spacing between the shear connector clusters was set at 48 in. The test results have shown that: (1) full composite action is achievable using either hooked reinforcing bars or shear studs as shear connectors in both 2 ft pocket spacing and 4 ft pocket spacing. The research also, recommended new formulas to design for the horizontal shear connection between the steel plane and the supporting girder and between the steel plane and the precast panel. As a result of these studies, forty-eight-inch spacing was successfully used on implementation projects in NE, TX, VA and Wisconsin. At its 2013 annual meeting, the AASHTO Highway Subcommittee on Bridges and Structures approved a change to Article 5.7.4.5 of the LRFD Bridge Design Specifications to permit a longitudinal spacing up to 48 in. but not greater than the beam depth. A1.4 Suehiro Viaduct, Kansai International Airport Line, Japan The RT added this and the following section to the literature review that was submitted in Interim Report 1. This section is about a full-depth precast system that was developed in Japan in early 1990s, which uses a variable depth panel and a system of discrete haunches. The next section is about the experimental program that is in progress at the Federal Highway Administration at Turner Fairbank Highway Research Center. The FHWA project has been investigating the possibility of extending spacing of the shear connectors beyond the current 24 inch limit for steel girders. This section gives a summary of the Suehiro Viaduct, Kansai International Airport Line, Japan (Matsui et al. 1994, Manabe & Matsui 2004). Some of the features of the precast deck panel system used on this bridge are similar to the main features of precast deck panel system that was developed in this project. Features of the deck panel system used on the Suehiro Viaduct project included: •

Deck panel had variable depth: A precast slab system was adopted in constructing of the Suehiro Viaduct on the Kansai International Airport Line because of its proven labor saving and higher durability. A variable depth precast panel (Π-shape), as shown in Figure 35, was adopted. The thickened ends of the panel provide enough space to support the panel and accommodate the leveling bolt system used to adjust for the panel’s elevation.


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Figure 35: Cross section of the precast panel (Matsui et al. 1994, Manabe & Matsui 2004) • • • • •

Shear connectors were provided only at the transverse panel-to-panel joints and at a wide spacing of 4 ft–11 in. (1500 mm), which simplified the production of the precast panels because no shear pockets were created in the panel, as shown in Figure 36. Discrete haunches, rather than continuous haunch, were used, where only the space between the steel girder and the thickened ends of the panels was filled with grout. The precast panels were transversely pretensioned, and the completed deck was longitudinally post-tensioned, as shown in Figure 37. The longitudinal PT was applied after the panel-to-panel joints were grouted and cured, but before the panel-to-girder and the panel-to-panel joints were grouted. Therefore, the full PT force was applied only on the deck. The superstructure was designed as non-composite girder, conforming to the Japanese specification.

Using this system helped the design engineer to: 1. Reduce the self-weight of the deck 2. Allow for splicing of the supporting steel girders without the need of using a thick haunch. 3. Reduce the amount of labor and material required to fill the haunch. 4. Reduce the construction time by about 40% compared to a cast-in-place slab.

Figure 36. The precast deck during construction showing the wide spacing of the shear connectors and the grout barrier for the panel-to-girder connection (Matsui et al. 1994)


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Figure 37. The precast deck before grouting the panel-to-panel and panel-to-girder joints (Matsui et al. 1994) An experimental program was developed to validate the concept, which included: •

Single slab test to check mode of failure for the individual precast panels (Figure 38): Testing showed that panels with PT failed in flexure by crushing of concrete, while panels without PT failed in punching shear. The failure load was 1.27 to 1.52 times higher than the design value.

•

Continuous slab test to measure the strength of the panel-to-panel joint (Figure 39): Three specimens were built using two panels that were made continuous. Three levels of PT stress were applied across the panel-to-panel joint: 78, 50 and 28 ksi (539, 343 and 196 N/mm2). Under service loads, there was no noticeable difference in deflection or strains. However, the specimen with the 28 ksi (196 N/mm2) PT stress showed a wider crack at failure at the bottom surface of the joint. The specimens were subjected to 1.5 million cycles of fatigue loading to test for possible leakage. No leakage was reported. Later, these specimens were tested to failure. Failure strength was about 1.7 times higher than that of a single panel, which proved that the panel-topanel connection is stronger that the panel.

Figure 38. Single slab test setup (Matsui et al. 1994)


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Figure 39. Continuous slab test setup (Matsui et al. 1994) In August 2015, the research team contacted Dr. Hideki Manabe, president of the CORE institute of Technology Corporation, Japan, and received the following information: •

No problems have been reported since the precast panels were put into service.

•

The level of longitudinal post-tensioning was designed considering safety factor for cracking and introduced 290 psi (2.0 N/mm2) of the floor region depth of the panel.

•

The superstructure was designed as non-composite girder, conforming to the Japanese specification. The design results were verified using finite element analysis.

•

Transverse section of panel was designed as a one-way channel-Shaped slab. On the other hands, longitudinal section of panel was designed as a flat plate.

•

This system has been used on 4 bridges in Japan

Comments from the research team on this system: There are many similarities between the precast panel system used in the Suehiro Viaduct and the precast panel system developed by the research team. The only difference between these systems is that the deck of the Suehiro Viaduct Bridge was designed as non-composite with the girder. Therefore, small amount of shear connectors were used to just anchor the precast slab with the supporting girders. However, the field instrumentation and analysis conducted by Dr. Manabe (Manabe & Matsui 2004) on the bridge found that the superstructure behave as a partial composite system. It is a common practice in the United States that slab/I-girder assemblies are designed as composite structures due to superimposed loads. Article 6.10.1.2 of the LRFD Specifications (AASHTO LRFD 2017) states that non-composite sections are not recommended but are permitted. A1.5

FHWA Experimental Program (Provines and Ocel 2014, NABC & WSBS)

Researchers at the Turner-Fairbank Highway Research Center, FHWA has been evaluating if the current AASHTO strength and fatigue limit states are applicable to clustered shear studs used for precast deck panel systems. Based on a review of the current domestic and international shear stud specifications, the researchers found that the AASHTO provisions warrant revisiting. The fatigue provisions may be overly conservative, while the strength provisions may be unconservative.


A-32

The experimental program includes 16 large-scale tests using four different configurations of shear stud spacings, which range from a typical cast in place deck detail with studs every 12 or 24 in. to configurations more conducive to precast panels with clustered shear studs spaced at 36 and 48 in. Of the 16 large-scale tests, 4 are static and 12 are fatigue tests to evaluate both the strength and fatigue AASHTO limit states. Upon completion of the large-scale tests, small-scale (push out) fatigue and static tests will also be conducted. Cast in place and precast push out tests will be performed to compare the two methods of concrete placement. The static tests will focus on evaluating the AASHTO minimum longitudinal and transverse stud spacing, while the fatigue tests will focus on evaluating the AASHTO shear stud constant amplitude fatigue limit of 3.5 ksi. Each large-scale test in this study consists of a 30 ft. long W27x84 rolled steel beam and two concrete deck panels fabricated by a PCI certified precast producer, as shown in Figure 40. Pockets were cast into the deck panels and were sized depending on the number of studs in each pocket. Table 2 presents the experimental test matrix with the four different shear stud cluster spacings.

Figure 40. Large-scale test beam with 36" cluster spacing (Provines and Ocel 2014) Table 2. Large-scale experimental test matrix (Provines and Ocel 2014)

The beams were designed to induce a shear failure in the studs for the static tests and to accelerate fatigue testing. The 12 studs in each shear span correspond to approximately 38% composite action. Since beams were designed as partially composite and AASHTO does not allow partial composite action, the AISC specifications were used to determine the flexural resistance and rigidity.


A-33

Prior to placing the concrete deck panels on the steel beams, the top flange was coated with a thin layer of grease so the majority of shear force transferred between the steel beam and the deck panels was transmitted through the shear studs. Grout with an expected strength of approximately 8.0 ksi was used to fill the pockets, haunch, and transverse joint in the center of the beam. The beams have two load points with an 11’-6” shear span on each end of the beam. All of the shear studs have a diameter of 7/8 in. and were selected due to their use in typical bridge construction. Clustered studs are spaced longitudinally at a pitch of 3.5 in. (4 times the stud diameter, 4d), which is slightly less than the minimum AASHTO LRFD spacing of 6d. The smaller pitch was chosen to minimize the length of the pockets and is currently allowed by some bridge owners such as Texas DOT. Table 3 provides a summary of the fatigue tests and includes the following information: the naming convention, basic stud geometry, initial average stress range on the shear studs in each shear span, and the number of cycles to failure. To date, 4 large-scale static and 7 large-scale fatigue tests have been completed. Table 3. Summary of S-N data for large-scale fatigue tests (Provines and Ocel 2014)

Throughout fatigue testing, measurements from the strain gauges in both the steel beam and the concrete deck were used to calculate the location of the neutral axis (N.A.). Figure 41 shows a plot of the location of the N.A. for the steel beam at four cross steel cross sections along the west shear span for beam 1F1. The calculated N.A. locations were then used to determine how composite action was affected during cycling. When testing began, the steel beam and concrete deck were expected to behave as one composite section. As the studs failed due to fatigue, the beam and deck were expected to behave as two separate flexural members because horizontal shear force was no longer being transferred between the two elements. The composite section and bare steel beam N.A. are also provided as a reference. Figure 42 shows S-N plot of completed large-scale tests obtained from the fatigue tests. Figures 43 & 44 shows the results obtained from the static tests. Figure 43 shows the moment-displacement curve for each of the four static tests. Figure 44 shows relative slip and uplift results at 90% of the ultimate load for static tests.


A-34

Figure 41. Location of steel beam N.A. for west shear span sections of beam 1F1 (Provines and Ocel 2014)

Figure 42. S-N plot of completed large-scale tests (Provines and Ocel 2014)

Figure 43. M-Δ data for static tests (Provines and Ocel 2014)

Figure 44. Relative slip (left) and uplift (right) results at 90% of the ultimate load for static tests (Provines and Ocel 2014)

The test results showed the following: • • •

Regardless the spacing between the clusters, the specimens were not able to reach the nominal design capacity. The measured flexural capacity was about 80 percent of the nominal design capacity. The static test results suggest a shear factor, closer in magnitude to the 0.8 factor found in some international stud provisions, should be applied to the shear stud strength equation in AASHTO. The extended stud cluster spacing up to 48 inch does not appear to have a negative effect on either the relative slip or uplift between the concrete deck and steel beam. This is consistent with the conclusions reported in NCHRP 12-65 (Badie & Tadros 2008). A failure criterion for shear studs in the large-scale fatigue tests has been defined as a complete loss in composite action monitored by the movement of the neutral axis in the steel beam.


A-35

It is important to mention that no special confinement was provided to the stud clusters in any of the specimens tested at FHWA. The only source of confinement was provided by the slab reinforcement that was designed using the LRFD Empirical Design Method. Experimental results obtained in NCHRP 12-65 (Badie & Tadros 2008) and recently at the University of Nebraska (Morcous et al. 2013) showed that full strength of the studs can be developed if special confinement in the form of steel tubes or individual ties is provided around the shear pockets. The research team strongly believes that confinement plays a critical role in developing the design capacity of the shear connectors, especially when the spacing extended spacing between stud clusters is used.


A-36

APPENDIX B ANALYTICAL PROGRAM This appendix was created to keep the size of the main report within a reasonable size. It presents the detailed results of some the issues investigated in the analytical program that are reported in Chapter 3 of the report. Table of contents B.1

Design Requirement No 6: Flexure Design of the Composite Section ........................... B-2

B.2

Design Requirement No 7: Deflection of the Composite Section ................................... B-7

B.3

Design Requirement No 8: Interface Shear ................................................................... B-11

B.4

Design Requirement No 9: Vertical Shear .................................................................... B-16

B.5

Design Requirement No 10: Distribution Factors ......................................................... B-18


B-1

B.1 Design Requirement No 6: Flexure Design of the Composite Section The vierendeel model was loaded only with the following combination of composite loads: DC Loads:

Barrier weight = (2 barriers)(0.3 k/ft/barrier)/(6 beams)

DW Loads:

Wearing surface = (girder spacing)(2 inch thick layer)(0.150 kcf)

Live Load:

HL93 with distribution factor for moment determined using the LRFD Specifications

SERVICE I limit state was used to determine the load factors. The loads were applied on the top chord of the vierendeel model. The following procedure was used to obtain the flexural stresses from the vierendeel model. At the section where the highest moment in the girder was recorded, moment in the top chord (slab) and in the bottom chord (beam) was recorded. The moment was used to determine the flexural stresses in the slab and the girder using their individual inertia and geometrical properties. Table 1 shows the matrix used in the parametric study. The same matrix and design criteria were also used to investigate interface shear and deflection of the composite section. Table 1. Matrix of the parametric study for flexure design of the composite section Case No. 1 (Baseline) 2 3 4 5 6 7 (baseline) 8 9 10 11 12

Span-todepth ratio

SPAN (ft)

20 80, 144 & 216

35

Girder spacing (ft)

Deck thicness (in)

Haunch thickness (in)

haunch size (ftxft)

6

7.5

2

2x2

6 6 12 6 6

7.5 7.5 7.5 10 10

6 2 2 2 6

2x2 1x1 2x2 2x2 2x2

6

7.5

2

2x2

6 6 12 6 6

7.5 7.5 7.5 10 10

6 2 2 2 6

2x2 1x1 2x2 2x2 2x2

Haunch Spacing

2ft, 4ft, 6ft, & 8ft

Note: Highlighted cells show the changes compared to the baseline case

Results of the parametric study are reported in Tables 2 to 4. For every case, the results obtained from the vierendeel model are compared with the results obtained using the simple Euler-Bernoulli beam analysis, where the composite beam is analyzed as a simply supported beam. Analysis of the results reported in Tables 2 to 4 shows that: Parametric investigation using the Vierendeel Model: 1. Increasing the spacing between the joints leads to: • Insignificant decrease in the compressive stresses at top fiber of the slab (the maximum decrease is about 100 psi) • Insignificant increase in the compressive stresses at bottom fiber of the slab (the maximum increase is about 139 psi)


B-2

•

2.

3. 4. 5.

Insignificant increase in the compressive stresses at top fiber of the girder (the maximum increase is about 83 psi for the concrete examples, i.e. 80 and 144 ft span, and about 183 psi for the steel girder case, i.e. 216 ft span) • Insignificant increase in the tensile stresses at bottom fiber of the girder (the maximum increase is about 59 psi for the concrete examples, i.e. 80 and 144 ft span, and about 252 psi for the steel girder case, i.e. 216 ft span) Insignificant change in normal stresses is reported when: • Increasing the thickness of the haunch from 2 to 6 inches (Compare case 1 versus Case 2, and Case 7 versus Case 8) • Changing the dimensions of the haunch from 24x24 inches to 12x12 inches (Compare case 1 versus Case 3, and Case 7 versus Case 9). • Changing the girder spacing from 6 ft to 12 ft (Compare case 1 versus Case 4, and Case 7 versus Case 10). • Changing thickness of the slab from 7.5 inches to 10 inches (Compare case 1 versus Case 5, and Case 7 versus Case 11). Changing the span-to-depth ratio (from 20 to 35) or the span length (from 80 to 216 ft) does not have any impact on the reported trends. Changing the type of girder (concrete versus steel) does not have any impact on the reported trends. In addition to the parameters shown in 9, the effect of changing the minimum specified strength of the concrete girder, for the 80 ft and 144 ft spans, was examined. It was found that changing the concrete strength from 6 ksi to 12 ksi resulted in insignificant change in the normal stresses.

Comparison between the vierendeel and simplified models: The simplified model gives very comparable results to the vierendeel model. Recommendation for determining flexural stresses in the composite section: It is safe to use the simplified model to determine the flexural stresses in the composite beam due to the superimposed dead and live loads. The simplified model utilizes the Euler-Bernoulli beam theory using the composite section properties.


B-3

Table 2. Normal stresses (80-ft span) Span-to-depth ratio = 20, span = 80 ft Haunch Spacing (ft)

Haunch thickness (in.)

Top of deck (ksi)

Bottom of deck (ksi)

Span-to-depth ratio = 35, span = 80 ft Top of girder Bottom of (ksi) girder (ksi)

Haunch Spacing (ft)


Case 1 2 Vierendeel 2 4 2 Baseline 6 2 Haunch: 24x24x2 in. 8 2 Slab Thickness: 7.5 in. (Case 2 ft - Case 8 ft) Girder spacing: 6 ft NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

-0.324 -0.334 -0.367 -0.402 0.079 -0.419 0.095

-0.415 -0.431 -0.451 -0.472 0.057 -0.397 -0.018

1.106 1.119 1.133 1.147 -0.040 1.099 0.008

2 2 Vierendeel 4 2 Baseline 6 2 Haunch: 24x24x2 in. 8 2 Slab Thickness: 7.5 in. (Case 2 ft - Case 8 ft) Girder spacing: 6 ft NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

-0.716 -0.701 -0.663 -0.620 -0.097 -0.485 -0.231

-0.327 -0.336 -0.366 -0.399 0.072 -0.315 -0.012

-0.327 -0.347 -0.371 -0.395 0.068 -0.196 -0.130

1.013 1.028 1.043 1.059 -0.046 0.995 0.018

2 6 Vierendeel 4 6 Change haunch 6 6 thickness to 6 in. 8 6 (Case 2 ft - Case 8 ft) NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

-0.733 -0.719 -0.688 -0.651 -0.082 -0.636 -0.097

-0.337 -0.345 -0.369 -0.398 0.062 -0.422 0.085

-0.401 -0.424 -0.443 -0.464 0.063 -0.400 -0.001

1.100 1.118 1.131 1.145 -0.045 1.099 0.001

2 2 Vierendeel 4 2 Change haunch 6 2 dimensions to 12x12 in. 8 2 (Case 2 ft - Case 8 ft) NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

-0.745 -0.724 -0.701 -0.668 -0.077 -0.609 -0.136

-0.207 -0.224 -0.241 -0.265 0.059 -0.341 0.135

-0.319 -0.346 -0.379 -0.417 0.098 -0.296 -0.023

1.589 1.609 1.632 1.656 -0.067 1.578 0.011

2 2 Vierendeel 4 2 Change girder spacing to 6 2 12 ft 8 2 (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified

-0.604 -0.594 -0.580 -0.556 -0.048 -0.514 -0.090

-0.196 -0.202 -0.212 -0.229 0.033 -0.281 0.086

-0.270 -0.284 -0.303 -0.324 0.054 -0.257 -0.013

0.976 0.986 0.999 1.012 -0.037 0.970 0.006

2 2 Vierendeel 4 2 Change slab thickness to 6 2 10 in. 8 2 (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified


-0.521 -0.523 -0.542 -0.563 0.043 -0.603 0.082

-0.514 -0.551 -0.595 -0.642 0.128 -0.480 -0.035

2.022 2.053 2.086 2.120 -0.098 2.004 0.018

-1.196 -1.188 -1.161 -1.128 -0.068 -0.940 -0.256

-0.528 -0.526 -0.542 -0.560 0.032 -0.483 -0.045

-0.296 -0.340 -0.390 -0.442 0.146 -0.129 -0.168

1.716 1.750 1.789 1.827 -0.112 1.702 0.014

-1.317 -1.311 -1.290 -1.263 -0.054 -1.228 -0.089

-0.526 -0.524 -0.535 -0.547 0.021 -0.607 0.081

-0.509 -0.546 -0.589 -0.635 0.126 -0.484 -0.025

2.020 2.050 2.082 2.116 -0.095 2.002 0.018

-1.235 -1.252 -1.241 -1.222 -0.013 -1.147 -0.088

-0.308 -0.286 -0.287 -0.294 -0.014 -0.398 0.089

-0.262 -0.319 -0.390 -0.467 0.205 -0.217 -0.045

2.813 2.859 2.911 2.966 -0.153 2.785 0.028

-1.083 -1.067 -1.060 -1.047 -0.036 -0.992 -0.091

-0.255 -0.266 -0.265 -0.268 0.013 -0.343 0.088

-0.260 -0.291 -0.331 -0.363 0.104 -0.234 -0.026

1.730 1.755 1.786 1.805 -0.075 1.716 0.015

-0.586 -0.568 -0.554 -0.532 -0.054 -0.419 -0.167

-0.191 -0.204 -0.211 -0.226 0.035 -0.228 0.037

-0.200 -0.218 -0.239 -0.264 0.064 -0.123 -0.077

0.890 0.902 0.916 0.932 -0.043 0.886 0.004

2 6 Vierendeel 4 6 Change slab thickness to 6 6 10 in. and Haunch 8 6 thickness to 6 in. (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified

-0.964 -0.950 -0.946 -0.936 -0.028 -0.819 -0.145

-0.274 -0.281 -0.277 -0.277 0.003 -0.317 0.042

-0.106 -0.143 -0.188 -0.238 0.132 -0.017 -0.089

1.471 1.500 1.534 1.571 -0.099 1.491 -0.020

Case 11

Case 6 2 6 Vierendeel 4 6 Change slab thickness to 6 6 10 in. and Haunch 8 6 thickness to 6 in. (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified

-1.318 -1.308 -1.279 -1.244 -0.074 -1.223 -0.095

Case 10

Case 5 2 2 Vierendeel 4 2 Change slab thickness to 6 2 10 in. 8 2 (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified

Bottom of girder (ksi)

Case 9

Case 4 2 2 Vierendeel 4 2 Change girder spacing to 6 2 12 ft 8 2 (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified

Top of girder (ksi)

Case 8

Case 3 2 2 Vierendeel 4 2 Change haunch 6 2 dimensions to 12x12 in. 8 2 (Case 2 ft - Case 8 ft) NA NA Simplified model Vierendeel (Case 2 ft) - Simplified


Case 7 -0.737 -0.722 -0.683 -0.639 -0.098 -0.632 -0.105

Case 2 2 6 Vierendeel 4 6 Change haunch 6 6 thickness to 6 in. 8 6 (Case 2 ft - Case 8 ft) NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

Top of deck (ksi)

Case 12

B-4



Top of deck (ksi)

Span-to-depth ratio = 35, span = 144 ft


Top of girder (ksi)


-0.832 -0.816 -0.776 -0.732 -0.099 -0.716 -0.116

-0.472 -0.486 -0.523 -0.563 0.091 -0.572 0.100

-0.598 -0.605 -0.613 -0.621 0.023 -0.585 -0.014

1.231 1.236 1.242 1.248 -0.016 1.227 0.004

-0.830 -0.812 -0.773 -0.730 -0.100 -0.540 -0.290

-0.481 -0.494 -0.528 -0.567 0.086 -0.421 -0.060

-0.534 -0.543 -0.552 -0.562 0.028 -0.357 -0.177

1.175 1.181 1.188 1.194 -0.019 1.140 0.035

-0.807 -0.808 -0.775 -0.737 -0.071 -0.720 -0.087

-0.509 -0.505 -0.534 -0.570 0.061 -0.576 0.068

-0.591 -0.599 -0.607 -0.614 0.024 -0.589 -0.002

1.231 1.237 1.242 1.248 -0.017 1.228 0.003

-0.811 -0.807 -0.782 -0.748 -0.063 -0.681 -0.129

-0.383 -0.384 -0.406 -0.438 0.054 -0.506 0.122

-0.516 -0.527 -0.541 -0.556 0.040 -0.503 -0.013

1.718 1.725 1.736 1.746 -0.028 1.713 0.005

-0.681 -0.674 -0.659 -0.634 -0.047 -0.585 -0.096

-0.337 -0.341 -0.355 -0.377 0.040 -0.423 0.086

-0.437 -0.443 -0.450 -0.459 0.022 -0.428 -0.009

1.109 1.114 1.119 1.125 -0.015 1.107 0.003

-0.674 -0.665 -0.649 -0.625 -0.049 -0.467 -0.207

-0.341 -0.347 -0.359 -0.379 0.038 -0.329 -0.012

-0.380 -0.388 -0.398 -0.407 0.027 -0.269 -0.111

1.054 1.059 1.066 1.072 -0.018 1.039 0.016

Haunch Spacing (ft)


Case 1 Vierendeel 2 2 4 2 Baseline 6 2 Haunch: 24x24x2 in. 8 2 Slab Thickness: 7.5 in. (Case 2 ft - Case 8 ft) Girder spacing: 6 ft NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

Vierendeel 2 2 4 2 Baseline 6 2 Haunch: 24x24x2 in. 8 2 Slab Thickness: 7.5 in. (Case 2 ft - Case 8 ft) Girder spacing: 6 ft NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

Case 2 2 6 Vierendeel 4 6 Change haunch thickness 6 6 to 6 in. 8 6 (Case 2 ft - Case 8 ft) NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

2 6 4 6 6 6 8 6 (Case 2 ft - Case 8 ft) NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

Vierendeel Change haunch thickness to 6 in.

Case 3 2 2 Vierendeel 4 2 Change haunch 6 2 dimensions to 12x12 in. 8 2 (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified

2 2 4 2 6 2 8 2 (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified

Vierendeel Change haunch dimensions to 12x12 in.



Vierendeel Change girder spacing to 12 ft



Vierendeel Change slab thickness to 10 in.




Vierendeel Change slab thickness to 10 in. and Haunch thickness to 6 in.

Top of deck (ksi)

Case 7 -1.462 -1.449 -1.414 -1.375 -0.087 -1.358 -0.105 Case 8 -1.422 -1.407 -1.373 -1.335 -0.088 -1.042 -0.381 Case 9 -1.460 -1.446 -1.418 -1.386 -0.074 -1.366 -0.093 Case 10 -1.342 -1.354 -1.334 -1.306 -0.036 -1.247 -0.095 Case 11 -1.190 -1.181 -1.168 -1.147 -0.043 -1.103 -0.087 Case 12 -1.138 -1.127 -1.115 -1.096 -0.042 -0.899 -0.240


Top of girder (ksi)


-0.832 -0.842 -0.872 -0.905 0.073 -0.910 0.078

-0.891 -0.906 -0.923 -0.941 0.049 -0.866 -0.025

2.370 2.381 2.394 2.406 -0.036 2.363 0.008

-0.844 -0.852 -0.881 -0.911 0.067 -0.684 -0.160

-0.699 -0.718 -0.738 -0.758 0.059 -0.436 -0.263

2.172 2.185 2.199 2.213 -0.041 2.145 0.027

-0.844 -0.852 -0.874 -0.900 0.057 -0.917 0.074

-0.884 -0.900 -0.917 -0.935 0.050 -0.874 -0.011

2.369 2.380 2.393 2.405 -0.036 2.363 0.006

-0.626 -0.610 -0.626 -0.649 0.023 -0.712 0.086

-0.648 -0.671 -0.700 -0.731 0.083 -0.624 -0.025

3.246 3.263 3.284 3.305 -0.059 3.237 0.009

-0.539 -0.546 -0.555 -0.571 0.032 -0.613 0.074

-0.581 -0.593 -0.609 -0.627 0.046 -0.565 -0.017

2.089 2.098 2.110 2.122 -0.033 2.084 0.005

-0.549 -0.555 -0.562 -0.576 0.027 -0.495 -0.054

-0.426 -0.441 -0.461 -0.482 0.056 -0.277 -0.149

1.906 1.917 1.931 1.945 -0.039 1.907 -0.001

B-5



Top of deck (ksi)



Top of girder (ksi)


-0.940 -0.922 -0.898 -0.868 -0.071 -0.901 -0.038

-0.749 -0.765 -0.788 -0.817 0.068 -0.763 0.014

-5.025 -5.054 -5.087 -5.123 0.098 -4.911 -0.114

11.299 11.323 11.350 11.384 -0.085 11.258 0.041

-0.943 -0.924 -0.899 -0.869 -0.074 -0.664 -0.279

-0.754 -0.770 -0.792 -0.820 0.066 -0.547 -0.207

-4.627 -4.664 -4.701 -4.740 0.113 -3.072 -1.555

10.932 10.960 10.988 11.016 -0.084 10.549 0.383

-0.943 -0.928 -0.907 -0.879 -0.064 -0.908 -0.035

-0.752 -0.767 -0.788 -0.815 0.062 -0.769 0.017

-5.008 -5.034 -5.063 -5.094 0.085 -4.953 -0.055

11.308 11.335 11.359 11.386 -0.078 11.268 0.039

-0.864 -0.856 -0.839 -0.817 -0.047 -0.829 -0.035

-0.638 -0.644 -0.660 -0.680 0.042 -0.661 0.024

-4.274 -4.327 -4.385 -4.447 0.173 -4.173 -0.101

15.434 15.477 15.523 15.570 -0.136 15.389 0.045

-0.768 -0.763 -0.750 -0.732 -0.036 -0.741 -0.027

-0.568 -0.571 -0.583 -0.599 0.032 -0.580 0.012

-3.788 -3.816 -3.849 -3.885 0.097 -3.707 -0.080

10.406 10.429 10.455 10.482 -0.077 10.376 0.030

-0.765 -0.760 -0.746 -0.729 -0.036 -0.580 -0.185

-0.570 -0.573 -0.584 -0.599 0.030 -0.440 -0.130

-3.428 -3.462 -3.503 -3.544 0.116 -2.410 -1.018

10.039 10.065 10.095 10.124 -0.085 9.830 0.210

Haunch Spacing (ft)


Case 1 Vierendeel 2 2 2 4 Baseline 6 2 Haunch: 24x24x2 in. 8 2 Slab Thickness: 7.5 in. (Case 2 ft - Case 8 ft) Girder spacing: 6 ft NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

2 2 Vierendeel 4 2 Baseline 6 2 Haunch: 24x24x2 in. 8 2 Slab Thickness: 7.5 in. (Case 2 ft - Case 8 ft) Girder spacing: 6 ft NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

Case 2 2 6 Vierendeel 4 6 Change haunch thickness 6 6 to 6 in. 8 6 (Case 2 ft - Case 8 ft) NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

2 6 4 6 6 6 8 6 (Case 2 ft - Case 8 ft) NA NA Simplified model Vierendeel (Case 2 ft) - Simplified

Vierendeel Change haunch thickness to 6 in.

Case 3 2 2 Vierendeel 4 2 Change haunch 6 2 dimensions to 12x12 in. 8 2 (Case 2 ft - Case 8 ft) Simplified model NA NA Vierendeel (Case 2 ft) - Simplified


Vierendeel Change haunch dimensions to 12x12 in.



Vierendeel Change girder spacing to 12 ft



Vierendeel Change slab thickness to 10 in.




Vierendeel Change slab thickness to 10 in. and Haunch thickness to 6 in.

Top of deck (ksi)

Case 7 -1.679 -1.663 -1.639 -1.610 -0.069 -1.635 -0.044 Case 8 -1.661 -1.644 -1.428 -1.592 -0.068 -1.240 -0.421 Case 9 -1.683 -1.671 -1.652 -1.626 -0.057 -1.646 -0.038 Case 10 -1.490 -1.485 -1.470 -1.449 -0.042 -1.457 -0.033 Case 11 -1.375 -1.371 -1.359 -1.343 -0.032 -1.347 -0.028 Case 12 -1.343 -1.339 -1.328 -1.313 -0.030 -1.094 -0.249


Top of girder (ksi)


-1.188 -1.202 -1.221 -1.246 0.057 -1.192 0.003

-7.458 -7.518 -7.599 -7.673 0.215 -7.261 -0.197

22.392 22.438 22.495 22.549 -0.157 22.331 0.060

-1.203 -1.214 -1.428 -1.258 0.055 -0.870 -0.333

-6.210 -6.288 -6.363 -6.445 0.235 -3.877 -2.334

21.126 21.177 21.235 21.293 -0.167 20.877 0.249

-1.189 -1.199 -1.215 -1.238 0.049 -1.202 0.013

-7.443 -7.498 -7.558 -7.627 0.183 -7.329 -0.114

22.406 22.444 22.494 22.544 -0.138 22.339 0.067

-0.906 -0.910 -0.923 -0.938 0.032 -0.924 0.017

-5.457 -5.560 -5.676 -5.811 0.355 -5.287 -0.170

30.425 30.509 30.601 30.676 -0.252 30.356 0.069

-0.833 -0.835 -0.845 -0.857 0.024 -0.840 0.006

-5.125 -5.183 -5.250 -5.339 0.214 -4.993 -0.132

20.459 20.505 20.558 20.617 -0.157 20.422 0.038

-0.843 -0.844 -0.852 -0.864 0.021 -0.657 -0.186

-4.054 -4.130 -4.206 -4.288 0.235 -2.671 -1.382

19.232 19.286 19.345 19.404 -0.172 19.215 0.016

B-6

B.2 Design Requirement No 7: Deflection of the Composite Section The vierendeel model was loaded only with the live load (i.e. HL93 model) with distribution factor for moment = 1.0, 1.33 dynamic effect added to the HS20 truck, and 1.0 load factor. The load was applied on the top chord of the vierendeel model. Results of the parametric study are reported in Tables 5 to 7. For every case, the results obtained from the vierendeel model are compared with the results obtained using the simple Euler-Bernoulli beam analysis, where the composite beam is analyzed as a simply supported beam. Analysis of the results reported in Tables 5 to 7 shows that: Parametric investigation using the Vierendeel Model: 1. Deflection increases when the spacing between joints increases. The maximum increase reported is about 5%, when the spacing between joints is set at 8 ft. 2. Deflection decreases when the thickness of haunch, girder spacing or thickness of the slab increases. This is due to the increase of the top chord inertia. 3. Changing the haunch dimensions has no effect on deflection. Comparison between the vierendeel and simplified models: Comparison between the vierendeel and simplified models showed that the vierendeel model showed a 5 to 7 percent increase in the deflection compared to the simple beam model when: (1) a thicker deck or haunch was used, (2) a higher span-to-depth ratio was ued, and (3) wider spacing between the shear connector joints was used. This observation showed that the simple beam model still can be used to determine the deflection of the composite beam after considering a proper reduction factor for the composite beam stiffness. This observation is acknowledged by the American Institute of Steel Structures Manual (AISC, 17th edition 2017), where Section I3 states that “Comparison to short-term deflection tests indicate that the effective moment of inertia, I eff , is 15 to 30 percent lower than that calculated based on linear elastic theory, I equiv . Therefore, for realistic deflection calculations, I eff should be taken 0.75 I equiv ”. This issue was further investigated in the experimental program and a more accurate reduction factor of the composite beam stiffness was developed, as shown in Sections 3.2 and 3.3 of the report.


B-7

Table 5. Deflection due to Live Loads (80-ft span) Span-to-depth ratio = 20, span = 80 ft

Haunch Spacing (ft)

Vierendeel Baseline Haunch: 24x24x2 in. Slab Thickness: 7.5 in. Girder spacing: 6 ft



Deflection Due to LL Difference % (Vierendeel Model) in.

2

Case 1 2

0.94

0.0%

4

2

0.95

1.7%

6

2

0.96

2.4%

8

2 Case 2 6 6 6 6 Case 3 2 2 2 2 Case 4 2 2 2 2 Case 5 2 2 2 2 Case 6 6 6 6 6

0.97

3.4%

0.83 0.85 0.86 0.87

0.0% 2.2% 3.3% 4.8%

0.94 0.96 0.96 0.97

1.0% 2.3% 3.0% 4.0%

0.77 0.78 0.79 0.80

0.0% 2.0% 3.2% 4.7%

0.82 0.83 0.84 0.85

0.0% 1.8% 2.9% 4.2%

0.72 0.74 0.75 0.76

0.0% 2.3% 3.8% 5.9%

Change haunch thickness to 6 in.

2 4 6 8

Change haunch dimensions to 12x12 in.

2 4 6 8

Change girder spacing to 12 ft

2 4 6 8

Change slab thickness to 10 in.

2 4 6 8

Change slab thickness to 10 in. and Haunch thickness to 6 in.

2 4 6 8


Deflection (Simplified Model) in.

0.96

Haunch Spacing (ft)


2

Haunch thickness (in.) Case 7 2



2.81

0.0%

4

2

2.83

0.8%

6

2

2.85

1.4%

2.88

2.4%

2.22 2.25 2.27 2.31

0.0% 1.4% 2.6% 4.3%

2.10

2.81 2.83 2.85 2.88

0.4% 1.1% 1.8% 2.9%

2.82

2.24 2.26 2.28 2.31

0.0% 1.0% 1.9% 3.2%

2.26

2.31 2.33 2.35 2.38

0.0% 0.9% 1.7% 2.9%

2.34

1.82 1.85 1.88 1.92

0.0% 1.6% 3.0% 5.0%

1.80

8

0.86


2 4 6 8

0.96


2 4 6 8

0.80


2 4 6 8

0.85


2 4 6 8

0.71


2 4 6 8

2 Case 8 6 6 6 6 Case 9 2 2 2 2 Case 10 2 2 2 2 Case 11 2 2 2 2 Case 12 6 6 6 6

2.82

B-8


Haunch Spacing (ft)





Haunch Spacing (ft)

Case 1 Vierendeel Baseline Haunch: 24x24x2 in. Slab Thickness: 7.5 in. Girder spacing: 6 ft

2

1.94

0%

4

2

1.97

2%

6

2

1.99

2%

2

2.00

3%


2 4 6 8


2 4 6 8


2 4 6 8


2 4 6 8


2 4 6 8


Case 2 6 6 6 6 Case 3 2 2 2 2 Case 4 2 2 2 2 Case 5 2 2 2 2 Case 6 6 6 6 6



Case 7

2

8


1.82 1.86 1.87 1.88

0% 2% 3% 3%

1.93 1.96 1.98 1.99

0% 1% 2% 3%

1.60 1.63 1.65 1.66

0% 2% 3% 4%

1.74 1.77 1.79 1.80

0% 2% 3% 4%

1.62 1.65 1.67 1.69

0% 2% 3% 4%

1.99


2

2

6.17

0%

4

2

6.21

1%

6

2

6.22

1%

2

6.24

1%

5.44 5.48 5.50 5.53

0% 1% 1% 2%

5.47

6.16 6.18 6.21 6.22

0% 0% 1% 1%

6.21

5.02 5.06 5.09 5.11

0% 1% 1% 2%

5.09

5.38 5.41 5.43 5.46

0% 1% 1% 1%

5.43

4.70 4.74 4.77 4.80

0% 1% 2% 2%

4.51

8

1.88


2 4 6 8

1.99


2 4 6 8

1.67


2 4 6 8

1.80


2 4 6 8

1.57


2 4 6 8


6.19

B-9


Haunch Spacing (ft)

Baseline Haunch: 24x24x2 in. Slab Thickness: 7.5 in. Girder spacing: 6 ft




2

Case 1 2

3.89

0.0%

4

2

3.90

0.1%

6

2

3.90

0.1%

2

3.90

0.2%

8


2 4 6 8


2 4 6 8


2 4 6 8


2 4 6 8


2 4 6 8



3.71 3.72 3.72 3.72

0.0% 0.1% 0.2% 0.3%

3.89 3.89 3.90 3.90

0.0% 0.1% 0.1% 0.2%

3.23 3.24 3.24 3.24

0.0% 0.2% 0.2% 0.3%

3.53 3.54 3.54 3.54

0.0% 0.1% 0.2% 0.3%

3.35 3.36 3.36 3.37

0.0% 0.2% 0.3% 0.5%


3.87

Haunch Spacing (ft)





2

Case 7 2

13.23

0.0%

4

2

13.24

0.0%

6

2

13.25

0.1%

2

13.25

0.1%

12.11 12.12 12.13 12.14

0.0% 0.1% 0.2% 0.3%

11.82

13.23 13.24 13.24 13.25

0.0% 0.1% 0.1% 0.2%

13.20

11.12 11.13 11.14 11.15

0.0% 0.1% 0.2% 0.3%

11.10

11.87 11.88 11.89 11.90

0.0% 0.1% 0.1% 0.2%

11.84

10.79 10.81 10.82 10.84

0.0% 0.1% 0.3% 0.4%

10.40

8

3.57


2 4 6 8

3.88


2 4 6 8

3.23


2 4 6 8

3.52


2 4 6 8

3.18


2 4 6 8


13.16

B-10

B.3 Design Requirement No 8: Interface Shear The vierendeel model was loaded with the following combination of composite loads: DC Loads:

Barrier weight = (2 barriers)(0.3 k/ft/barrier)/(6 beams)

DW Loads:

Wearing surface = (girder spacing)(2 inch thick layer)(0.150 kcf)

Live Load:

HL93 with distribution factor for moment determined using the LRFD Specifications

STRENGTH I limit state was used to determine the load factors. The loads were applied on the top chord of the vierendeel model. The following procedure was used to obtain the interface shear from the vierendeel model: • •

The maximum shear generated in the joints (middle element of the vertical members of the vierendeel model) at a distance “d v ” from the end support is recorded. The shear flow = Maximum shear force/haunch spacing

The results obtained from the vierendeel model are compared with the results obtained from the simple beam model. The simple beam model utilizes the Euler-Bernoulli Beam Theory with the composite section properties. The shear flow from the simplified model is determined as follows: • •

The maximum vertical shear force at a distance “d v ” from the end support is recorded. The shear flow = Maximum shear force/ d v

For both models, the distance “d v ” is taken as the greater of 0.9d e and 0.72h c , where: de

= effective depth from the extreme compression fiber to the resultant of the tensile reinforcement (an average value of 0.9h c was used)

hc

= overall depth of the composite section

Results of the parametric study are reported in Tables 8 to 10. For every case, the results obtained from the vierendeel model are compared with the results obtained using the simple Euler-Bernoulli beam analysis, where the composite beam is analyzed as a simply supported beam. Analysis of the results reported in Tables 8 to 10 shows that: Parametric investigation using the Vierendeel Model: 1. Interface shear (i.e. shear flow) decreases when the spacing between joints increases. Regardless the span length or the span-to-depth ratio, the interface shear decreases by about 10 percent when the spacing between joints increases from 2 ft to 8 ft. 2. Changing the thickness of the haunch or the slab has a small effect on the interface shear, especially when the span-to-depth ratio is low. 3. Interface shear decreases when the span length increases. Comparison between the vierendeel and simplified models: Interface shear determined by the simple beam model is always higher than the interface shear determined by the vierendeel model. Ratio of shear flow determined by the simple beammodel to the shear flow determined by the vierendeel model is about 1.15 to 1.30 across the board. Recommendation for determining interface shear in the composite section: It is safe and reasonable to use the simplified model as an approximate approach. In this case, it is expected that the horizontal shear reinforcement will be somewhat overestimated.


B-11

A more accurate estimate of the interface shear can be determined using the vierendeel model. Please, note that the values of horizontal shear reported in Tables 8 to 10, developed by using the vierendeel or simple beam model, are not intended to be used for design of real bridges. These tables are only developed to conduct the parametric study and to compare the vierendeel model with the simple beam model.


B-12

Table 8. Interface shear (80-ft span) Span-to-depth ratio = 20, span = 80 ft

Haunch Spacing (ft)

Vierendeel Baseline Haunch: 24x24x2 in. Slab Thickness: 7.5 in.

2 4 6 8


2 4 6 8


2 4 6 8


2 4 6 8


2 4 6 8


2 4 6 8


Haunch thickness (in.) Case 1 2 2 2 2 Case 2 6 6 6 6 Case 3 2 2 2 2 Case 4 2 2 2 2 Case 5 2 2 2 2 Case 6 6 6 6 6


Maximum Shear flow Simplified horizontal shear - Vierendeel Model (V/dv) Vierendeel Model Model (kip/ft) (kips) (kip/ft.) 71.16 135.87 180.71 245.76

35.58 33.97 31.62 30.72

68.23 126.73 171.24 231.50

34.11 31.68 29.97 28.94

79.74 144.05 185.95 252.26

39.87 36.01 32.54 31.53

115.70 220.00 294.00 398.45

57.85 55.00 51.45 49.81

75.96 145.23 192.76 262.14

37.98 36.31 33.73 32.77

72.00 134.26 180.46 243.64

36.00 33.57 31.58 30.46

Haunch Spacing (ft)

47.46

Vierendeel Baseline Haunch: 24x24x2 in. Slab Thickness: 7.5 in.

2 4 6 8

44.17


2 4 6 8

47.94


2 4 6 8

66.56


2 4 6 8

45.35


2 4 6 8

42.31


2 4 6 8

Maximum Shear flow Simplified horizontal shear - Vierendeel Haunch Model (V/dv) Vierendeel Model thickness (in.) (kip/ft) Model (kips) (kip/ft.) Case 7 2 133.75 66.87 2 256.88 64.22 75.71 2 340.17 59.53 2 463.35 57.92 Case 8 6 122.89 61.45 6 230.58 57.65 68.00 6 310.91 54.41 6 420.80 52.60 Case 9 2 135.55 67.78 2 259.84 64.96 76.45 2 341.18 59.71 2 464.61 58.08 Case 10 2 206.51 103.26 2 395.19 98.80 106.10 2 525.66 91.99 2 714.04 89.26 Case 11 2 136.20 68.10 2 261.69 65.42 70.70 2 364.35 63.76 2 471.81 58.98 Case 12 6 123.58 61.79 6 232.24 58.06 63.89 6 312.67 54.72 6 423.23 52.90

B-13


Span-to-depth ratio = 20, span = 144 ft Maximum Shear flow Haunch Spacing Haunch thickness horizontal shear Vierendeel - Vierendeel Model (ft) (in.) Model (kips) (kip/ft.)

Simplified Method (V/dv) (kip/ft)

Haunch Spacing (ft)

2

2

97.56

48.78

4

2

187.19

46.80

6

2

275.70

45.95

8

2

359.19

44.90

Case 1 Vierendeel Baseline Haunch: 24x24x2 in. Slab Thickness: 7.5 in. Girder spacing: 6 ft

2

2

4 6 8

2

25.73

2

98.42

24.61

2

144.83

24.14

188.61

23.58


2 4 6 8

6 6 6 6


2 4 6 8

2 2 2 2


2 4 6 8

2 2 2 2


2 4 6 8

2 2 2 2


2 4 6 8

6 6 6 6



Case 7

51.46

Case 2 50.64 96.10 138.55 180.72 Case 3 36.17 64.97 112.59 157.30 Case 4 86.11 164.02 241.46 314.50 Case 5 56.81 109.08 159.89 207.86 Case 6 55.64 105.48 152.38 197.88

Maximum Shear flow horizontal shear - Vierendeel Vierendeel Model Model (kips) (kip/ft.)


38.51


64.34

Case 8 25.32 24.02 23.09 22.59

36.86


2 4 6 8

6 6 6 6

36.17 32.48 28.15 26.22

38.73


2 4 6 8

2 2 2 2

43.06 41.01 40.24 39.31

52.74


2 4 6 8

2 2 2 2

28.41 27.27 26.65 25.98

37.46


2 4 6 8

2 2 2 2

35.90


2 4 6 8

6 6 6 6

27.82 26.37 25.40 24.73

94.14 179.79 260.17 340.37 Case 9 55.68 105.45 195.87 282.01 Case 10 155.45 297.13 438.20 571.07 Case 11 104.31 200.40 294.78 383.84 Case 12 99.54 189.87 275.28 359.50

47.07 44.95 43.36 42.55

60.08

55.68 52.72 48.97 47.00

64.70

77.72 74.28 73.03 71.38

88.05

52.15 50.10 49.13 47.98

61.61

49.77 47.47 45.88 44.94

57.69

B-14



Haunch Spacing (ft)



2 4 6 8

2 2 2 2


2 4 6 8

6 6 6 6


2 4 6 8

2 2 2 2


2 4 6 8

2 2 2 2


2 4 6 8

2 2 2 2


2 4 6 8

6 6 6 6


Maximum Shear flow horizontal shear - Vierendeel Vierendeel Model Model (kips) (kip/ft) Case 1 46.93 91.09 134.03 163.12 Case 2 46.25 89.60 130.75 160.52 Case 3 52.81 99.65 143.16 172.99 Case 4 76.70 149.20 218.20 267.44 Case 5 51.58 100.19 147.16 179.27 Case 6 50.54 97.86 142.81 175.14

23.47 22.77 22.34 20.39 23.12 22.40 21.79 20.07 26.41 24.91 23.86 21.62 38.35 37.30 36.37 33.43 25.79 25.05 24.53 22.41 25.27 24.46 23.80 21.89


Haunch Spacing (ft)


33.70


2 4 6 8

2 2 2 2

32.69


2 4 6 8

6 6 6 6

33.83


2 4 6 8

2 2 2 2

45.35


2 4 6 8

2 2 2 2

33.06


2 4 6 8

2 2 2 2

32.09


2 4 6 8

6 6 6 6

Maximum Shear flow horizontal shear - Vierendeel Vierendeel Model Model (kips) (kip/ft) Case 7 85.88 166.48 245.92 298.05 Case 8 84.19 163.49 237.33 291.97 Case 9 89.55 171.77 250.20 303.20 Case 10 134.51 261.21 384.20 468.29 Case 11 92.22 178.81 263.85 320.10 Case 12 89.60 173.96 252.55 310.57


42.94 41.62 40.99 37.26

57.61

42.09 40.87 39.56 36.50

54.87

44.78 42.94 41.70 37.90

57.83

67.26 65.30 64.03 58.54

77.47

46.11 44.70 43.97 40.01

55.87

44.80 43.49 42.09 38.82

53.29

B-15

B.4 Design Requirement No 9: Vertical Shear Since the slab is supported on the girder only at the locations of the discrete joints, only the web of the girder should be used in the design of the vertical shear reinforcement, without any help from the slab. In a typical bridge, the non-composite loads (i.e. girder, haunch and slab weight) are supported by the girder, while the composite loads (i.e. parapet, wearing surface and transient loads) are supported on the composite slab-girder system. The shear force due to the non-composite loads can be easily determined using the simple Euler-Bernoulli Beam Theory. The shear force due to the composite loads can be determined using one of the following models. The first model is the vierendeel model as discussed earlier. This model gives a more realistic picture of the behavior of the slab-girder system because the slab is connected with the girder only at the locations of the discrete joints. In this case, the shear force that is reported in the bottom chord of the vierendeel model (i.e. the girder), should be used to design for the vertical reinforcement in the girder. The second model is the simplified model using the simple Euler-Bernoulli Beam Theory. In order to compare the effect of using both models on the amount of vertical reinforcement in the girder, the research team selected Case 1 through Case 5 for the 80 ft span, and ran the analysis using these models. The following loads were considered in the analysis: Non-composite loads: Girder weight = 0.798 kip/ft Slab weight = (0.150 kcf)(Slab thickness)(Girder spacing) Composite loads: Barrier weight = (2 barriers)(0.3 k/ft/barrier)/(6 beams) Wearing surface = (girder spacing)(2 inch thick layer)(0.150 kcf) Live Load: HL93 with distribution factor for moment determined using the LRFD Specifications STRENGTH I limit state was used to determine the load factors. Table 11 gives a summary of the parametric study as well as the results of the required shear reinforcement. The last two columns of this table show the comparison of the required spacing of 2 No. 5 bars, between the vierendeel and the simplified model. Analysis of the results has shown that the shear force due to the composite loads obtained from the simplified model is about 10 percent higher than the shear forces obtained from the vierendeel model, regardless the haunch spacing, haunch dimensions, girder spacing or thickness of the slab. However, this increase has a small effect on the spacing of the shear reinforcement. Recommendations for determining vertical shear in composite sections: • •

It is safe and reasonable to use the simplified model to determine the vertical shear due to composite. The girder web without any help from the slab should be used to check for vertical shear.


B-16

Table 11. Vertical Shear due to non-composite and composite loads 80-ft span, Span-to-depth = 20

Vertical shear due to nonHaunch Spacing (ft) composite loads (kips)

Vertical shear due to composite loads (kips) Vertical Vertical Shear Shear (Vierendeel (Simplified model) model)

Total Vertical Shear (kips) Vierendeel model

Simplified model

Vc (kips)

Vs = (Vu/0.9)-Vc (kips)

Spacing of 2#5 bars (in.)

Beta = 2.0, f'c = 6 ksi, Vierendeel Simplified Vierendeel model model model bv = 7 in., dv = 38.4 in.

Simplified model

case 1 Vierendeel Baseline Haunch: 24x24x2 in. Slab Thickness: 7.5 in. Girder spacing: 6 ft

4

160.10 62.92

223.02 183.20

8

167.80

206.19 246.12

41.61

230.72

6.93 231.85

214.74

6.16 6.65

Case 2 Change haunch thickness to 6 in.

4 8


4 8


4 8


4 8

62.92

160.20 167.00

183.20

223.12 229.92

246.12

41.61

206.30 213.85

231.85

6.92 6.68

6.16

162.90 166.48

183.20

225.82 229.40

246.12

41.61

209.30 213.28

231.85

6.83 6.70

6.16

203.97 223.30

255.14

291.78 311.11

342.95

41.61

282.59 304.07

339.44

5.05 4.70

4.21

142.10 157.19

183.20

213.10 228.19

254.20

41.61

195.17 211.93

240.83

7.32 6.74

5.93

Case 3 62.92 Case 4 87.81 Case 5 71.00

* d v was determined based on the height of the girder


B-17

B.5 Design Requirement No 10: Distribution Factors B.5.1 Finite element (FE) details Distribution factor for moment and shear are key components for design of a bridge superstructure. Article 4.6.2.2 of the AASHTO LRFD Specifications provides a group of tables that are used to determine these factors for interior and exterior beams of slab-beam bridges. Provisions of this article come primarily from the research conducted by Zokaie et al. (1991), where the slab was assumed to be supported by a continuous haunch. The RT ran the following investigation to make sure that the provisions of Article 4.6.2.2 are safe to be used with slab-beam bridges where the slab is supported by a system of discrete joints. A three-dimensional (3D) finite element (FE) model was used in the investigation. In this model, the full superstructure of a bridge was modeled. The slab and the haunch were modeled using the 8-node linear reduced integration brick elements (C3D8R). Each supporting girder was modeled using a set of 8 equivalent beams spread over a distance equal to the width of the top flange of the girder. The equivalent beams were modeled using 3D frame elements that take into consideration the shift of the girder centroid from the bottom soffit of the haunch in their stiffness matrix. Geometrical properties of each set of equivalent beams (including height, moment of inertia and cross sectional area) were equal to those of a single beam line. The contact surfaces between the slab and the discrete joints, and between the discrete joints and the girders were fully tied to emulate full composite action. Figure 1 shows a schematic of the FE model used in the investigation.

Figure 1. Details of the FE model used in the investigation for the distribution factors Discrete joints were spaced at 2, 4, 6, and 8 ft, on center (Cases B2, B4, B6 and B8 respectively). Dimensions of the discrete joints for all these cases were taken as follow: Length (parallel to traffic) = 12 in. Width (normal to traffic) = width of the top flange of the supporting girder ABAQUS, a commercial finite element (FE) package; was used to build the FE models. The analysis was conducted at the Colonial One High Performance Computing Facility at the George Washington University. The following steps were used to determine the Live load distribution factor for moment (DFM): 1. Each FE model was then analyzed due to non-composite and composite dead loads plus the LRFD HL-93 live load. Three live load scenarios were considered; i.e. one lane loaded, two lanes loaded and three lanes loaded. In each live load scenario, stresses at the point of maximum bending moment of the interior girder were collected and the resulting bending moment was calculated.


B-18

2. Distribution factor for moment was determined as follows.

( M ) (m) ∑M

DFM j =

j n

i

i =1

Where: DFMj = Live load distribution factor for moment of girder j M j = Live load bending moment of girder j (determined form Step 1) n

∑M i =1

m

i

= Sum of live load moment for all girders

= LRFD multi presence factor = 1.2 for one lane loaded, 1.0 for two lanes loaded, 0.85 for three lanes loaded

The steps used to determine the live load distribution factor for shear (DFV) were similar to the steps used to determine the DFM except that the location of the HL-93 live load model was adjusted to maximize the shear force towards the end of the girder. The DFV was calculated as follow:

DFV j =

(V ) ( m ) ∑V j

n

i =1

i

Where: DFVj = Live load distribution factor for shear of girder j V j = Live load shear of girder j n

∑V = Sum of live load shear for all girders i =1

m

i

= LRFD multi presence factor = 1.2 for one lane loaded, 1.0 for two lanes loaded, 0.85 for three lanes loaded

B.5.2 Calibration of the FE model This case was used to validate the FE methodology developed to model the girders with a set of equivalent beams. The case study consisted of a single 60 ft long, 23.82 inch wide x 72 inch deep beam, and an 8-inch thick slab made composite with the beam. The dimensions of the beam were selected to match the height and moment of inertia of the Florida new I-Beam (FIB72). Three values were considered for the slab width; 1.986 ft, 6 ft and 10 ft. For each slab width, the RT built two FE models. Both models used the 8-node brick element to model the slab. The first model used the 8-node brick element to model the girder, and the slab and beam are connected using surface-to-surface tying. The second model used the equivalent beams concept to model the girder, where the original beam was replaced by 5 equivalent beams as shown in Figure 2, and the slab and beam are connected using surface-to-node tying. The composite slab-beam system was analyzed under the weight of the beam and the slab assuming elastic material behavior, f c' = 5 ksi and wc = 150 pcf for the slab and beam.


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Figure 2. Case study No. 1: The FE models using the 5 equivalent beam lines Table 12 shows the comparison of the maximum deflection between the two models as well as the comparison with the analytical solution using the Bernoulli-Euler Beam Theory that is commonly used in the analysis. Table 13 shows the normal stress distribution at midspan for the case with 120-inch wide slab. Table 12. Case study No. 1: Deflection at midspan (inch)

1.986 ft wide slab 6 ft wide slab 10 ft wide slab

FE Model 1 (Brick Elements for the girder) 0.13291 0.12052 0.11903

FE Model 2 (5 equivalent beams for the girder) 0.13685 0.11822 0.11633

Analytical solution (Bernoulli-Euler Beam Theory) 0.13290 0.11320 0.10951

(Positive deflection indicates downward displacement)

Table 13. Case study No. 1: Normal stresses in the slab (ksi) for slab width = 120 inch Distance from top surface of the slab (in.) 0 (Slab top surface) 2 4 6 8 (slab bottom surface) 8 (beam top surface) 80 (beam bottom surface)

FE Model 1 (Brick Elements for the girder) -0.249090 -0.240882 -0.224429 -0.209201 -0.198836 -0.198836 +0.43776

FE Model 2 (5 equivalent beams for the girder) -0.241012 -0.236619 -0.227858 -0.219192 -0.214896 -0.214896 +0.43776

Analytical solution (Bernoulli-Euler Beam Theory) -0.25776 -0.24037 -0.22299 -0.20560 -0.18821 -0.18821 +0.43774

(Positive stress indicates tension)

B.5.3 Parametric study The RT selected four design examples that represent a wide range of parameters that are commonly used on bridges today. Table 14 summarizes the basic design criteria of these examples. Example 2 was adopted from Design Example 9.1(b) of the PCI Bridge Design Manual (2011), and Example 3 was adopted from Design Example 1 of the American Iron and Steel Institute (1999), with some minor changes.


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Table 14. Basic design criteria of the design examples

The DFM and DFV determined for the four examples was compared with the distribution factors determined according to the AASHTO LRFD Specifications. For each case, the analysis was conducted for a case with a continuous haunch (Case B0) and a haunch spacing from 2 to 8 ft (Cases B2 to B8). In order to study the effect of changing some of the basic criteria on the distribution factors, the following parametric investigation was conducted, as shown in Table 15.


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Table 15. Criteria of the parametric investigation Parameters 1- Girder concrete strength 2- Slab concrete strength 3- Slab thickness 4- Haunch length 5- Haunch thickness

Example considered in the investigation Example 1 Example 1 Example 1 Example 3 Example 3

Change From 8 ksi to 12 ksi From 4 ksi to 8 ksi From 7.5 in. to 10 in. From 12 in. to 24 in. From 2 in. to 6 in.

The distribution factors for moment and shear obtained from the FE analysis and the LRFD Specifications are given in Tables 16 through 19, and Figures 3 through 12. Figure 3 and 4 show the percentage of bending moment generated by the girder and the slab/haunch, respectively. These figures give a clear idea about the effect of increasing the haunch spacing on the distribution of the total moment between the slab and the girder. Table 20 gives the distribution factors after changing some of the basic criteria, and compare them with the distribution factors obtained from the basic example and the distribution factor obtained from the LRFD Specifications as well. The FE investigation on the distribution factors shows that: 1. The DFM and DFV of the AASHTO LRFD Specifications are always higher than those obtained by the FE analysis regardless the number of loaded lanes, spacing between the discrete joints, type of the supporting girders, and span length of the bridge. This observation is consistent with the results obtained from similar previous studies that provided comparison between the LRFD DFM with DFM determined by FE analysis. For example, Parr et al. (2001) found that the DFM obtained from the FE analysis was 6 to 28 percent lower than that obtained using the LRFD DFM. Also, see May (2008) and Gheitasi and Harris (2014) had similar observations. The RT team believes that modeling the slab as a continuum using solid brick elements allows the analysis to capture the arching effect inside the slab and to realistically distribute the live load to a relatively large number of girders. Also, the RT believes that the grillage analysis, that was used in early 1990s (Zokaie et al. 1991) to develop the formulas for the distribution factors and adopted by the LRFD Specifications (2015), was modeled the slab as “wire frame” element, and therefore did not fully capture the multi-dimensional behavior of the slab. It led to relatively high (conservative) values of distribution factors. 2. The DFM and DFV increases as the spacing between the discrete joints increases. However, this increase is insignificant. 3. Investigation of the DFM shows that percentage of moment resisted by the girder (compared to that resisted by the slab) slightly increases when the spacing between the discrete joints increases from 2 to 8 ft. This behavior is illustrated in Figures 11 and 12, which give the breakdown of the bending moment between the slab and the girder. The FE analysis also shows almost no increase of the bending moment resisted by the girder alone as the spacing between joints increases from 2 to 6 ft. 4. The DFV is not sensitive to the spacing between the discrete joints.


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6. The RT believes that lower values of DFM and DFV could be achieved from the FE analysis if the traffic barriers and intermediate diaphragms were incorporated in the analysis. This is because the barriers and diaphragms increase the stiffness of the deck and enhance its ability to distribute live load to more girders. For this reason and also there are many variations of barriers and intermediate diaphragms across the United States, the RT did not incorporate these elements into the analysis. 7. The parametric study conducted to study the effect of changing some of the basic criteria and reported in Table 16 shows that: • • •

Increasing the girder stiffness, increases the girder ability to attract more loads and leads to a minor increase in the distribution factors (Parameter 1). Increasing the slab stiffness, increases the slab ability to distribute the loads to a larger number of girders and leads to a minor decrease in the distribution factors (Parameters 2 & 3). Increasing the haunch thickness or length does have almost no effect on the distribution factors (Parameters 4 & 5).

Recommendation: It is conservative and reasonable to use the distribution factor for moment and shear given by the LRFD Specifications for slab-I Beam bridges, where the slab is supported by discrete joints up to 8 ft spacing.


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Figure 3. Example 1: Span 100 ft, New FIB-36

Figure 4. Example 2: Span 120 ft, PCI AASHTO BT-72


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Figure 5. Example 3: Span 160 ft, Built-up Steel Girder

Figure 6. Example 4: Span 216 ft, Built-up Steel Girder


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Table 16. Distribution factors of Example 1 Example 1 Number DFM of lanes 1 FE 2 1 LRFD 2

Haunch Spacing B0

B2

B4

B6

B8

0.257 0.390

0.259 0.398

0.256 0.391 0.385 0.533

0.264 0.391

0.265 0.403

Example 1 DFV FE LRFD

Table 17. Distribution factors of Example 2

Haunch Spacing

Number of lanes 1 2 1 2

B0

B2

B4

B6

B8

0.500 0.680

0.500 0.690

0.510 0.690 0.600 0.671

0.510 0.690

0.510 0.690

Table 18. Distribution factors of Example 3 Example 3 DFM FE LRFD

Number of lanes 1 2 1 2

Example 3 Number of DFV lanes 1 FE 2 1 LRFD 2

Example 2 Number DFV of lanes 1 FE 2 1 LRFD 2

Haunch Spacing B0

B2

B4

B6

B8

0.448 0.638

0.454 0.645

0.463 0.655 0.499 0.732

0.472 0.665

0.473 0.665

Haunch Spacing B0

B2

B4

B6

B8

0.602 0.641

0.590 0.670

0.580 0.664 0.720 0.884

0.580 0.667

0.600 0.655

Table 19. Distribution factors of Example 4

Haunch Spacing B0

B2

B4

B6

B8

0.420 0.652

0.420 0.627

0.428 0.663 0.533 0.830

0.425 0.652

0.421 0.650

Haunch Spacing B0

B2

B4

B6

B8

0.801 1.060

0.801 1.061

0.793 1.063 0.870 1.130

0.801 1.061

0.782 1.062


Example 2 Number DFM of lanes 1 FE 2 1 LRFD 2

Example 4 Number DFM of lanes 1 FE 2 1 LRFD 2 Example 4 Number DFV of lanes 1 FE 2 1 LRFD 2

Haunch Spacing B0

B2

B4

B6

B8

0.335 0.487

0.336 0.489

0.420 0.501 0.434 0.674

0.419 0.494

0.429 0.506

Haunch Spacing B0

B2

B4

B6

B8

0.617 0.773

0.620 0.774

0.625 0.774 0.760 0.952

0.625 0.773

0.624 0.773

B-26

1.200 1.100 1.000 0.900 0.800

DFM

0.700 0.600

LRFD: Two lanes

0.500 0.400

LRFD: One lane

0.300 0.200

One-Lane

0.100

Two Lanes

0.000 B0

B2

B4

B6

B8

Haunch Spacing 1.200 1.100 1.000 0.900 0.800

LRFD: Two lanes

0.600

LRFD: One lane

DFM

0.700

0.500 0.400 0.300

One-Lane

0.200

Two Lanes

0.100 0.000 B0

B2

B4

B6

B8

Haunch Spacing

Figure 7. Distribution factors of Example 1


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1.200 1.100 1.000 0.900 0.800

LRFD: Two lanes

DFM

0.700 0.600 0.500

LRFD: One lane

0.400 0.300

FE: One Lane

0.200

FE: Two Lanes

0.100 0.000

B0

B2

B4 Haunch Spacing

B6

B8

1.200 1.100 1.000 0.900

LRFD: Two lanes

0.800

LRFD: One lane

DFV

0.700 0.600 0.500

FE: One Lane

0.400

FE: Two Lanes

0.300 0.200 0.100 0.000 B0

B2

B4

B6

B8

Haunch Spacing



B-28

1.200 1.100 1.000 0.900

LRFD: Two lanes

0.800

DFM

0.700 0.600

LRFD: One lane

0.500 0.400

FE: One Lane

0.300

FE: Two Lanes

0.200 0.100 0.000 B0

B2

B4 Haunch Spacing

B6

B8

1.200

LRFD: Two lanes

1.100 1.000 0.900

LRFD: One lane

0.800

DFV

0.700 0.600 FE: One Lane

0.500

FE: Two Lanes

0.400 0.300 0.200 0.100 0.000 B0

B2

B4 Haunch Spacing

B6

B8



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1.200 1.100 1.000 0.900 0.800

DFM

0.700

LRFD: Two lanes

0.600 0.500

LRFD: One lane

0.400 0.300

FE: One Lane

0.200

FE: Two Lanes

0.100 0.000 B0

B2

B4 Haunch Spacing

B6

B8

1.200 1.100 1.000

LRFD: Two lanes

0.900 0.800

LRFD: One lane

DFV

0.700 0.600

FE: One Lane

0.500

FE: Two Lanes

0.400 0.300 0.200 0.100 0.000 B0

B2

B4 Haunch Spacing

B6

B8



B-30

100

Percentage of moment resisted by Girder

95 one Lane

90

Two Lanes

Percentage

85

Three Lanes

80 75 70 65 60 55

Haunch Spacing (ft)

50 0

2

4

6

8

Figure 11: Percentage of the live load moment generated by the girder (Design Example 2, Concrete Girder, Span = 120 ft) 50 Percentage of moment resisted by Slab & Haunch

45 one Lane

40

Two Lanes

Percentage

35

Three Lanes

30 25 20 15 10 5

Haunch Spacing (ft)

0 0

2

4

6

8

Figure 12: Percentage of the live load moment generated by the slab and the haunch (Design Example 2, Concrete Girder, Span = 120 ft)


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Table 20. Effect of changing the design parameters on the distribution factor DFV (Two lanes)

DFM (Two lanes) Parameter under investigation

B6

B8

LRFD

B6

B8

LRFD

1- Change girder concrete strength of Example 1 From 8 ksi to 12 ksi Base line (Concrete St. = 8 ksi)

0.391

0.403

0.690

0.690

0.694

0.694

0.690

0.690

0.679

0.679

0.690

0.690

0.540

0.540

1.061

1.061

1.061

1.062

1.061

1.061

1.071

1.071

0.533 (Concrete St. = 12 ksi)

0.397

0.414

0.671

2- Change slab concrete strength of Example 1 From 4 ksi to 8 ksi Base line (Concrete St. = 4 ksi)

0.391

0.403

0.671

0.533 (Concrete St. = 8 ksi)

0.365

0.376

3- Change slab thickness of Example 1 From 7.5 in. to 10 in. Base line (Thickness = 7.5 in.)

0.391

0.403 0.533

(Thickness = 10 in.)

0.366

0.360

0.671

4- Change haunch length of Example 3 From 12 in. to 24 in. Base line (Length = 12 in.)

0.652

0.650 0.830

(Length = 24 in.)

0.649

0.640

1.130

5- Change haunch thickness of Example 3 From 2 in. to 6 in. Base line (tThickness = 2 in.)

0.652

0.650 0.830

(Thickness = 6 in.)


0.667

0.657

1.130

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APPENDIX C SHOP DRAWINGS This appendix presents the shop drawings and pictures taken during production of the Precast Panels and Large Scale Concrete Beam used in the experimental program


C-1

Figure 1. Details of the 3-ft long precast panels used for all push-off specimens (with concrete and steel girders) NOTE: The top lip of the shear key was made of solid thickness of 2 inches during fabrication


C-2

Figure 2. Details of the 6-ft long precast panels used for the large scale beam with concrete girder NOTE: The top lip of the shear key was made of solid thickness of 2 inches during fabrication


C-3

Figure 3. Details of the 2-ft long precast panels used for the large scale beam with concrete girder NOTE: The top lip of the shear key was made of solid thickness of 2 inches during fabrication


C-4

Figure 4. Details of the 6-ft long precast panels used for the large scale beam with steel girder NOTE: The top lip of the shear key was made of solid thickness of 2 inches during fabrication


C-5

Figure 5. Details of the 2-ft long precast panels used for the large scale beam with steel girder NOTE: The top lip of the shear key was made of solid thickness of 2 inches during fabrication


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Figure 6. Wood forms used for fabrication of the precast deck panels

Figure 7. 2-ft long precast panels used for the large scale beam with concrete girder


C-7

Figure 8. 2-ft long precast panels used for the large scale beam with steel girder

Figure 9. Precast deck panels in the storage yard

Figure 10. 6-ft long precast deck panels in the storage yard used for the large scale beam with concrete girder


C-8

Figure 11. 6-ft long precast deck panels in the storage yard used for the large scale beam with steel girder

Figure 12. Shear key after sand blasting


C-9

Figure 13. General dimensions of the concrete girder


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Figure 14. Details of the concrete girder


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Figure 15. Details of the shear connector assembly

Figure 16. Shear connector assembly


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