prestressed concrete
yeney
03-DesignOfCurvedSplicedPrecastConcreteUBeamBridges.pdf
A PCI Report
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F i r s t E d i t i o n
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B a l l o t e d b y t h e P C I C o m m i t t e e o n B r i d g e s
a n d t h e P C I Te c h n i c a l A c t i v i t i e s C o u n c i l
T h i s m a t e r i a l i s d i s s e m i n a t e d u n d e r t h e s p o n s o r s h i p o f t h e U . S . D e p a r t m e n t o f
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U . S . G o v e r n m e n t d o e s n o t e n d o r s e p r o d u c t s o r m a n u f a c t u r e r s . Tr a d e m a r k s o r m a n u f a c t u r e r s ’
n a m e s a p p e a r i n t h i s m a t e r i a l o n l y b e c a u s e t h e y a r e c o n s i d e r e d e s s e n t i a l t o t h e o b j e c t i v e
o f t h e m a t e r i a l . T h e y a r e i n c l u d e d f o r i n f o r m a t i o n a l p u r p o s e s o n l y a n d a r e n o t
i n t e n d e d t o r e f l e c t a p r e f e r e n c e , a p p r o v a l , o r e n d o r s e m e n t o f a n y o n e p r o d u c t o r e n t i t y.
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Phone: 312-786-0300 Fax: 312-621-1114
www.pci.org
200 West Adams Street I Suite 2100 I Chicago, IL 60606-5230 Phone: 312-786-0300 I Fax: 312-621-1114 I www.pci.org
200 West Adams Street Suite 2100 Chicago, IL 60606
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www.pci.org
200 West Adams Street I Suite 2100 I Chicago, IL 60606-5230 Phone: 312-786-0300 I Fax: 312-621-1114 I www.pci.org
200 West Adams Street Suite 2100 Chicago, IL 60606
Phone: 312-786-0300 Fax: 312-621-1114
www.pci.org
C B - 0 3 - 2 0
F i r s t E d i t i o n
G u i d e D o c u m e n t f o r t h e D e s i g n o f
Cu r ve d , S p l i c e d P r e c a s t Co n c r e t e U - B e a m B r i d g e s
B a l l o t e d b y t h e P C I C o m m i t t e e o n B r i d g e s
a n d t h e P C I Te c h n i c a l A c t i v i t i e s C o u n c i l
T h i s m a t e r i a l i s d i s s e m i n a t e d u n d e r t h e s p o n s o r s h i p o f t h e U . S . D e p a r t m e n t o f
Tr a n s p o r t a t i o n i n t h e i n t e r e s t o f i n f o r m a t i o n e x c h a n g e u n d e r D T F H 6 1 ‐ 1 3 ‐ D ‐ 0 0 0 1 0 Ta s k
N o . 5 0 0 9 . T h e U . S . G o v e r n m e n t a s s u m e s n o l i a b i l i t y f o r t h e u s e o f t h e i n f o r m a t i o n . T h e
U . S . G o v e r n m e n t d o e s n o t e n d o r s e p r o d u c t s o r m a n u f a c t u r e r s . Tr a d e m a r k s o r m a n u f a c t u r e r s ’
n a m e s a p p e a r i n t h i s m a t e r i a l o n l y b e c a u s e t h e y a r e c o n s i d e r e d e s s e n t i a l t o t h e o b j e c t i v e
o f t h e m a t e r i a l . T h e y a r e i n c l u d e d f o r i n f o r m a t i o n a l p u r p o s e s o n l y a n d a r e n o t
i n t e n d e d t o r e f l e c t a p r e f e r e n c e , a p p r o v a l , o r e n d o r s e m e n t o f a n y o n e p r o d u c t o r e n t i t y.
200 West Adams Street I Suite 2100 I Chicago, IL 60606-5230 Phone: 312-786-0300 I Fax: 312-621-1114 I www.pci.org
200 West Adams Street Suite 2100 Chicago, IL 60606
Phone: 312-786-0300 Fax: 312-621-1114
www.pci.org
200 West Adams Street I Suite 2100 I Chicago, IL 60606-5230 Phone: 312-786-0300 I Fax: 312-621-1114 I www.pci.org
200 West Adams Street Suite 2100 Chicago, IL 60606
Phone: 312-786-0300 Fax: 312-621-1114
www.pci.org
200 West Adams Street I Suite 2100 I Chicago, IL 60606-5230 Phone: 312-786-0300 I Fax: 312-621-1114 I www.pci.org
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Phone: 312-786-0300 Fax: 312-621-1114
www.pci.orgA PCI Report
Copyright © 2020 By Precast/Prestressed Concrete Institute
First printing, 2020
This document has been prepared and reviewed through an extensive Precast/Prestressed Concrete Institute (PCI) Committee process to present a Guide Document on The Design
of Curved, Spliced U-Beam Bridges. Substantial effort has been made to ensure that all collected data and information included in this report are accurate. PCI, the committee
members, the authors, and the quoted agencies cannot accept responsibility for any errors or oversights in this report, the use of this material, or in the preparation of any design
and engineering plans. This document is intended for reference by professional personnel who are competent to evaluate the significance and limitations of its contents and who are able to accept responsibility for the application of the material it contains. Actual condi-
tions on any project must be given special consideration and more specific evaluation and engineering judgment may be required that are beyond the intended scope of this work. The contents do not necessarily reflect the official views or policies of the agencies men-
tioned, and do not constitute a standard or policy for design or construction.
Library of Congress Control Number: 2020937997 Print book ISBN 978-1-7335488-8-5
Ebook ISBN 978-1-7335488-9-2
All rights reserved. No part of this book may be reproduced in any form without the written permission of the Precast/Prestressed Concrete Institute, except by a reviewer who wishes to
quote brief passages in a review written for inclusion in a magazine or newsletter.
Publisher’s Cataloging-In-Publication Data (Prepared by The Donohue Group, Inc.)
Names: PCI Committee on Bridges, issuing body. | PCI Technical Activities Council, issu- ing body. | Precast/Prestressed Concrete Institute, issuing body, publisher.
Title: Guide document for the design of curved, spliced precast concrete u-beam bridges / balloted by the PCI Committee on Bridges and the PCI Technical Activities Council.
Description: First Edition. | [Chicago, Illinois] : Precast/Prestressed Concrete Institute, [2020] | “A PCI report.” | Includes bibliographical references.
Identifiers: ISBN 9781733548885 (print) | ISBN 9781733548892 (ebook) Subjects: LCSH: Bridges--Design and construction--Handbooks, manuals, etc. | Precast
concrete construction--Handbooks, manuals, etc. Classification: LCC TG300 .G85 2020 (print) | LCC TG300 (ebook) | DDC 624.2/5--dc23
Printed in U.S.A.
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FOREWORD Precast, prestressed concrete has been used extensively in the nation’s highway bridges beginning in 1949. The rigorous construction of the interstate highway system in the 1950s, and the subsequent development of higher performance materials and methods, resulted in the recognition that precast, prestressed concrete is the most durable, cost-effective bridge construction solution for the span ranges in which it is applicable.
PCI is acknowledged to be the body of knowledge of the precast and precast, prestressed concrete industry. Since 1954, PCI has researched, refined, and published the technology of this industry. PCI developed comprehensive guidelines and standards for drafting, design, production, quality control, and installation of precast concrete. It administers the industry’s first and most comprehensive family of certification programs for personnel, production, and erection of precast concrete―all of which are predicated on a continuous process of quality improvement.
This Guide Document for the Design of Curved, Spliced Precast Concrete U-Beam Bridges has been developed as a resource for bridge engineers. In nine chapters, the guide documents the advancement of curved, spliced U-beam bridge technology. This technology, which originated and progressed initially in Colorado over approximately 20 years, has evolved through the collaboration of designers, contractors, and owners. Much of the current technology is in its second or third generation. Agencies and builders have shown interest in replication of curved, spliced U-beam bridge technology in several areas of the United States. However, there are certain areas of practice that have not been quantified. This has made it difficult for owners and the design community to fully embrace the technical solutions needed to design, construct, deliver, and maintain curved, spliced U-beam bridge systems.
There was a great need to capture the new advancements in complex and simple concrete bridge technologies. With assistance provided by the Federal Highway Administration and in collaboration with the American Association of State Highway and Transportation Officials, PCI enlisted a team of subject matter experts and educational course developers to meet this need. In addition to this guide, four training courses have been developed to facilitate the use of the curved, spliced concrete technology and will be available through the PCI eLearning Center. All participants in developing the guide and the associated courses have practical experience in the design of concrete bridge solutions, and many have conducted university research and have NCHRP research program development experience. Teams of subject matter experts reviewed and critiqued each new manual and course.
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TRAINING This Guide Document for the Design of Curved, Spliced Precast Concrete U-Beam Bridges has been developed as a resource for bridge engineers. Four companion courses based on this document also have been developed. In nine chapters and appendices, the guide document presents a summary of current curved, spliced U-beam bridge technology through reference to completed projects and via the use of a prototype example to step though the basics of the design and engineering of these bridge structures.
Four instructor-led training (ILT) courses have been developed and delivered to facilitate the use of this guide. These are now being converted to eLearning modules. The correlation between the chapters of the guide and the four courses is shown in the figure below.
Correlation between the Guide Document for the
Design of Curved, Spliced Precast Concrete U-Beam Bridges and training courses
The Guide Document for the Design of Curved, Spliced Precast Concrete U-Beam Bridges and the related courses present aspects of current technologies through generous reference to past projects and the use of a prototype example. In the example, important aspects of curved, spliced precast concrete U- beam bridge design are discussed and presented in sufficient detail to allow competent designers to replicate and extend this technology.
The target audience of the Guide Document for the Design of Curved, Spliced Precast Concrete U-Beam Bridges and its related courses includes bridge engineers of all experience levels, owners, and contractors with interest in learning about and delivering this developing technology. There is no cost to enroll in of the courses.
Training Course T350
Title: Introduction, Implementation and Delivery
This broad-based course is summarizes the history and more recent development of curved, spliced precast concrete U-beam bridges primarily through reference to several projects. In addition, terminology for components used in this and later courses are defined. An overview of project delivery, selection of design criteria, and specifying a U-beam bridge are presented in five submodules as follows:
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1 Develop understanding of curved, spliced, U-Beam technology • Early development • Typical applications
2. Understand U-beam cross sections, major components of U-beam systems, and fabrication techniques • Precast cross sections • Precast fabrication • Handling and transportation • Components of curved, spliced U-beam systems
3. Understand the role of the designer, specialty engineer, and project specifications in project delivery • Designer role and stated assumptions • The role of the specialty engineer • Project technical specifications • Construction engineering report • Geotechnical topics
4. Understand the role of design criteria in stating important design assumptions, especially those not clearly defined in current design codes • Emerging technology, emerging design codes • Design assumptions • Limit states – permanent structure • Limit states – construction phase
5. Understand critical elements and constraints for preliminary layout and sizing of a curved, spliced U-beam bridge • Typical Section • Falsework towers, strongbacks, and ground splices • Preliminary design guidance
After completing this course, the student will to understand the following:
• History and development of curved, spliced precast concrete U-beam bridge technology • Major components associated with curved, spliced precast concrete U-beam bridges • Design and contractual elements related to project delivery • Applicability of concept and preliminary design engineering
Training Course T353
Title: Modeling, Analysis and Design Considerations
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The second course uses a prototype bridge to develop an understanding of the methodologies and techniques used to model, analyze, and design curved, spliced precast concrete U-beam bridges. Two submodules are presented as follows:
1. Assumptions and techniques to develop a structural model to analyze the bridge • Define prototype bridge • Materials • Section properties • Construction sequence • Model layout • Temporary works and support conditions • Pier fixity • Results • Time-dependent forces and stresses • Deflections, camber, and buildup
2. Critical items for design during temporary phases of construction and in the permanent condition • Handling, transport, and lifting out of forms • Sectional design for ultimate limit states • Sectional design for service limit states • Geometry control
After completing this course, the student will understand: • Modeling and analysis of curved, spliced precast concrete U-beam bridges
− Development of model − Staged construction − Time-dependent effects
• Superposition of stage forces and stresses • Structural behavior and deformations • Basics of plan preparation and deliverables
Training Course T356
Title: Design Details
Curved, spliced precast concrete U-beam bridges require component design of various details. The third course contains one module covering the topics listed below. The course content illustrates possible details for U-beam bridges based on past projects and an understanding of engineering principles for these elements:
• Typical section and post-tensioning • Lid slab and deck • Precast tongue section • Interior haunch • Blisters
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• Diaphragms • Bearings
After completing this course, the student will be able to understand fundamental concepts related to the design and engineering of various design details of curved, spliced precast concrete U-beam bridges.
Training Course T358
Title: Design Example
The fourth course uses examples developed for the prototype bridge. Detailed calculations are presented with commentary related to the engineering of these components. Reference is made to the design criteria presented in the first course.
The course is presented in one module and steps through design examples as follows: • Sample index of calculations • Flexure at service limit state • Flexure at strength limit state • Web design at service limit state - principal tensile stress • Web design at strength limit state • Camber and buildup
After completing this course, the student will be able to:
• Understand the scope of design for a curved, spliced precast concrete U-beam bridge • Prepare calculations for various components of curved, spliced precast concrete U-beam bridges • Understand important design principles of curved, spliced precast concrete U-beam bridges
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DEVELOPMENT AND REVIEW Throughout the development of this document, strict adherence to PCI policies has been followed, including a series of comprehensive reviews. The outline and each draft were reviewed by the PCI Committee on Bridges and the AASHTO Committee on Bridges, Technical Subcommittee on Concrete (T-10). The PCI Committee on Bridges reviewed and balloted the final draft. The document was submitted to the PCI Technical Activities Council (TAC) for assurance that it meets the institute’s standards for technical content and quality guidelines for presentation. Primary and secondary comments resulting from these ballots were resolved by the primary authors and subsequently approved by the reviewing committees.
ACKNOWLEDGEMENTS During the development of this document, the primary authors, along with PCI members Gregg Reese, Maher Tadros, Ozzie Bayrak, Andy Mish, and Reggie Holt spent time to resolve many of the outstanding issues related to known best practices. Their hard work and determination to bring this manual and training forward is appreciated.
Many others in addition to the contracted team engaged in discussions at the meetings and read one or more of the progression of drafts. PCI wishes to thank all these professionals for their time and expertise. Many of the state highway officials who participated in the writing and review of this document are acknowledged below.
This PCI document was developed with the oversight of the PCI Committee on Bridges. The following is a list of the active voting members of this committee at the time this document was balloted.
Finn Hubbard, Chair Fickett Structural Solutions
Reid Castrodale Castrodale Engineering Consultants, PC
Andy Ko STV Incorporated
Glenn Myers, Vice-Chair Atkins North America
William R. Cox (retired) American Segmental Bridge Institute
Todd Lang HDR
Steve Seguirant, TAC Liaison Concrete Technology Corp.
David Deitz Palmer Engineering
Michael Laviolette HDR
Sameh S. Badie George Washington University
Kevin R. Eisenbeis Burns & McDonnell
Z. John Ma University of Tennessee-Knoxville
Mr. Gregory Aaron Banks, PE WSP
Roy L. Eriksson Eriksson Technologies, Inc.
Eric E. Matsumoto California State University
Oguzhan Bayrak University of Texas at Austin
Hussam (Sam) Fallaha Florida Dept. of Transportation
Michael L. McCool Beam, Longest & Neff LLC
Shrinivas Bhide Consultant
R. Jon Grafton Formerly Oldcastle Precast, Inc.
Richard Miller University of Cincinnati
JP Binard Precast Systems Engineering
Mark Hoppe (Retired) Kansas DOT
Andrew Mish Modjeski and Masters Inc.
Richard Brice Washington State Dept. of Transportation
Troy Jenkins Northeast Prestressed Products LLC
Andrzej S. Nowak Auburn University
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Active voting members of PCI Committee on Bridges (cont.)
Pinar Okumus SUNY, University at Buffalo
Gregg Reese Modjeski and Masters Inc.
Eric Steinberg Ohio University
Michael Oliva University of Wisconsin
Bruce W. Russell Oklahoma State University
Yuhe Yang PCI Northeast
Tanarat Potisuk Oregon Dept. of Transportation
Francesco M. Russo Michael Baker International
William N. Nickas, Staff Liaison (Non-voting) Precast/Prestressed Concrete Institute
Chuck Prussack (Retired) Oldcastle Precast Inc.
Monica Schultes MM Schultes Consulting
Mary Lou Ralls Newman Ralls Newman LLC
Rita Seraderian PCI Northeast
The following are consulting members of the PCI Committee on Bridges. Consulting members are not held to the same strict attendance standards as voting members as set forth in the PCI Group Operations Manual. Many of these members attended numerous meetings and participated in committee work including oral and written reviews of the documents.
Tess Ahlborn Michigan Technological University
William Colquett Alabama Dept. of Transportation
Zhengzheng Fu Louisiana Dept. of Transportation & Development
Musa R. Alawneh e.construct Fz LLC
John S. Dick J. Dick Precast Concrete
David Garber Florida International University
Alex Aswad (Retired) Pennsylvania State University
Daniel Dowling Michael Baker International
James S. Guarre Berger ABAM/WSP
James M. Barker The Collaborative Inc.
Bill Dreher (Retired) Wisconsin Dept. of Transportation
Antonio M. Garcia Garcia Bridge Engineers
Dean Bierwagen Stanley Consultants
D. Scott Eshleman Stanley Consultants Inc.
Silvio Garcia Hardesty & Hanover
Scott R. Canfield Johnson, Mirmiran & Thompson Inc.
Mohamed Essili Consultant
Hossein Ghara Volkert
Vijay Chandra VC Consulting LLC
Jim Fabinski EnCon United
Michael Haas Collins Engineers Inc.
Dave Chapman Jr. Knife River Corporation Northwest
Matt Farrar Idaho Dept. of Transportation
Ziad Hanna Alfred Benesch & Company
Francisco De Jesus Chitty Florida International University
Pedro Fernandez David Evans & Associates
Susan Hida Caltrans
Mi Geum Chorzepa University of Georgia
Gregg Freeby Formerly Texas Dept. of Transportation
Fouad Jaber Nebraska Dept. of Roads
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Consulting Members of the PCI Committee on Bridges (cont.)
Brian Jenner Forterra Building Products
Robert J. Peterman Kansas State University
Christopher Michael Vanek WSP
Bruce Johnson (Retired) Oregon Dept. of Transportation
Scott Phelan David Evans and Assoc.
Colin Wayne Van Kampen Modjeski and Masters Inc.
Sam Keske Wiss, Janney, Elstner Associates Inc.
Basile G. Rabbat (Retired) Consultant
Edward Wasserman Modjeski and Masters Inc.
Bijan Khaleghi Washington State Dept. of Transportation
Hugh David Ronald Atkins North America
Daniel Werner Plum Creek Structures
Mary Ellen Kimberlin Ohio Prestressers Association
Joe E. Salvadori Michael Baker International
Kevin Western Minnesota Dept. of Transportation
Charles W. Leidholdt Hamilton Form Company Ltd.
Steven L. Schwarz HR Green Inc.
Chris White Volkert
Lisette Shana Ludena T.Y. Lin International Group
Gudmund Setberg Caltrans
Hartanto Wibowo Iowa State University
Tom Macioce Pennsylvania Dept. of Transportation
Mohsen A. Shahawy SDR Engineering Consultants, Inc.
Christopher S. Williams Purdue University
Marc Maguire University of Nebraska – Lincoln
C. Shawn Sun Louisiana Technical University
Brian Witte Parsons
Farshad Mazloom Kie-Con Inc.
C. Douglas Sutton (Retired) Purdue University
Carin L. Roberts-Wollmann, PE Virginia Polytechnic Institute and State University
Bob Mills Hamilton Form Company, Ltd.
Maher Tadros e.Construct
Wael Zatar Marshall University
George Morcous University of Nebraska – Lincoln
David A. Tomley Thompson Engineering
Miloslav Zeman Dura-Stress Inc.
Azam Nabizadeh University of Wisconsin – Milwaukee
Kyle Turner Michael Baker International
The following current and past members of the AASHTO Subcommittee on Bridges served on the Technical Committee for Concrete (T-10). Many of these engineers are also voting and consulting members of the PCI Committee on Bridges. They also served as an advisory group with the FHWA- AASHTO-PCI Contract task order no 5010 (DTFH61-11-D-00010-T-5010), “Advanced Precast Element Design and Construction State of Practice,” under which this product was developed.
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Many state highway agency employees and AASHTO staff reviewed draft documents and work plans. Below are listed those that routinely participated in this multiyear endeavor.
Kevin Western (Chair T-10) Minnesota Dept. of Transportation
Strat Cavros AASHTO Staff
Arielle Ehrlich Minnesota Dept. of Transportation
Matt Farrar (Vice Chair T-10) Idaho Dept. of Transportation
Nancy Daubenberger (past member) Minnesota Dept. of Transportation
Jamie Farris Texas Dept. of Transportation
Patrica Bush AASHTO Staff
Bill Dreher (Retired) Wisconsin Dept. of Transportation
Gregg Freeby (Retired) Texas Dept. of Transportation
Zhengzheng (Jenny) Fu Louisiana Dept. of Transportation & Development
Bruce Johnson (past member) Oregon Dept. of Transportation
Tanarat Potisuk Oregon Dept. of Transportation
Sue Hida (past member) Caltrans
Bijan Khaleghi Washington State Dept. of Transportation
Will Potter Florida Dept. of Transportation
Mark Hoppe Kansas Dept. of Transportation
Robert Landry (retired) New Hampshire Dept. of Transportation
Gudmund Setberg Caltrans
Reggie Holt (Ex Officio member) Federal Highway Administration
Tom Macioce Pennsylvania Dept. of Transportation
Loren Risch (Retired) Kansas Dept. of Transportation
Fouad Jaber Nebraska Dept. of Roads
Jim McDonnell AASHTO Staff
PCI staff and the institute’s many dedicated members would like to express their gratitude to Jim McDonnell, Patricia Bush, and Strat Cavros of the AASHTO staff for the opportunity to serve as subconsultant on this Federal Highway Administration assignment. Their project management, guidance, and patience throughout this assignment have been invaluable and are deeply appreciated. The forward-thinking conceptualization of the need for this guide by Reggie Holt of the Federal Highway Administration should also be acknowledged as key to the project’s success. Kris Brown, John Dick, and Henry Russell served as technical editors for this document and the courses.
Lastly, a thank you to the primary authors, Bob Anderson and Trevor Kirkpatrick of AECOM Technical Services, Inc. Their willingness to meet multiple times with interested engineers, the PCI Committee on Bridges, and AASHTO T-10, the technical committee on concrete design, to harmonize the text of this guide and its four companion courses is a great contribution to advancing the use of this emerging concrete bridge technology, today and for generations to come.
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INFORMATION FOR USERS
U1.0 About This Document This document is available as an electronic “eBook” and in a hardcopy version. A simple log-in to the PCI website is all that is needed to download this and other free resources. The print on demand hardcopy version must be purchased through the PCI Bookstore for a small fee.
U1.1 Structure of the Document
U1.1.1 Using Links Links are provided from the Table of Contents to all numbered sections. The user may conveniently jump to a page number or to a section number. Links are provided to the websites of many of the cited references and to topics for additional information.
U1.1.2 Numbered Paragraphs Each main section in the text is identified with a decimal numbering system similar to the system used for various AASHTO specifications and the PCI Bridge Design Manual. This is the system used to organize this page you are reading. The hierarchy of the system is also apparent by the type size and font used in the titles of the sections.
U1.1.3 Page Header The header on every page identifies the subject and the title of the document.
U1.1.4 Page Footer The lower right corner shows the month and year of publication. In the center is the page number. Revised pages will show “a,” “b,” etc. following the page number and a new date in the right corner. This method will be useful in determining the most current revision.
U1.1.5 Figures and Tables All figures and tables are numbered to indicate the section where they first appear. Example: Figure 3.2-1 is found in Section 3.2 and Figure 3.2-2 is the second figure to appear in the same section. Figures and tables referenced in the text are in bold type.
U1.2 Revisions and Registration Revisions to this document are expected. To receive revisions, or notices of revisions, it is necessary to register your copy of the guide. This registration is automatically created if you use the PCI Bookstore to download your eBook copy.
U1.2.1 Registering Your Copy There is no cost or obligation to be registered. Those obtaining an eBook through the PCI website will be automatically registered to the email address registered.
U1.2.2 Errors and Omissions Your help will be appreciated in locating errors and identifying omissions. Please contact PCI with your suggestions at [email protected].
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U1.2.3 Dissemination of Corrections Corrections to this document if required will be assembled and a notice emailed to those registered. The replacement pages will readily identify the change and the page will be identified as revised in the footer.
Two methods are used to disseminate changes. Simple corrections, revisions, and improvements will be posted as “Errata” on the PCI Publications website, https://www.pci.org/publicationerrata. Or, select “Errata” on the Publications home page, then look for the title of this document.
Complex revisions that involve more than a few pages may require the user to redownload the entire document. There will be no cost for this download. Instructions will be emailed as noted above.
In the future, when a new edition is required, an email will notify registered users. Please keep your contact information current so you can be notified.
U1.3 Exchange of Suggestions
U1.3.1 Send Your Suggestions Your suggestions and comments concerning this document will be greatly appreciated. Call, write or e- mail to “Bridge Engineer” at the location and telephone number on the inside cover page, or email [email protected].
U1 3.2 Our Suggestion We strongly urge the designer, in the early stages of a project, to contact one or more PCI-Certified precast concrete manufacturers. The manufacturer can advise about local experience and capability. The producer can often help with suggested solutions and cost estimates. They can provide specific design information about special local, state or regional precast sections. A current list of PCI-Certified producers is readily available on the PCI website at www.pci.org.
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES___TABLE OF CONTENTS
TOC- 1 (April 2020)
TABLE OF CONTENTS TABLE OF FIGURES ........................................................................................................................................... TOF-1
CHAPTER 1 CURVED, SPLICED PRECAST CONCRETE U-BEAM CONCEPT ....................................... 1-1
1.1 GENERAL ................................................................................................................................................... 1-1
1.2 OBJECTIVE ................................................................................................................................................. 1-1
1.3 LIMITS OF APLICABILITY.................................................................................................................... 1-2
1.4 DEFINITIONS AND GLOSSARY OF TERMS .................................................................................... 1-2
1.5 NOTATION ................................................................................................................................................. 1-4
1.5.1 Loads ................................................................................................................................................... 1-4
1.5.2 General ............................................................................................................................................... 1-5
1.6 UNITS .......................................................................................................................................................... 1-6
1.7 REFERENCE CODE ................................................................................................................................. 1-6
CHAPTER 2 - IMPLEMENTATION OF CURVED, SPLICED U-BEAM SYSTEM .................................... 2-1
2.1 GENERAL ................................................................................................................................................... 2-1
2.1.1 Review of Projects ......................................................................................................................... 2-1
2.1.2 U-Beam Cross Section .................................................................................................................. 2-3
2.1.3 Span-to-Depth Ratios ................................................................................................................... 2-3
2.2 FABRICATION AND CONSTRUCTION ............................................................................................. 2-4
2.2.1 U-Beam Fabrication ...................................................................................................................... 2-4
2.2.2 Transportation in Yard ................................................................................................................ 2-7
2.2.3 Transportation to and at Site .................................................................................................... 2-9
2.2.4 Temporary Falsework and U-Beam Placement .............................................................. 2-11
2.2.5 Lid Slabs .......................................................................................................................................... 2-14
2.2.6 Closure Joints ................................................................................................................................ 2-15
2.2.7 Post-Tensioning ........................................................................................................................... 2-15
2.2.8 Deck Screeding ............................................................................................................................. 2-18
CHAPTER 3 - PROJECT DELIVERY ..................................................................................................................... 3-1
3.1 DESIGNER ROLE AND STATED ASSUMPTIONS .......................................................................... 3-1
3.2 SPECIALTY ENGINEER ROLE AND SUBMITTALS ...................................................................... 3-2
3.3 TECHNICAL SPECIFICATIONS ........................................................................................................... 3-3
3.3.1 Erection Plan ................................................................................................................................... 3-3
3.3.2 Geometry Control Procedures .................................................................................................. 3-4
CHAPTER 4 - DESIGN CRITERIA ........................................................................................................................ 4-1
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4.1 GENERAL.................................................................................................................................................... 4-1
4.2 LIMIT STATES – CONSTRUCTION PHASE ..................................................................................... 4-1
4.3 TORSIONAL CHECKS ............................................................................................................................. 4-2
CHAPTER 5 - PRELIMINARY DESIGN AND SPAN LAYOUT ...................................................................... 5-1
5.1 USE OF STRAIGHT AND CURVED SECTIONS ............................................................................... 5-1
5.2 LID SLAB AND DECK.............................................................................................................................. 5-1
5.3 FALSEWORK TOWERS .......................................................................................................................... 5-2
5.3.1 Temporary Tower Size and Configuration ........................................................................... 5-3
5.3.2 Lateral Loads and Sway Bracing in Towers ......................................................................... 5-3
5.4 STRONGBACKS ........................................................................................................................................ 5-4
5.5 GROUND SPLICING ................................................................................................................................. 5-4
5.6 SECTIONAL DESIGN FOR SERIVE LIMIT STATE......................................................................... 5-5
5.6.1 Span-to-Depth Ratio ..................................................................................................................... 5-5
5.6.2 Parametric Data .............................................................................................................................. 5-5
5.6.3 Effect of Radius ............................................................................................................................... 5-9
5.6.4 Effect of Pier Fixity ..................................................................................................................... 5-10
CHAPTER 6 - MODELING AND ANALYSIS ...................................................................................................... 6-1
6.1 SELECTION OF PROTOTYPE BRIDGE ............................................................................................. 6-1
6.2 MATERIALS ............................................................................................................................................... 6-2
6.3 CONSTRUCTION SEQUENCE AND AGE AT CONSTRUCTION ................................................. 6-2
6.4 SPLICE LOCATIONS AND BOUNDARY CONDITIONS ................................................................ 6-8
6.5 SECTION PROPERTIES ......................................................................................................................... 6-8
6.6 TEMPORARY WORKS ......................................................................................................................... 6-11
6.7 DISTRIBUTION FACTOR ................................................................................................................... 6-11
6.8 PIER FIXITY ............................................................................................................................................ 6-12
6.9 THREE-DIMENSIONAL MODELING – FLEXURE, SHEAR, AND TORSION ...................... 6-12
6.10 PRINCIPAL WEB STRESS .............................................................................................................. 6-15
6.11 TRANSVERSE DECK SLAB ............................................................................................................ 6-16
6.12 GEOMETRY CONTOL PROCEDURES ........................................................................................ 6-17
6.12.1 Camber Requirements .............................................................................................................. 6-17
6.12.2 Rotation of U-Beam Section .................................................................................................... 6-18
6.12.3 Build-Up Calculation and Deck Screeding ......................................................................... 6-19
CHAPTER 7 - DESIGN CONSIDERATIONS ....................................................................................................... 7-1
7.1 PLANT HANDLING, TRANSPORT, AND LIFTING OUT OF FORMS ....................................... 7-1
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7.1.1 Internal Bracing .............................................................................................................................. 7-2
7.1.2 Overturning ...................................................................................................................................... 7-3
7.1.3 Lifting ................................................................................................................................................. 7-3
7.2 SECTIONAL DESIGN FOR ULTIMATE LIMIT STATE ................................................................. 7-7
7.2.1 Longitudinal Reinforcing Check ............................................................................................... 7-8
7.2.2 Transverse Web Reinforcing ..................................................................................................... 7-8
7.2.3 Reinforcing Parameters............................................................................................................... 7-9
7.3 SECTIONAL DESIGN FOR SERVICE LIMIT STATE ................................................................... 7-10
7.3.1 Longitudinal Stress Check ....................................................................................................... 7-10
7.3.2 Principal Stress Check ............................................................................................................... 7-10
CHAPTER 8 - DESIGN DETAILS .......................................................................................................................... 8-1
8.1 TYPICAL SECTION AND POST-TENSIONING ............................................................................... 8-2
8.2 LID SLAB AND DECK DETAILS .......................................................................................................... 8-4
8.3 PRECAST CONCRETE TONGUE ......................................................................................................... 8-5
8.4 INTERIOR HAUNCH CONNECTION.................................................................................................. 8-8
8.5 BLISTERS ................................................................................................................................................ 8-10
8.6 DIAPHRAGM .......................................................................................................................................... 8-13
REFERENCES ......................................................................................................................................................... Ref-1
APPENDIX A - ABBREVIATED STRUCTURAL DESIGN CRITERIA ......................................................... A-1
A.1 INTRODUCTION TO ABBREVIATED STRUCTURAL DESIGN CRITERIA ................................. A-1
APPENDIX B – DESIGN DETAILS ........................................................................................................................ B-1
APPENDIX C – SAMPLE SPECIFICATIONS ...................................................................................................... C-1
APPENDIX D - INTRODUCTION TO EXAMPLE CALCULATIONS ........................................................... D-1
D.1 EXAMPLE TABLE OF CONTENTS FOR CALCULATIONS .............................................................. D-2
D.2 FLEXURE AT SERVICE LIMIT STATE .................................................................................................. D-6
D.3 FLEXURE AT STRENGTH LIMIT STATE ........................................................................................... D-20
D.4 WEB PRINCIPAL AT SERVICE LIMIT STATE PRINCIPAL TENSILE STRESS ...................... D-37
D.5 WEB DESIGN AT STRENGTH LIMIT STATE .................................................................................... D-40
D.6 CAMBER ........................................................................................................................................................ D-59
APPENDIX E - PCI STANDARDS ........................................................................................................................... E1
APPENDIX F - PCI-PROJECT QUESTIONNAIRE RESPONSES ................................................................... F-1
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TABLE OF FIGURES Figure 2.1. Comparison of cross sections of U-beams used for recent projects in Colorado and Florida. ......................................................................................................................................................................... 2-3
Figure 2.2 Specialized casting forms. ............................................................................................................... 2-5
Figure 2.3 U-beam reinforcing details. ............................................................................................................ 2-6
Figure 2.4 Precast concrete section with thickened bottom slab. ........................................................ 2-6
Figure 2.5 U-beam section and straddle carriers. ....................................................................................... 2-7
Figure 2.6 Steel lifting spreader. ........................................................................................................................ 2-8
Figure 2.7 Spreader bar attachments. .............................................................................................................. 2-8
Figure 2.8 Transportation of U-beam to site. ............................................................................................. 2-10
Figure 2.9 Transportation of U-beam at site. ............................................................................................. 2-10
Figure 2.10 Temporary falsework towers .................................................................................................. 2-12
Figure 2.11 U-beam framing. ............................................................................................................................ 2-13
Figure 2.12 U-beam lid slab examples. ......................................................................................................... 2-15
Figure 2.13 U-beam with tongue section. .................................................................................................... 2-17
Figure 2.14 Post-tensioned details. ................................................................................................................ 2-18
Figure 2.15 Deck screeding preparations for U-beam bridge. ............................................................ 2-19
Figure 5.1 Typical layout of deck slab reinforcing. ..................................................................................... 5-1
Figure 5.2 Ground splice. Photo: AECOM. ....................................................................................................... 5-4
Figure 5.3 Span versus span-to-depth ratio of composite U-beam. ..................................................... 5-6
Figure 5.4 Span versus gross area of U-beam section. .............................................................................. 5-6
Figure 5.5 Span versus average weight of post-tensioning. .................................................................... 5-7
Figure 5.6 Span versus maximum web shear reinforcing (per web)................................................... 5-7
Figure 5.7 Extreme top and bottom compression fiber for precast and composite cross sections. ....................................................................................................................................................................... 5-9
Figure 6.1 Prototype bridge elevation and typical section. ..................................................................... 6-3
Figure 6.2 Assumed construction sequence .................................................................................................. 6-4
Figure 6.2 (continued) Assumed construction sequence. ........................................................................ 6-5
Figure 6.2 (continued) Assumed construction sequence. ........................................................................ 6-6
Figure 6.3 Analysis model for prototype bridge. ......................................................................................... 6-9
Figure 6.4 Section properties. .......................................................................................................................... 6-10
Figure 6.5 Flexure in right U-beam from permanent loads. ................................................................. 6-13
Figure 6.6 Flexure in right girder. .................................................................................................................. 6-14
Figure 6.7 Shear in right girder. ...................................................................................................................... 6-14
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Figure 6.8 Torsion in right girder. .................................................................................................................. 6-15
Figure 6.9 Principal web stress........................................................................................................................ 6-16
Figure 6.10 Global longitudinal modeling of transverse section. ....................................................... 6-17
Figure 6.11 U-beam build-up (exaggerated view). .................................................................................. 6-20
Figure 7.1 Torsional analysis and demand. ................................................................................................... 7-4
Figure 7.2 Spreader bar and lifting hooks. ..................................................................................................... 7-4
Figure 7.3 Lifting, transport, and falsework evaluations. ......................................................................... 7-5
Figure 7.4 Deformations and stress on U-beam segment. ....................................................................... 7-7
Figure 8.1 Typical section of prototype bridge. ........................................................................................... 8-2
Figure 8.2 Post-tensioning of prototype bridge. .......................................................................................... 8-3
Figure 8.3 Post-tensioning coupling details at field splice. ...................................................................... 8-4
Figure 8.4 Typical slab reinforcement. ............................................................................................................ 8-4
Figure 8.5 Typical lid slab reinforcement before main deck placement. ........................................... 8-5
Figure 8.6 Typical slab reinforcement detail over top flange. ................................................................ 8-5
Figure 8.7 Tongue extension elevation reinforcement. ............................................................................ 8-6
Figure 8.8 Tongue extension section reinforcement. ................................................................................. 8-7
Figure 8.9 Tongue extension isometric view of reinforcement. ............................................................ 8-7
Figure 8.10 Haunch detail at piers. ................................................................................................................... 8-8
Figure 8.11 Haunch reinforcement detail (assuming construction joint). ........................................ 8-9
Figure 8.12 Plan view of top blister. .............................................................................................................. 8-10
Figure 8.13 Partial elevation of top blister.................................................................................................. 8-11
Figure 8.14 Section of top blister. ................................................................................................................... 8-11
Figure 8.15 Isometric view of top blister. .................................................................................................... 8-12
Figure 8.16 Block-out for top flange post-tensioning blister. .............................................................. 8-12
Figure 8.17 Elevation view of interior diaphragm at pier 2. ................................................................ 8-13
Figure 8.18 Concrete box with centered bearing, similar to diaphragm for prototype. ........... 8-14
Figure 8.19 Diaphragm loads for shear. ....................................................................................................... 8-14
Figure 8.20 Diaphragm beam action due to applied torsional loads. ............................................... 8-15
Figure 8.21 Qualitative strut-and-tie models for diaphragm. .............................................................. 8-16
Figure 8.22 Strut-and-tie model for tendon anchorage force distribution into the diaphragm at ends of unit. ............................................................................................................................................................. 8-17
Figure 8.23 Transverse view of bearing. ...................................................................................................... 8-18
Figure 8.24 Longitudinal view of grouted fixed bearing. ...................................................................... 8-19
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CURVED, SPLICED PRECAST CONCRETE U-BEAM CONCEPT
1.1 GENERAL In North America, the advancement of curved, spliced U-beam bridge technology originated and progressed principally in Colorado over approximately 20 years and has evolved through the collaboration of designers, contractors, and governing agencies. Much of the current technology is in its second or third generation. Many of the predecessor projects were delivered under contractor alternative design proposals, which were supported by the governing agency, and with alternative project delivery systems. This has allowed the technology to receive direct contractor input to obtain constructible and economically feasible solutions.
Agencies and builders have shown interest in replicating curved, spliced U-beam bridge technology in several areas of the country. Indeed, the popularity of the curved, spliced U- beam system as described in this document is increasing exponentially. As more information and design guidance become available, including this document, more technical solutions will be available to governing agencies and the design community to design, construct, deliver, and maintain curved, spliced U-beam bridge systems.
In nearly all documented cases, curved, spliced U-beam bridge systems have resulted in significant savings in initial cost compared with more traditional solutions. Furthermore, this design solution could provide even greater benefits with respect to aesthetics and the life-cycle costs related to longevity and maintenance.
1.2 OBJECTIVE The objective of this document is to provide up-to-date guidelines for preliminary and final design of curved, spliced U-beam systems. Primarily through examples and references to constructed projects, information is presented for the design and detailing of the primary components of curved, spliced U-beam bridge systems. This document is not intended to be all- encompassing, nor should it limit the ingenuity of design professionals in developing innovative solutions. Rather, it serves to communicate the current state of the art as represented by recent successfully completed projects. This document draws on PCI’s State-of- the-Art Report CB-01-12, Curved Precast Concrete Bridges,1 for examples of bridges that have been successfully constructed during the past 20 years. The U-beam system presented in this document relies heavily on the concept of lid slabs, which was developed for those projects in Colorado around the year 2000. The intent of this document is to describe the design and construction of over 20 bridges during the past 15 years. The contemporary prototype example presented is representative of the majority of projects that have been constructed.
It is assumed that individuals employing this document possess a fundamental understanding of pretensioned and post-tensioned concrete. Also, an understanding of modeling and analysis, including behaviors produced by time-dependent effects of concrete, is recommended.
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This document introduces and defines an example bridge for demonstration purposes. The example bridge is considered representative of curved, spliced U-beam bridge systems and is referred to throughout this document.
1.3 LIMITS OF APLICABILITY This document has been prepared and reviewed through an extensive PCI committee process and is intended for use by practicing engineers. It provides information related to the state-of- the-art analysis, modeling, design, and detailing of curved, spliced U-beam bridges. It is intended to supplement and complement existing documents from the American Association of State Highway and Transportation Officials (AASHTO). Substantial effort was made to ensure that all collected data and information included in this document are accurate. PCI, the committee members, the authors, and the quoted agencies cannot accept responsibility for any error or oversights in the guide document, the use of this material, or in the preparation of any design or engineering plans.
Furthermore, this document is intended for use by individuals who are competent to evaluate the significance and limitations of its content and recommendations, and who will accept responsibility for the application of the material herein. Actual conditions on any project must be given special consideration, and more specific evaluation and engineering judgment may be required that are beyond the scope of this work. It is the responsibility of the user of this document to identify, follow, and implement all relevant and appropriate health and safety practices. The user must determine the applicability of all regulatory limitations before applying this document and must comply with all applicable laws and regulations, including but not limited to the U.S. Occupational Safety and Health Administration (OSHA) health and safety standards. This document does not necessarily reflect the official views or policies of the agencies mentioned, and does not constitute a standard or policy of design or construction.
1.4 DEFINITIONS AND GLOSSARY OF TERMS The following terms are used in this document.
Camber — The deformation of the concrete profile at the stage of construction under consideration due to the additive effects of prestress, dead load, support removal, and time- dependent deformations (creep and shrinkage).
Casting bed — A special formwork arrangement, usually consisting of moveable bulkheads of the cross-section shape with side and interior molds capable of horizontal movement, designed and fabricated into an assembly for making single or multiple superstructure spliced U-beam segments.
Closure joints — Cast-in-place concrete sections located between U-beam segments and/or diaphragms. (During erection, all U-beam segments of a span or multiple spans are supported by falsework, strongbacks, or other techniques until the closure joints are placed and have met or exceeded the specified compressive strength and the longitudinal post- tensioning has been installed to make them self-supporting as indicated on the plans.)
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Cover, concrete — Distance between the outermost surface of embedded reinforcement and the closest surface of the concrete.
Deflection — Movement, both translation and rotation, of a member under an applied load.
Development length — The distance required to develop the specified strength of a reinforcing bar or prestressing strand .
Discontinuity — Abrupt change in geometry or loading.
Effective depth of section — Distance measured from extreme compression fiber to centroid of longitudinal tension reinforcement.
Effective prestress — Stress remaining in prestressing steel after all losses have occurred.
Embedment length — Length of reinforcement o r a n c h o r provided beyond a critical section over which transfer of force between concrete and reinforcement may occur.
Erection elevation — The elevation at which a segment is set in the structure at the time it is erected. (This is profile grade corrected by the amount of deflection calculated to occur from that stage onwards. See also “camber.”)
Ground splice - Two U-beam segments properly blocked and made into a single segment on the ground by casting a closure joint between the U-beam segments and subsequently post- tensioning. The combined U-beam segments are then incorporated as one U-beam segment into the permanent structure.
Headed deformed bars — Deformed bars with heads attached at one or both ends to mechanically anchor reinforcement bars in tension as an alternative to standard hooks or development lengths.
Lid slab — A field-cast or precast partial-depth portion of the deck slab located between the top flanges of a single U-beam.
Stirrup — Reinforcement used to resist shear and torsion stresses in a structural member. Stirrups are typically bars, wires, or welded-wire reinforcement either single leg or bent into L, U, or rectangular shapes, perpendicular to or at an angle to longitudinal reinforcement.
Strength, design — Nominal strength multiplied by a strength reduction factor Φ.
Strength, nominal — Strength of a member or cross section calculated in accordance with provisions and assumptions of the strength design method before application of any strength- reduction factors.
Strength, required — Strength of a member or cross section required to resist factored loads.
Strut-and-tie model — A f r a m e w o r k o r truss model of a structural member or of a D region in such a member, made up of struts and ties connected at nodes and capable of transferring the factored loads to the supports or to adjacent B regions.
Transfer length — Length over which the effective pretensioning force is transferred to the concrete by bond and friction in a pretensioned member.
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U-beam segment — A modular section of the superstructure consisting of the U-beam cross- section shape and length as detailed in the plans. U-beam pier segments may have a variable- thickness bottom slab that can be cast monolithically, or as a secondary placement, as detailed in the plans.
1.5 NOTATION This section defines notation used in this document. Notation used in the appendices is defined in those sections.
1.5.1 Loads Permanent loads:
CR = force effects due to creep
DC = dead load of structural components and nonstructural attachments
DW = dead load of wearing surfaces and utilities
EH = horizontal earth pressure load
EL = miscellaneous locked-in force effects resulting from the construction process
PS = secondary forces from post-tensioning for strength limit states; total prestressing forces for service limit states
SH = force effects due to shrinkage
Transient loads:
BR = vehicular braking force
CE = vehicular centrifugal force
CEQ = construction equipment
CLL = construction live load
CT = vehicular collision force
CV = vessel collision force
DIFF = differential (unbalanced) dead load from one cantilever
EQ = earthquake load
EL = locked in forces/stresses from primary and secondary effects of post-tensioning
FR = friction load
IM = vehicular dynamic load allowance
LL = vehicular live load
LS = live load surcharge
PL = pedestrian live load
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SE = force effect due to settlement
TG = force effect due to temperature gradient
TU = force effect due to uniform temperature
WA = water load and stream pressure
WL = wind on live load
WS = wind load on structure
1.5.2 General A = member cross-sectional area
Acp = total area enclosed by outside perimeter of concrete cross section
Af = area of reinforcement required for transverse flexure
Aps = area of prestressed reinforcement steel on the tension face of the beam
As = area of nonprestressed steel in flexural tension zone; or, area of nonprestressed steel in the tie of a strut-and-tie model
Astrand = area of a single prestressing strand (0.217 in.2 for 0.6 in. diameter strands)
Av = area of reinforcement required for longitudinal shear and torsion
b = width of compression face of member
c = distance from extreme compression fiber to the neutral axis
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement
D = depth of composite section
f’c = compressive strength of concrete for use in design
f’ci = design concrete compressive strength at time of transfer of prestress for pretensioned members and at time of initial loading for nonprestressed members; design concrete strength at time of application of tendon force for post-tensioned members
fpc = compressive stress in concrete after all prestress losses have occurred either at the centroid of the cross section resisting transient loads or at the junction of the web and flange where the centroid lies in the flange.
fpe = effective stress in prestressing steel after allowance for all losses
fpu = nominal ultimate stress of prestressing steel (270 ksi for low-lax strands)
fr = modulus of rupture of concrete
I = moment of inertia
L or l = span length
M = moment
N = number of post-tensioning strands
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pc = total length of outside perimeter of concrete cross section
P = factored applied post-tensioning force
R = r a d i u s
R = reaction
tBF = thickness of U-beam bottom flange
T = torsion
Tcr = n o m i n a l torsional cracking resistance
Tu = applied factored torsional moment
V = shear
ρ = reinforcement ratio
= resistance factor
σallow = allowable tensile stress
σservice-PT = service stress without post-tensioning
1.6 UNITS This document uses primarily U.S. customary units.
1.7 REFERENCE CODE All references to the AASHTO LRFD specifications refer to the eighth edition of the American Association of State Highway and Transportation Officials’ AASHTO LRFD Bridge Design Specifications.2 Notation and definitions used here generally conform to those of the eighth edition AASHTO LRFD specifications, but may differ in some cases if needed for the purposes of this document.
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IMPLEMENTATION OF CURVED, SPLICED U-BEAM SYSTEM
2.1 GENERAL Curved, spliced U-beams have been implemented in more than 30 projects since the 1960s, and this number continues to grow. With each success, the scope of such projects broadens.
Numerous areas become more refined and more fully developed with the further application of curved, spliced U-beams, including:
• consistency of design requirements, including those related to handling and transport
• design guidance for concrete torsion
• increased use of high-performance materials, including lightweight concrete
• more efficient cross sections and longer spans
• application of external tendons
This document gives practical guidance for the implementation of curved, spliced U-beams for typical applications related to the current state of the art. This guidance is not meant to limit innovation of designers, fabricators, or builders. Rather, it provides a basis for professionals in the design and construction industry to progress the vital topic of curved, spliced U-beams.
2.1.1 Review of Projects This document builds on the significant body of work presented in PCI’s State-of-the-Art Report CB-01-12, Curved Precast Concrete Bridges,1 which discusses the development and evolution of curved precast concrete structures.
Table 2.1 summarizes recent U-beam designs undertaken in Colorado and Florida. The Florida designs have generally used the standard PCI U-beam shapes presented in appendix F. PCI developed these standards over the past decade through industry collaboration, to promote consistent shapes and span ranges for projects nationwide.
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Table 2.1. Partial summary of recent U-beam designs Bridge name Location Span
configuration, ft
Back span/
main span
Cross
section
@ midspan
Cross
section
@ pier
Deck
thickness
Span/depth
(deck + U-
beam)*
Beam
spacing
RampK,I-
25/SH-270
CO 158-200-200-
200-200-158
0.79 7 ft
(tBF = 6 in.)†
7 ft (tBF = 1 ft 6
in.)
9.0 in. 25.8 24 ft 2 in.
Austin Bluffs
Overpass
CO 132-210-140-110 0.67 7 ft
(tBF = 8 in.)
7 ft
(tBF = 2 ft 0
in.)
10.0 in. 26.8 25 ft 4 in.
Ramp A, SH-
58/l-70
CO 154-205-235-187,
148-205-186,
187-200-200-187
0.8,
0.91,
0.94
8 ft (tBF = 8 1/8
in.)
8 ft (tBF = 8 1/8
in.)
10.0 in. 26.6 19 ft 0 in.
West Bijou St.
over
Monument
Creek
CO 106-135-148-86 0.71 5 ft
(tBF = 6 in.)
5 ft
(tBF = 1 ft 4
in.)
9.0 in. 25.7 20 ft 4 in.
I-25 over US-
85 CO 153-240-154 0.64 7 ft 2 in.
(tBF = 6 in.)
7 ft 2 in.
(tBF = 1 ft 8
in.)
9.0 in. 30.3 18 ft 8 in.
SH-120 /
Arkansas
CO 81-112-145-71 0.49 4 ft
(tBF = 6 in.)
4 ft
(tBF = 6 in.)
8.5 in. 30.8 24 ft 2 in.
I-95
Interchange
@ SR 202
FL 145-200-231-191,
191 -229-1 55
0.83, 0.73,
0.68
7 ft
(tBF = 6 in.)
7 ft
(tBF = 1 ft 8
in.)
9.0 in. 29.8 23 ft 9 in.
SH-85 over
Platte River
CO 147-188-147 0.78 6 ft 6 ft 9.0 in. 27.9 19 ft 4 in.
Bronco CO 86-148-135 0.58, 0.91 6 ft 6 ft 8.0 in. 22.2 25 ft 0 in.
Ramp 1, I-
25/SH-85
CO 145-191-147,
149-170-193-139,
119-177-187-131
0.77,
0.72,
0.7
6 ft
(tBF = 8 in.)
6 ft (tBF = 1 ft 6
in.)
9.0 in. 28.6 22 ft 0 in.
C-470 over
SH-85
CO 133-110-132-
165-160-148
0.93 6 ft
(tBF = 8 in.)
6 ft
(tBF = 1 ft 6
in.)
8.0 in. 24.8 17 ft 6 in.
Arbor Road CO 141-135 3 ft 9 in.
(tBF = 5 in.)
3 ft 9 in.
(tBF = 1 ft 0
in.)
6.0 in. 33.2 9 ft 4 in.
Boggy Creek FL 141-216-202-157,
157-189-216-127
0.65, 0.78,
0.59
7 ft
(tBF = 9 in.)
7 ft
(tBF = 1 ft 9
in.)
9.5 in. 27.7 25 ft 8 1/2
in.
I-25 Trinidad CO 115-131-250-
175-181 0.7 6 ft 5 in. 9 ft 9.5 in.§ 25.5‡ 13 ft 0 in.
Ramp Y CO 100-190-228-
228-230-177
0.78 7 ft 2 in.
(tBF = 8 in.)
7 ft 2 in.
(tBF =1 ft 8
in.)
8.5 in. 29.2 17 ft 6 in.
408/417
Interchange
FL 129-159-159-
159-129
129-159-164-159
139-169-168
134-183-193-169
149-179-149
0.81, 0.81,
0.81, 0.97
0.82, 0.99,
0.73, 0.88,
0.83
7 ft
(tBF = 9 in.)
7 ft (tBF = 1 ft 9
in.)
10.0 in.§ 24.7 19 ft 9 in.
19 ft 9 in.
24 ft 10
in.
24 ft 10
in.
24 ft 9 in.
Note: tBF = thickness of U-beam bottom flange.
* Longest span of the bridge is used for span-to-depth ratio.
† tBF is used if the U-beam is internally haunched.
‡ Depth of composite section at pier (haunched section) is used to calculate span-to-depth ratio.
§ Includes ½ in. sacrificial wearing surface.
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For the projects presented in Table 2.1, the average span-to-depth ratio (L/D) equals 28 for the composite U-beam, beam plus deck slab, with a range from 22 to 33 depending on the project.
Appendix F provides additional information pertaining to parameters from numerous constructed projects.
2.1.2 U-Beam Cross Section The conception and evolution of curved, spliced U-beams has been presented previously.3 Figure 2.1 compares 84 in. deep cross sections for recent projects in Colorado and Florida.
Figure 2.1. Comparison of cross sections of U-beams used for recent projects in Colorado and Florida.
Figures 2.1 shows that the PCI Type U84-4 uses a 10 in. thick web, compared with the 9 in. web thickness shown and commonly used for the Colorado section. The Colorado cross section was designed to allow variable web thicknesses from 7.5 to 10 in., which was achieved by varying the internal forms. The thicker web allows installation of larger tendon ducts and hence larger post-tensioning forces. By contrast, the area and weight of the PCI-U84-4 is slightly larger than the Colorado section. The PCI sections, presented in appendix F, were developed with industry inputs from governing agencies, contractors, designers, and precasters, and represent the most recent evolution of the current state of the art.
2.1.3 Span-to-Depth Ratios Spliced, curved U-beam systems are able to achieve slender span-to-depth ratios of 30:1 and greater with:
• attention to the span layout
• suitable beam spacing
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• use of continuous span units
• moderate curvatures from 750 to 1000 ft in the alignments
Simple spans, inefficient end-span layouts of continuous units, and highly curved alignments less than 750 ft may lead to span-to-depth ratios of less than 30:1.
2.2 FABRICATION AND CONSTRUCTION This section offers a stepwise discussion on fabrication and construction aspects of spliced, curved U-beam bridge systems, from form procurement through integration of the product into the final structure.
2.2.1 U-Beam Fabrication Formwork for spliced curved U-beams generally has the following characteristics:
• ability to articulate in the horizontal plane
• outer form
• interior mold
Section 6.12 includes additional discussion related to precast concrete formwork and geometry control.
Horizontally curved U-beams are cast in sections in steel forms, which can be set to accommodate various radii. Figure 2.2 shows two such forms. The formwork used to cast U- beams is generally chorded at 5 to 8 ft intervals based on what is currently available. The chorded surfaces blend together to give the appearance of a smooth, curved surface. Precast concrete beam manufacturers currently have the ability to cast U-beams with a radius as small as 500 ft; however, smaller radii may be achieved through careful design and construction coordination with local suppliers.
Figure 2.2 shows an example of an outer form and inner mold. The use of self-consolidating concrete has been found to be beneficial to accommodate single-stage concrete placement. Generally, prestressing is applied in phases. Stage 1 prestressing is for individual sections, especially to address handling and transportation conditions, and most commonly consists of internal bonded post-tensioned tendons or pretensioned strands. Unbonded internal or external post-tensioned tendons, or unbonded post-tensioned monostrand tendons, have been suggested for stage 1 prestressing; however, there is no known application of unbonded tendons in existing bridge inventories. These prestressing scenarios may be applied in the yard for lifting and transport and may or may not be considered in final design, depending on local practice. Stage 2 post-tensioning for continuity of the full unit is applied in the field after the sections have been lifted into place and lid slabs, splice closures, and diaphragms have been cast. The prestressed structure then resists remaining dead loads, support removal loads, superimposed dead loads, live loads, and other transient loads. To satisfy unique scenarios, and where deck replacement is not an issue, the designer may use stage 3 post-tensioning, which is applied after the deck has been constructed and gains strength. Additionally, the lid slab may be cast before shipping, if not precluded by weight restrictions.
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As will be discussed in section 7.1, it is structurally advantageous to add prestress after lifting the member from the form and transporting the precast concrete section in the yard and before leaving the plant, to give greater torsional capacity and to control cracking. Reiterating, the initial post-tensioning (stage 1) is normally done all at the same time, generally after the U- beams are lifted from the forms while in yard storage, and always before the tubs are placed on the delivery vehicle. To date, and as discussed in the previous paragraph, projects have used pretensioned strands and bonded and grouted initial post-tensioning tendons to provide the initial prestressing required for stage 1. For the bonded, grouted systems, round and flat ducts have both been used with flat ducts, potentially providing more compact duct arrangements and smaller anchorage zone dimensions. Nevertheless, the use of flat ducts is cautioned in situations where the fluid head of concrete is significant and may result in unacceptable deformations to the ducts during casting.
The precast concrete U-beam sections contain post-tensioning ducts in the bottom flange and webs, and for pier segments, in the top flanges and webs. The sections may be removed from the forms as mildly reinforced members or may be partially post-tensioned if needed to control handling stresses. In some cases, the bottom flange may contain special monostrand tendons that are tensioned before lifting the U-beam from the bed. However it is done, all sections are generally prestressed by post-tensioning before leaving the plant. There are exceptions, where the beam length is short and the radius is large, that will meet criteria with only mild reinforcing steel.
a) Steel casting form. Precast concrete lid slabs are visible in the background.
b) Section of interior mold for casting trapezoidal U-beam.
Figure 2.2 Specialized casting forms.
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Reinforcing bar cages with post-tensioning ducts installed are prefabricated, or “pre-tied”, and lifted into the formwork systems (Fig. 2.3). Cages may also be tied in the formwork based on preference. Figure 2.3(a) shows welded-wire web reinforcement bent in a custom bending machine. Figure 2.3(b) shows the finished fabricated reinforcement cage ready to be inserted in the tub form. The headed reinforcing bar terminations may be used to reduce congestion of this reinforcement as it protrudes into the deck slab.
a) Custom hydraulic machine to bend fabricated no. 5 welded-wire reinforcement.
b) Preassembled reinforcing cage with post- tensioning ducts.
Figure 2.3 U-beam reinforcing details.
a) Prepared for secondary concrete placement.
b) Monolithically cast thickened bottom slab. Photo: Modjeski and Masters.
Figure 2.4 Precast concrete section with thickened bottom slab.
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Figure 2.4(a) shows a two-stage approach to thicken the bottom flange of the precast concrete U-beam. The precast concrete section in Fig. 2.4(a) has threaded reinforcing bar inserted into form savers on the interior faces at the bottom of the webs. The concrete surface has been intentionally roughened to ¼ in. amplitude to improve bond with the secondary concrete casting. This approach saves weight for U-beam segment transportation and eliminates the required modification of the interior form to accommodate the thickening if cast with the U- beam. However, this approach adds labor and materials for the tying of reinforcing bar and the casting of the secondary concrete placement in the field, and necessitates design checks for shear stress and shear reinforcement across the cold joint. For recent bridges in Florida, the contractor was given the option to construct the bottom slab thickening as either precast in the form or as a secondary placement, for which the monolithic option was chosen.4 Figure 2.4(b) shows a monolithically cast thickened bottom flange.
2.2.2 Transportation in Yard Figures 2.5 through 2.7 show straddle carriers, spreader bars, and attachment details used for lifting and handling the U-beams in the casting yard. Straddle carriers are used to lift and maneuver the U-beams. Depending on the precaster’s equipment, spreader bars may be offset to align the lifting force in the same plane as center of gravity of the U-beam section (Fig. 7.3). Clevises and straps are generally used to transfer the horizontal component of the lift weight to the spreader bar.
Figure 2.5 U-beam section and straddle carriers. Photo: Dura-Stress
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Figure 2.6 Steel lifting spreader.
Figure 2.7 Spreader bar attachments.
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2.2.3 Transportation to and at Site Figure 2.8 shows a steerable trucking configuration for transporting precast concrete sections of spliced U-beams. The beams are supported approximately 15% of the overall length from the ends of the unit, that is, near the 0.15 points, to increase the cantilever overhangs and reduce longitudinal and torsional moments at midspan. With this arrangement, negative moments in the cantilevers are increased and both top and bottom compression and tension limits need to be checked. Moreover, the support location should be determined for each stage of construction such as during storage, transport, and handling. Variations of curvature, length, thickened slabs, end diaphragms, and tongue details are factors that affect: 1) the location of the U-beam centroid; 2) the design of stage 1 prestressing; and 3), the selection and optimization of support locations. Similar to spreader bars, and depending on the equipment available to the hauler, the tub can be placed so the centroidal axis of the U-beam align with the center of truck support resistance without inducing overturning into the system. The stresses induced in the U-beam due to these various support locations that exist during construction must be countered with the stage 1 prestressing in order to keep them within allowable limits.
Some longitudinal prestressing must be installed before transport to assist the section in resisting applied forces including torsional cracking limits. As explained in section 7.1 and appendix A, it is recommended by Washington DOT that the section is designed to resist its own self-weight plus dynamic allowances of 20% of self-weight upwards and 20% of self- weight downwards for transport.5 The designer may elect to increase these percentages considering the feasibility of the selected shipping route, hauling equipment, and consideration of local practice. Further discussion in section 7.1.3 indicates that when the beam is erected on temporary supports and before stressing continuity post-tensioning is likely the controlling temporary load case. For more information regarding transportation analysis methodologies, see the PCI Bridge Design Manual.11
a) U-beam at plant, ready for transport.
b) Arrival of U-beam at site. Photo: Modjeski and Masters.
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c) Arrival of U-beam at site.
Figure 2.8 Transportation of U-beam to site.
Figure 2.9 Transportation of U-beam at site. Photo: Modjeski and Masters.
Figure 2.9 shows a photo of a U-beam handled at the job site with eccentric spreader bars, which help to balance U-beam twist associated with a two-crane pick.
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2.2.4 Temporary Falsework and U-Beam Placement An advantage of curved precast concrete construction is that it employs minimal shoring compared with cast-in-place construction. Correspondingly, the layout of temporary falsework, if used, is an important aspect of design. The length of U-beam segments may be influenced by precaster plant lifting capacity, shipping limits, and contractor crane capacity. Site constraints such as clearances to traffic lanes and shoulders, utility interferences and obstructions, and available falsework locations may also dictate the length of U-beam segments. Figure 2.10 shows several examples of feasible tower layouts. In general, the towers are roughly placed at the span’s points of contraflexure to minimize forces at the closure joints. The layout of falsework towers need not be perpendicular to the centerline alignment. For example, the temporary towers can be skewed for a pair of U-beams and the concrete framing of the diaphragms and closure joints can be offset. Also, U-beam lines can be designed completely independently with different splice locations if necessary due to site constraints.
Where insufficient space exists for support from towers below, U-beams can be suspended from above by strongbacks [Fig. 2.11(a)]. Strongbacks are attached to an adjacent U-beam and cantilevered to hang an adjacent U-beam; the other end is typically supported by a shoring tower or permanent pier. In the case of strongbacks, and depending on the length of the cantilevering U-beam, significant additional top post-tensioning, temporary and/or permanent, is generally required to control stress conditions over the piers. Straddle bents and cantilevered shoring bents are other options when there is insufficient space for a conventional tower.
a) Temporary towers located at U-beam splices and resting on foundations supported by precast concrete piles. Photo: J Dick Precast Concrete Consultant.
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b) Single tower used at splice location are cross-braced to withstand hurricane-force winds.
c) Temporary cast-in-place concrete columns with sand jacks and steel positioning beams to support the U-beams at splices. The columns are later removed and discarded.
Figure 2.10 Temporary falsework towers
a) Cantilevered U-beams made integral at pier. Note the drop-in U-beam hung from strongbacks over traffic. Photo: Modjeski and Masters.
b) U-beam supported at integral pier before casting of bedding grout. Photo: Modjeski and Masters.
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c) U-beam tongues support U-beams at abutment.
Figure 2.11 U-beam framing.
Figures 2.11(a) and 2.11(b) show framing configurations with integral pier bents. Whether integral or on bearings, mild steel or transverse post-tensioning is commonly used and extends through the diaphragm and U-beam. In Fig. 2.10(b), the U-beam is temporarily supported by the falsework towers until bedding grout beneath the U-beam is cast. Integral bents eliminate bearings and provide advantages for both initial cost and long-term maintenance. Nonetheless, the use of integral bents needs to be evaluated with attention paid to the articulation of the entire structure composed of superstructure, substructure, and temporary works. The demands primarily due to shrinkage, temperature, redistribution of forces caused by creep, and the associated costs of substructures to accommodate these loads should be considered. In all cases, continuity post-tensioning and the associated compatibility and equilibrium of the continuous system affect pier forces.
Figure 2.11(c) shows the U-beam segment supported by a tongue section at the abutment. The tongue section is also presented in Fig. 2.12, section 8.3, and appendix B. The main function of the tongue section is to install the U-beam directly on the permanent bearing during erection. This eliminates the need for falsework and accommodates thermal movements during construction more reliably than temporary shoring. Early projects had the U-beams stop short of the bearing location and a full-depth diaphragm was cast, which accomplishes the same result as far as the final design is concerned. Thus, the tongue section is primarily a constructability feature. The use of the tongue also allows setting of the U-beam segment while providing a second-stage post-tensioning anchorage zone interface. The remainder of the end
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diaphragm construction is accomplished in the field. The tongue section allows reduction of U- beam segment weight for transport and handling, aids for fit-up tolerances at the abutments, a precast concrete bearing seat, and field installation of the post-tensioning anchorage zone.
During a short window of time in the field operations, that is, before the load is transferred to permanent U-beam bearings at piers, the system is on falsework, closure joints are cast, and before post-tensioning, the U-beam system is sensitive to the effects of settlement at the falsework towers, which will induce tensile stresses over the piers. Design and field inspection protocols should be established to monitor settlement of temporary shoring. Concerns related to settlement at the falsework towers can be mitigated and remedied by: using low bearing pressures for spread footing design, use of deep foundations, monitoring settlements over a period of time before grouting bearings and casting closures, and developing contingency plans including shimming or jacking to correct settlements and/or misalignments. Second- stage post-tensioning should occur shortly after the closures gain strength to limit the time window for potential settlement and also cyclical events related to thermal and shrinkage stresses imposed on early-age (and low-early-strength) closure joint concrete.
2.2.5 Lid Slabs Lid slabs, for which cast-in-place and precast concrete solutions have been employed, are used to close the open cross section and give more torsional resistance to each U-beam of the bridge system. Figure 2.12 shows examples of lid slabs. Lid slabs may be constructed in the precast concrete yard; however, they are generally cast/constructed in the field after the beams are erected on falsework, along with the closure joints between U-beam segments and before the application of main longitudinal post-tensioning. This sequence saves weight during transportation and erection of the U-beams and extends the length of the U-beam segments, which are generally constrained by transport weights. Local practice may allow other lid slab options meeting structural performance and constructability needs.
For either lid slab solution, cast-in-place or precast, the means and methods used for construction are fairly conventional. The designer is alerted to make adequate checks to accommodate horizontal shear flow at the interface of the lid slab and top flanges of the U- beams where the transfer of stresses, due primarily to vertical shear and torsion, occurs. Additionally, cast-in-place or stay-in-place concrete panels contribute to the ultimate positive moment capacity of the section and therefore shear flow across the interface between the lid slab and deck slab should be checked per code provisions.
Field surveys of the U-beams erected on the temporary supports are required to establish the benchmarks for calculating the lid slab elevation at this phase of construction. During erection of the lid slabs (precast or cast-in-place), field survey procedures must be established to set the haunch thickness to the correct geometry and assure the lid slabs are cast to the correct elevation. The lid slab elevation and lid slab haunch must account for anticipated cambers and deflections during subsequent stages of construction.
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a) U-beam at abutment with forms ready for the cast-in-place concrete lid slabs. Photo: J Dick Precast Concrete Consultant.
c) Precast concrete lid slabs stored in the precast concrete plant.
b) Precast concrete lid slabs with deck overhang cantilevers and precast concrete stay-in-place deck panels between U-beams.
d) Removable grout bedding form under precast concrete deck panels.
Figure 2.12 U-beam lid slab examples.
2.2.6 Closure Joints Casting closure joints connecting the ends of the precast concrete U-beam segments is a necessary step before application of second-stage post-tensioning. In general, a minimum gap of 2 ft for the closure joints allows enough space to correct small misalignments of post- tensioning ducts, perform watertight field coupling of ducts in accordance with local practice, give appropriate space and cover to reinforcing at the gap, and allow transition between U- beams erected with slightly different cross slopes or elevations. Thickened sections around the perimeter at closure pours have also been used in shorter splices (approximately 2 ft) to relieve congestion. Gaps of 3 to 4 ft have been used to give more room for post-tensioning jacking and for installation of reinforcing bar at closures.
2.2.7 Post-Tensioning The normal application of first-stage (in the yard) and second-stage (in the field) post- tensioning offers some challenges. For the first-stage post-tensioning (the first-stage may also be pretensioned), there is the need to define this work scope for either the precaster or the
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contractor. The contractor may prefer a sole source for the U-beams, while the precaster may or may not want to self-perform this work item. Hence, the division of work is a contractual issue to be addressed between the contractor and precaster, and is generally within the scope of the post-tensioning supplier/subcontractor. For the installation of second-stage post- tensioning, attention should be given to the physical space for jacks, the trimming of strands during the post-tensioning process, the amount of loss along the tendon length, and installation of strands over long runs of duct. During stressing, and because U-beams can move relative to each other, the post-tensioned structure should be treated as a system and the sequence of stressing examined. This includes the consideration of intermediate diaphragms and possibly deck forms.
In recent projects, a gap of 3 ft at closures and 4 ft at expansion joints has been adequate to successfully tension four 15-strand tendons using end U-beam segments incorporating a tongue section (Fig. 2.13).4 Nonetheless, these distances are considered minimums; second- stage post-tensioning can be difficult and professional installation is recommended. Some suppliers may need more than these minimums, and jacking clearance aspects should be resolved in the design phase or subsequently in review of the shop drawings. Large elongations of several feet can be expected for the initial stressing of a continuity tendon, so a full-size jack stressing from an open end is recommended if possible. Stressing from the opposite end is also common to account for losses along the length of the tendon and can normally be accomplished with a short-stroke jack. Tendon lengths of 890 ft with (19) 0.6 in. strand in 4 in. nominal diameter ducts, and about 1345 ft with (27) 0.6 in. strand in 4.75 in. diameter ducts, have been successfully installed.
Figures 2.14(a) and 2.14(b) show typical post-tensioning details. In Fig. 2.14(b) the closure is the width of the web. Also, because of space limitations and potential post-tensioning and reinforcement congestion, well-consolidated concrete should be achieved. High-flow concrete, self-consolidating concrete, or simply smaller aggregate sizes may be considered to attain good results.
The decision to use unbonded or bonded post-tensioning and the amount of each is left to the designer and the governing agencies. Unbonded (greased and sheathed tendons) are commonly protected at their ends by proprietary caps. For bonded tendons, grouting proceeds subsequent to the tendon stressing. Governing specifications generally prescribe grouting within two weeks after the tendons are seated to their final stress, to prevent corrosion of the strands in the humid environment of the ducts. Procedures and materials for grouting will follow normal protocols established by the engineer and governing agency. This discussion is outside the scope of this document. The designer is alerted to show details and locations for inlets at low points and grout vents to allow for burping of accumulated air, negate voids, and uniform protection of the strands by the grout. Refer to PTI M50.3-12, Guide Specification for Grouted Post-Tensioning,8 for the latest industry guidance related to the grouting of post- tensioning tendons.
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Figure 2.13 U-beam with tongue section.
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a) Post-tensioning anchorages installed at abutment diaphragms.
b) Duct splices and reinforcement ready for closure placement at section splice.
Figure 2.14 Post-tensioned details.
2.2.8 Deck Screeding Deck screeding is performed very similarly to a conventional prestressed concrete beam system (Fig. 2.15). The use of standard overhang brackets is common. The profiles of the beams are surveyed after the second-stage post-tensioning has been applied. The rails for the screed machine are set to account for this as-built survey so that the deck thickness is maintained within the general tolerance specified by the governing agency. The rails are set to produce the target profile taking into account all losses and long-term camber and deflection, as well as creep and shrinkage, from the casting of the deck to a target day (ranging from 4000 days to infinity, depending on preferences of the engineer and governing agency).
For some governing agencies, it is important to consider deck replacement during the design process. In some areas, a major deck rehabilitation or replacement may be necessary during the service life of the bridge. For deck replacement, it is not necessary to reshore the bridge, provided that all post-tensioning was applied before deck placement, and the lid slab, if evaluated to be in good condition, remains in place. If the lids slabs are removed during a deck replacement, it may be necessary to reshore the structure with temporary falsework. Also, lateral forces in the webs due to post-tensioning would need to be accounted for in the rehabilitation if the lid slab is removed, resulting in an open section. For rehabilitations, the entire structure should undergo design checks, including sizing and locations of setting jacks.
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To summarize, an engineer should evaluate the need for temporary shoring and the effects of removal of the deck slab to determine whether the lid slab should remain and only a partial deck removal specified.
Figure 2.15 Deck screeding preparations for U-beam bridge. Photo: AECOM.
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PROJECT DELIVERY Depending on the project delivery method, the contract documents developed by the governing agency, engineer of record (EOR), and contracting team may vary.
For a design-build project, the governing agency may prescribe various performance requirements in terms of the roadway geometrics, horizontal and vertical clearance, load carrying capacity, and durability expectations. Many of the engineering tasks are performed by the design-build contracting team, including the EOR, during the pre-bid to communicate the bidder’s intention, and post-bid to prepare construction documents necessary to build the structures and for governing agency review to confirm compliance with the project’s performance specifications.
For a design-bid-build project, the EOR is employed by the governing agency and generally the contract documents are developed to greater detail during the pre-bid phase. Indeed, the development of precise design-bid-build contract documents is encouraged; nonetheless, they are not intended to preclude innovation and need to provide flexibility for the contractor and his specialty engineer and precast concrete fabricator. The contract documents need to communicate a feasible way to construct the bridge structure and may be modified by the contracting team to suit the chosen means and methods.
This section describes many of the typical design considerations and construction practices that are now being used to build curved, spliced U-beam bridges.
3.1 DESIGNER ROLE AND STATED ASSUMPTIONS Paragraph 2.5.3 of the AASHTO LRFD specifications2 identifies constructability issues that should be considered during design. The EOR should clearly state any assumptions made in the contract documents, and these should be confirmed by the governing agency. The following list discusses several items that the governing agency may desire to be shown.
• stress limits at various stages of construction including
- transfer of prestress and lifting from bed
- transportation
- erection
- temporary erection stresses
- final stresses, including live load
(Refer to section 4 and appendix A for further discussion related to design stress limits.)
• assumed construction loads
• post-tensioning loss assumptions
• post-tensioning staging, sequence, and verification of jacking clearances
• transportation and construction loading criteria and construction load factors
• determination of splice regions
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• U-beam lifting, bracing, pick points, and storage locations
• U-beam erection and stressing sequences, including age of U beams, cast-in-place closure joints, f’c, and f’ci
• expected short- and long-term deflections and cambers
• expected build-ups
3.2 SPECIALTY ENGINEER ROLE AND SUBMITTALS The project specifications for curved, spliced U-beam projects generally require that the contractor retain a competent, knowledgeable specialty engineer who is registered in the project’s state and has a minimum amount of experience in the design and construction of complex post-tensioned concrete structures, staged construction, and temporary works. Specific recommendations for registration and length of experience records are the purview of the governing agency and EOR. The specialty engineer often works with the contractor to identify possible savings that can be realized through adjustment of section lengths or other procedures that take advantage of the contractor’s specific expertise and equipment. All such revisions are normally coordinated with and approved by the EOR. Depending on the project delivery method and contractual setup, the EOR and specialty engineer may be the same or separate entities, and may be a representative to either the governing agency or the contractor.
The owner often specifies the duties and responsibilities of the specialty engineer. These duties may include the following:
• Step-by-step erection sequence, ages of U-beams at erection and closure pours .
• Temporary works and bracing.
• U-beam lifting, bracing, pick points, and storage locations.
• Define construction loads.
• Falsework locations and loads.
• Construction controls: define maximum deflections, cambers, and build-up thicknesses.
• Post-tensioning and grouting procedures and equipment; quality assurance.
• Field survey and geometry control.
• Time-dependent analysis with stress and force summary is recommended and should be specified in the contract documents.
• Truck and crane placement with radius of operation diagrams.
• If a thickened bottom slab is required, determine details and whether it should be field-cast or plant-cast.
• Determine location and forming for interior post-tensioning blisters and stressing buttresses (if required). Note that locations of interior post-tensioning blisters should
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be clearly called out on the contract documents and are only the responsibility of the specialty engineer if there is a material change.
• Temporary supports or strongbacks.
• Lid slab design and detailing.
• Construction sequence.
As recommended industry practice, the sample technical specification included in appendix C provides for a separate pay item for specialty engineering of curved, spliced, precast, prestressed concrete U beams.
3.3 TECHNICAL SPECIFICATIONS Appendix C contains an example set of technical specifications for a representative design-bid- build project and for the bidding of an alternate bridge design. Key elements of the specifications are highlighted in the following sections. To clarify that the erection plan in section 3.3.1 is a required submittal document, it may be worthwhile to include a bid item for this component in design-bid-build project delivery scenarios.
The contractor, or his agent, shall coordinate submittals and information included in the erection plan. Specific guidance related to this topic is beyond the scope of this document; further information can be found in Brice (2018).9
3.3.1 Erection Plan The erection plan is a submittal document developed by the contractor’s specialty engineer that communicates intended means and methods to be used during erection of the U-beams and includes the basis of design, erection sequence and operations, and geometry control procedures. The erection plan may follow the construction sequence outlined in the contract documents or, with approval of the EOR, the design scheme presented in the contract documents can be modified by the specialty engineer to recognize unique project requirements and innovations developed by the contractor.
Significant components of the erection plan are the contractor’s intended construction sequence and means and methods to achieve the U-beam erection. Steps of an example construction sequence, with discussion related to means and methods, are listed as follows:
• Construct foundations, piers, and abutments; post-tension pier caps if necessary and grout ducts.
• Erect temporary supports or strongbacks.
• Fabricate U-beams; tension and grout bottom flange ducts.
• Erect shoring towers. Some U-beams may be spliced together on the ground, but this is unusual and requires large cranes for the heavier lifts.
• Erect U-beam segments with bracing.
• Cast all bottom slab thickening, closure joints, and diaphragms over interior piers including expansion piers.
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• Connect substructure to superstructure if made integral.
• Close open topped U-beams by forming and casting relatively thin (approximately 4¼ in. thick) lid slabs, or place and grout precast concrete lid slabs to make the section torsionally rigid. Grout for precast concrete lid slabs should be confined to the limits of the lid slab to leave the rest of the top flange available for forms or precast concrete slabs that span between U-beams.
• Tension full-length tendons. During this stage, the U-beams lift off the temporary supports and only bear on permanent supports.
• Tension bottom or top continuity tendons, if required.
• Grout all ducts.
• Remove shoring towers.
• Form and cast the full-thickness deck slab, or install precast concrete stay-in-place deck panels between U-beams and cast the remaining structural deck. Options may exist to cast the deck shored or unshored. A later stage of post-tensioning may also be possible after the deck has been cast.
• Cast approach slabs and bridge rails.
• Install expansion joints.
• Install membrane or latex-modified concrete topping, if required.
While not always specific requirements, the preceding list describes components that are commonly required by the contract documents.
3.3.2 Geometry Control Procedures U-beam casting is similar to any other precast concrete girder, with the additional concern of setting the curved forms on the desired radius before casting. The setup in the precast concrete yard includes capability for assessing the geometry of the setup before casting and transport.
The geometry control procedures cover all geometry control operations in the precast concrete yard and at the project site and is compatible with the chosen methods of casting and erection, including erection survey, elevation and alignment control.
The geometry control procedures portion of the erection plan includes:
• A geometry control procedure for survey controls and procedures, observations, checks, computational and/or graphical methods and correction techniques. The length, sweep, and camber for the precast concrete U-beam segments fall under owner tolerance specifications, which are followed by the EOR and specialty engineer with camber calculations and later measurement.
• U-beam setting elevations for temporary falsework and permanent piers and proposed methods to make adjustments to these elevations to account for tolerances and settlement of the temporary foundations.
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• The U-beam build-ups at each web to be set in the field include the theoretical geometric horizontal alignment, profile grade, and superelevation appropriately combined with the camber accounting for future deformations. The U-beams are set on falsework; for lid slabs, survey the construction elevations (fills) at tenth or twentieth points, and then survey to determine the construction elevations (fills) for casting the deck. U-beams do not require complex geometry control plans like those of segmental bridges and are essentially no different than conventional girders except that pairs of webs for a particular beam rotate about the U-beam axis.
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4.1 GENERAL Articles 5.12.3 and 5.12.3.4 of the AASHTO LRFD specifications2 give the primary code guidance regarding design aspects of curved, spliced precast concrete U-beam bridge systems. Topics including shear and torsional checks and guidance related to erection stage analysis may be considered by the design professional and the governing agency. This document echoes that guidance. AASHTO LFRD specifications Article C3.12.3 gives guidance related to the exclusion of thermal gradient effects based on local performance experience. As the state of the art moves forward, there will be further consensus developed for the interpretation of AASHTO LRFD specifications and it is likely design specifications will be broadened to fully encompass the general case of curved, spliced precast concrete U-beam design. AASHTO LRFD specifications provides supplementary guidance in Article 5.12.5 for special concrete design cases.
Note that the discussion of this section is brief and will be expanded on by use of example in later sections and by information found in the appendices.
4.2 LIMIT STATES – CONSTRUCTION PHASE Construction of the U-beam system includes the following load phases:
• Plant handling:
- cast U-beams and move to storage (with or without prestress);
- consider pick points and dunnage locations and stress limits.
• Transportation to site:
- post-tension U-beams before transport;
- support conditions during transport.
• Erection at site:
- placement of U-beams on falsework;
- weight of casting diaphragms, closures and lid slabs on erected U beams;
- effects of longitudinal temperature changes and construction live loads;
- effects of wind on bridges during construction;10
- stressing of any partial continuity tendons, if appropriate;
- support of drop-in U-beams on strongbacks, if appropriate;
- cast remaining closures, check effects of temperature changes;
- stress longitudinal continuity post-tensioning;
- remove falsework towers;
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- add weight of wet deck concrete;
- add superimposed loads on composite deck and U-beam.
At each of these steps, checks are performed to ensure the service and strength limits of the U- beams and other associated elements, including temporary works, are satisfied and the bridge system remains stable.
As stated in section 3.1, assumptions by the EOR are included in the contract documents. A description of construction loads and suggested load combinations are found in appendix A, section A3.7. For service level checks, the stresses derived from the appropriate limit state combinations are compared with the limits found in appendix A, section A5.2.
4.3 TORSIONAL CHECKS On projects that have been constructed to date, open U-beam sections have demonstrated sufficient torsional strength and rigidity for all construction loadings considering self-weight and reasonable construction live loadings for typical beam lengths of approximately 100 ft. While sections that have currently been used have been robust in this regard, longer U-beams with thinner webs with external post-tensioning have been suggested that did not have surplus torsional strength and rigidity, which presented serious difficulties in transport and handling. It is essential to close the cross section as soon as possible in the construction process to avoid potentially negative outcomes from loss of rigidity due to undesirable cracking, and certainly before casting the deck slab.
Torsional checks are made at the service and ultimate limit states during construction and after the structure has been erected in its permanent configuration. Following the guidance of AASHTO LFRD specifications, torsional effects are recommended to be investigated when Tu > 0.25Tcr, where the cracking torque Tcr is derived based on St. Venant’s principles. Furthermore, it is recommended that service level torsion be limited to 0.5Tcr to prevent torsional cracking and unacceptable distortions.7 It is acknowledged that the torsional behavior of the open section is complex and involves many contributing stress behaviors. Nonetheless, by placing pick points and dunnage at locations to reduce torsional demands below the cracking torque limit derived using AASHTO recommendations, this service limit state is addressed.
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5.1 USE OF STRAIGHT AND CURVED SECTIONS This document focuses on the implementation of a curved, spliced U-beam bridge system. There are situations when the radius of the baseline curve is so large it approaches a straight line; consequentially, the curved structure in this situation can be accommodated using a chorded (tangent) beam segment approach. The PCI Bridge Design Manual,11 chapter 12, states that it is desirable to limit the arc-to-chord offset to 1.5 ft and that the edge of the top flange of the beam is no closer than 0.5 ft to the slab edge. Rather than making a specific recommendation about where the cutoff should be made, the decision of whether to use straight or curved segments is left to the designer and governing agency to meet the overall goals of the project in terms of costs and aesthetics.
5.2 LID SLAB AND DECK Cast-in-place concrete lid slabs are used between webs of the precast concrete U-beams to create a closed section and control box distortion during intermediate stressing of post- tensioning tendons and placement of the cast-in-place concrete deck. For the prototype bridge discussed in section 6, the total concrete deck thickness was assumed to be 10 in. over the concrete U-beams and overhang, and 8.75 in. between the concrete U-beams, including a ½ in. sacrificial thickness.
The designer should be aware that with an often-used 4.25 in. thick lid slab, the bottom cover to the top layer of reinforcing will dictate the deck slab thickness at the interior of the girders (Fig. 5.1). This figure shows that for an 8.75 in. deck and 4.25 in. lid slab with no. 6 and 5 longitudinal and transverse top reinforcing, respectively, the bottom cover to the top longitudinal bars to the lid slab will be 5/8 in. which does not provide adequate clearance based on the size of aggregate typical to deck slab concrete.
Figure 5.1 Typical layout of deck slab reinforcing.
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The typical section shown in Fig. 5.1, including U-beam and deck, is well suited for a 44 ft wide bridge using stay-in-place deck forms, but the optimum solution may vary significantly based on approved materials and local preference. Overhangs of 6 ft are considered unusual and difficult to form in many locations, and may drive the design. Thinner lid slabs have been used: 3½ to 4 in. for cast-in-place and 3 in. for precast concrete panels. These designs lessen reinforcing bar cover for the lid slab and allow more tolerance in deck steel placement. Additionally, smaller aggregate sizes can be used to provide more flexibility in deck steel placement.
5.3 FALSEWORK TOWERS Significant to the design of the falsework towers is their placement and application of factored loads. The design engineer locates the towers to facilitate a feasible solution, including the determination of length and weight of girders. Section lengths are selected to consider transport weight and facilitate placement of temporary towers to avoid traffic or other obstacles. Generally, the EOR makes the original determination, often by assuming a maximum length and transport weight of about 100 ft and 250 kip, respectively; however, it is recommended to confirm these assumptions with the governing agency. Additionally, splice regions are usually located near inflection points, if possible, to minimize longitudinal flexural demands at the closure placements. In general, splice regions are best located where it is most advantageous either for design or for construction, and designed accordingly. Poor location of splice regions can force significant modifications by the construction engineer prior to construction. Further, the construction engineer may optimize falsework tower placement to leverage the contractor’s chosen means and methods. In either case, the placement of falsework is a fundamental objective of curved, spliced U-beam analysis and design. The falsework tower placement needs to address structural aspects of the U-beam bridge system and the functional points, including maintenance of traffic, delivery and laydown of the field sections, crane placement, and interface with utilities and drainage structures. As horizontal clearance from traffic loads is a very important design condition, maintenance of traffic should be considered when developing the location and design of falsework towers and may require the use of straddle bents. Limitations in placement of shoring near live traffic during construction should be determined by the governing agency or EOR and design loadings identified. Proximity to traffic may require unacceptable design impact loads that must be designed for or protected against during construction. Locations where these conditions may exist, as well as all relevant design assumptions and requirements, should be included in the contract plans.
Towers require foundations, vertical support members, and girder support frames. The frame supports may use sand jacks and/or shims used to accurately support the girder section at the correct cross slope and elevation at the closure pours and diaphragms. Experience suggests using a separate tower under each girder line for flexibility of adjustments is particularly useful in locations with poor soils. Foundations in poor soils may need deep foundations to reduce the footprint, minimize settlement, or to resist uplift. Towers are generally designed by the contractor’s specialty engineer, and the EOR’s design plans usually provide horizontal and vertical girder reactions. Wind loadings for girders on towers should be considered. The initial
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build-out condition of a single girder on a tower that will eventually support two girders should be investigated for stability.
Tolerance to build falsework towers should be anticipated. Commonly, shims and sand jacks provide for suitable vertical tolerance of the tower legs and have been successfully employed. Shims may be wooden, neoprene, or steel plate, and these may be used in combination and will allow precise placement of field sections for the benefit of geometry control of the U-beam system. Field surveys of the temporary pads at the falsework towers occur as a step in the contractor’s geometry control plan.
5.3.1 Temporary Tower Size and Configuration Shoring towers with a capacity of 400 kip typically use an 8 × 8 ft pattern with tower legs commonly offset 4 ft from the centerlines of the closure placements. The offset produces a structural system that:
• reduces the effective span of the U-beam segments;
• creates a footprint for the temporary structure to resist overturning;
• allows room for an effective lateral bracing system of the falsework towers.
During the build-out and under certain load conditions, particularly when the girders are made continuous and the second-stage post-tensioning is applied, pairs of legs may see a reduction of load to the point of becoming non-load-supporting. This means all load may be supported by two or four of the falsework tower legs. An analysis program incorporating staging, tower leg stiffness, and fuse elements can be used to model this situation. Nevertheless, determining the type of shoring that may be used is not entirely possible during the design-bid-build process and will vary greatly depending on the means and methods used by the contractor. Sensitivity of the design to a variable such as the stiffness of temporary works may be desirable and, if significant, should be clearly detailed in the contract plans. Temporary works are best when designed to be simple structures that tolerate variable site conditions such as variable soil, settlement, and workmanship.
The designer communicates the assumptions made in the original design, such that, they can be confirmed and managed by the construction engineer. For example, the vertical and lateral loads are best noted on the plans, and these confirmed during the development of the bid price. The plans shall note the layout and geometry assumed for the falsework towers. The EOR generally reviews a falsework submittal from the contractor to ensure that the proposed system fits with the design parameters used for the structure.
5.3.2 Lateral Loads and Sway Bracing in Towers Falsework towers resist vertical and lateral loads. Vertical loads will be primarily from gravity. Lateral loads, primarily from wind and possibly other effects if advised by the governing agency, will likely be the predominant lateral force effects. Lateral loads, which produce both horizontal and overturning forces, are carried from their point of application to the foundations. Lateral bracing of the falsework towers carry load through truss action and also help to brace the column elements at the four corners of the towers.
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5.4 STRONGBACKS Most commonly, strongbacks are used to support midspan field segments in situations where falsework towers cannot be placed due to restrictions below and should be considered during the design phase. In practice, the use of strongbacks is complicated by the weight of the field sections and by stress limits of the U-beam segment over pier cantilever. For both points, additional temporary or permanent post-tensioning may need to be applied to meet stress conditions during erection and when construction is finalized. The anchorage of the post- tensioning and its interface with the strongback hardware must be checked to assure fit-up of all pieces. Furthermore, the length of the free cantilever will affect the magnitude of bending moment and stress over the pier. The cantilevers are usually kept as short as possible to limit the amount of stress; however, the configuration of the strongbacks must consider stresses at all the points of the U-beam system and should be incorporated into the time-dependent analysis of the structure during design.
5.5 GROUND SPLICING Ground splicing is used when a section of the bridge is too long and/or too heavy to fabricate as a full length girder, or where jobsite constraints do not allow temporary falsework towers. Splicing U-beam segments on the ground in the field is accomplished by connecting two U- beam segments on the ground with cast-in-place closures and post-tensioning. The advantage of ground splicing is that the weight of the pieces that are transported from the plant to the site is reduced. The disadvantage is that they create additional complexity for the anchorage of post-tensioning and create larger, heavier pieces for crane transport. The use of ground splicing is a design decision that must occur early in the project and be weighed with overall project goals and constraints. Figure 5.2 shows an example of a ground splice.
Figure 5.2 Ground splice. Photo: AECOM.
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5.6 SECTIONAL DESIGN FOR SERIVE LIMIT STATE The following sections discuss guidelines for preliminary design of precast concrete U-beam bridges.
5.6.1 Span-to-Depth Ratio Composite structure span-to-depth ratios of 25 to 30 for interior and end spans have been found to be reasonable for design. Greater values may be achieved with some effort by varying the overall section depth or by applying additional post-tensioning in the negative moment region over the piers.
Industry experience has shown when larger span lengths are sought after, the design is controlled by service tensile stress limit at splice locations or at the piers. As span lengths increase, the splice locations may deviate from the optimal quarter points simply because girders get too heavy or too long to fabricate, transport, or construct. Falsework locations, typically constrained by the site conditions, also affect optimization. U-beam designs are largely governed by splice locations and along with it, service level stresses in positive and negative moment regions. Furthermore, span arrangements based on practical limitations may be difficult to optimize.
5.6.2 Parametric Data Figures 5.3 through 5.6 show relationships between maximum bridge span and design parameters. The data presented in the graphs is derived from parametric analysis studies and industry surveys.
Figure 5.3 shows the maximum span versus span-to-depth ratios of the composite U-beam section. Figure 5.4 shows the maximum span versus the gross area of the U-beam section. Data are shown for the gross area at midspan as well as the gross area at the piers (where thickened bottom slabs are employed). Figure 5.5 shows maximum span versus the average weight of post-tensioning. The weight of post-tensioning is calculated as the total weight divided by the plan area of the entire bridge deck (lb/ft2). Finally, Fig. 5.6 shows the span versus the maximum amount of transverse reinforcing (web shear reinforcing). The transverse reinforcing is represented as square inches per foot per web at the controlling location in the maximum span.
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Figure 5.3 Span versus span-to-depth ratio of composite U-beam.
Figure 5.4 Span versus gross area of U-beam section.
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Figure 5.5 Span versus average weight of post-tensioning.
Figure 5.6 Span versus maximum web shear reinforcing (per web).
The values for span presented here are for initial design and planning purposes. The collected data may not capture the effect of nonuniform spans, skewed piers, optimized end-span length, or other design considerations one is likely to encounter during a typical project. For these reasons, the design values presented here are to be verified by the engineer during the design process.
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The maximum span versus average weight of post-tensioning graph includes both 15 and 19 strands for the continuity tendons. In some instances, it is desirable to use a particular U-beam size for portions of the bridge with spans that are less than the maximum possible span. In this case, economy may be achieved by reducing the number of strands in the continuity or spot tendons. Other projects, including some listed in appendix F, showed prestressing quantities varies roughly between 4.0 and 6.0 lb/ft2 (pretensioning and post-tensioning).
Neglecting secondary effects and assuming an approximate tendon eccentricity, the required number of strands at either the positive or negative moment region may be approximated by the following equations:
(ksi or psi)
Where
N = number of post-tensioning strands
allow = allowable tensile stress
PTservice− = service tensile stress without post-tensioning (assumed to be the same sign as sigma allow)
A = member cross-sectional area of the precast or composite section
pe f = effective stress in post-tensioning after allowance for all losses (approximated as
0.6 puf )
pu f = nominal ultimate stress of prestressing steel (270 ksi for low-relaxation strands)
strand A = area of post-tensioning strand (0.217 in.2 for 0.6 in. diameter strands)
e = strand eccentricity at the section being considered (calculated assuming the strand eccentricity is approximately 0.85 of the depth of the U-beam)
y = distance from extreme top or bottom compression fiber to the neutral axis of the precast or composite section
I = moment of inertia of the precast or composite section
Figure 5.7 shows the distance from the extreme top and bottom compression fiber for the precast concrete U-beam, precast concrete U-beam with lid slab, and precast concrete U-beam with lid slab and concrete deck (see Figure 6.4 for values). The precast U-beam carries the weight of the wet lid slab, the precast concrete U-beam with lid slab carries the weight of the wet concrete deck, and the precast concrete U-beam with lid slab and concrete deck carries live load and superimposed dead load. Generally using the composite values of A, I and y will result in the most conservative approximation of the number of strands required. The actual strand quantity will be refined as the design proceeds.
𝑁 = 𝜎𝑠𝑒𝑟𝑣𝑖𝑐𝑒 −𝑃𝑇 − 𝜎𝑎𝑙𝑙𝑜𝑤
𝑓𝑝𝑒 𝐴𝑠𝑡𝑟𝑎𝑛𝑑 1 𝐴 + 𝑒𝑦 𝐼
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a) Precast U-beam
b) Precast U-beam with Lid Slab
c) Precast Concrete U-beam with Lid Slab and Concrete Deck
Figure 5.7 Extreme top and bottom compression fiber for precast and composite cross sections.
5.6.3 Effect of Radius For a straight bridge, adjacent girders are the same length, and concentric gravity loads are equally shared by the girders. As the radius of curvature of a bridge decreases, the length of the girder on the outside of the curve becomes longer than the length of the interior girder, and the proportion of gravity loads distributed to the outside girder increases. For this reason, the outside girder (the longest girder) likely limits the design.
For comparison, Table 5.2 shows the approximate length of the outside girder for a typical span of the prototype bridge developed in section 6 for the radii discussed in Section 2.1.3.
The radius of curvature has a small to moderate effect on the longitudinal design moments of a closed U-beam section at typical levels of curvature. If the outside girder length increases a 200 ft span to an effective span of 205 ft for a 500 ft radius, the length increases by 2.5% and the
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longitudinal and torsional moments increase by 5% (the length squared). The outside girder line will always be subjected to more dead load and live load, yet the inside and outside girders are nearly always designed similarly. Furthermore, if a single spine model is used, proper determination of the distribution factor for live load for the outside girder line is significant. Experience has shown that determination of the live-load distribution factor can be conservatively determined by using the lever rule or other methods which are also not significantly affected by curvature. Special situations may also apply. For example, if piers are not radial but parallel, girder lengths can be roughly equal or even shorter on the outside girder line. Furthermore, if the girder lines are shifted, the deck can produce counterbalancing torsions for composite loads and shift deck dead loads away from the exterior girder to the interior.
Article 4.6 of the AASHTO LRFD specifications discusses the analysis type recommended for varying degrees of curvature. Indeed, section 4.6.1.2.3 states that a three-dimensional single curved girder line model is sufficient if the degree of curvature within a single span is between 12 and 34 degrees. The designer should decide, in developing the model, the significance of the degree of curvature, force effects (including torsion) to the outside girder, and application of distribution factor. It is noted that a dual spine model accounts for the girder length effect and live-load distribution factor within the model.
Table 5.2. Girder lengths for 200 ft curved span (22 ft 8 in. girder spacing) Bridge
centerline
radius, ft
Column A Column B
B/A Length of interior girder, ft Length of outside girder, ft
Straight (R = infinite)
200 200 1.00
1000 198 202 1.02
750 197 203 1.03
500 195 205 1.05
5.6.4 Effect of Pier Fixity Curved U-beam bridges are generally well suited for flyover ramp bridges, where the piers are relatively tall and slender, and the number of bearings can be reduced due to the relative flexibility of the substructure. To lower the cost of bearings and bearing maintenance, it may be advantageous to examine the super- to substructure articulation by using integral piers or fixed bearings versus expansion bearings. Generally, multiple fixed piers provide more piers to spread any longitudinal loads such as braking, wind, earthquake, and the like, and makes the center of motion more certain than with many sliding bearings. However, fixing bearings or making piers integral increases forces in the substructure due to post-tensioning, time- dependent effects, and temperature. Increased substructure and foundation costs must be weighed against potential cost savings through the use of bearings.
Foundation costs due to the extra moments can be mitigated by using drilled shafts (if economical), oriented such that they do not pick up axial load from longitudinal superstructure loads. Pier fixity is achievable with shorter piers provided there is sufficient foundation
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longitudinal flexibility. The foundation conditions will typically determine if frame action between the substructure and superstructure is feasible and that the frame has sufficient strength and flexibility to accommodate volume changes. Very stiff foundations, such as footings founded on multiple piles can generate large forces under design movements when combined with inflexible piers. Locally stiff piers may still be used in a rigid frame if they are combined with taller, more flexible piers. Locating the center of rigidity of the frame to limit movement at stiffer pier locations is a design methodology to accommodate stiff substructure and foundation elements. Girder lines can also have independent supports. The designer may also take advantage of flexibility from creep effects in the structural system and a reduction in stiffness due to permissible column cracking.
The prototype bridge discussed in section 6, and shown in Fig. 6.1, was analyzed for combinations of fixed bearings and integral piers. The piers analyzed were 20 ft tall from the top of foundation cap to top of beam seat. Table 5.3 shows the resulting bottom of column longitudinal moment for the controlling pier in each case. The effects of longitudinal wind and temperature gradient are neglected for this study because they do not contribute to the Strength I load case. Braking loads are distributed equally according to the number of fixed bearing or integral piers. Live load is for HL-93 loading placed for maximum longitudinal moment at the base of the column. Time-dependent effects are for long term losses. Axial loads and transverse moment caused by the bridge curvature or eccentric loading is not shown here but contribute to the loading demands on the piers and must be considered for design. The base of column was assumed fixed for all cases.
Table 5.3. Longitudinal moment resultants for pier fixity study
Load Load
factor
Longitudinal moment for controlling pier, kip-ft
Fixed bearing Integral
Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
Pier
3
Piers
3 and 4
Piers
2, 3, and 4
Pier
3
Piers
3 and 4
Piers
2, 3, and 4
DC 1.25 -2 1400 2647 378 4253 2716
EL-PT 1.00 20 -16,759 -31,616 -38 -16,607 -30,550
CR&SH 1.00 -9 935 3414 -771 1758 2600
TU 0.50 0 -9903 -19,237 0 -9823 -19,231
LL 1.75 51 -4387 -2690 9311 -4021 -2739
BR 1.75 2254 -1127 -751 1127 -564 -376
Strength I N/A 4043 -28,675 -40,534 17,929 -22,468 -39,622
Table 5.3 shows that there is significant increase in the longitudinal moment at the base of the columns for cases with more fixed bearings or integral piers. The predominant component of longitudinal moment is secondary effects of post-tensioning and uniform temperature.
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Cases 2 and 3 have similar base moments as cases 5 and 6 (multiple fixed bearing and multiple integral piers, respectively). Although the piers in cases 5 and 6 are subject to double curvature, in this study the long spans of the superstructure are relatively flexible compared with the substructure, providing relatively little restraint to the top of the column for load cases involving superstructure axial shortening. In this study, the moment at the top of the column for case 6 uniform temperature loading is approximately 8000 kip-ft, or approximately 40% of the base moment.
In contrast, the results of cases 1 and 4 (one fixed bearings or integral pier) differ. The predominant difference is due to compatibility between the superstructure and substructure for live loading for the case with integral piers. In the fixed bearing case, superstructure rotations are accommodated through bearing rotation, and the rotations do not result in significant column moment.
For the integral pier case, the total axial force in the superstructure is higher, necessitating additional post-tensioning to control stresses in the superstructure. The effect in this study likely results in 2 to 3 additional strands at the pier location. The effect of axial loads and differential stiffness between the substructure and superstructure is lessened for taller, more flexible piers. It is clear from the study that design related to fixed and integral scenarios points to the need for an articulation study early in the design process.
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MODELING AND ANALYSIS
6.1 SELECTION OF PROTOTYPE BRIDGE This section uses a prototypical example to describe representative modeling and analysis techniques used with curved spliced precast concrete U-beam bridges. The prototype was chosen to be representative of typical curved bridge applications and was selected to be a 700 ft long unit comprising four spans with lengths 150, 200, 200, and 150 ft, respectively. The prototype bridge is on a curved alignment with a radius of 750 ft about the centerline of the deck. The curvature was such that the right U-beam is longer than the left U-beam (that is, the beams curve left as looking at the stations ahead).
The prototype bridge is 45 ft 1 in. wide with two 1 ft 6½ in. barriers, a 12 ft inside shoulder, two 12 ft lanes, and a 6 ft outside shoulder. Two precast concrete U-beams (PCI Type U84-4) spaced 11 ft 4 in. from the centerline of the bridge support the superstructure. An optimized arrangement puts the U-beam centerlines approximately 22 ft apart with roughly 12 ft between the tips of the flanges and 6 ft cantilever overhangs. To conform to the AASHTO LRFD specifications,2 the slab depth is 10 in. at the cantilever and interior of the beams and 8.75 in. between beams. All deck thicknesses propose the use of ½ in. sacrificial thickness. Additionally, the 10 in. thickness interior to the beams is set to provide cover under the top layer of reinforcing bar of greater than ½ in., as discussed in section 5.2.
The span length divided by the depth of composite U-beam for the interior span is 25.5, a value consistent with the partial summary of recent U-beam designs discussed in chapter 2. Depending on the span arrangement and other design factors, including bridge width and beam spacing, a deeper or shallower U-beam section may be appropriate.
Figure 6.1 shows the elevation and cross section of the prototype bridge, and further attributes are briefly discussed in the following paragraphs and expanded on in later sections.
The beginning of the bridge was assumed to be supported by an end bent with an idealized roller support. The end of the bridge was assumed to be supported by an expansion pier with an idealized roller support, showing the possibility of adjacent units. The first and last interior piers were assumed to be on expansion bearings idealized as roller support, and the middle interior pier were assumed to support the superstructure on fixed bearings idealized as pins.
Although Fig. 6.1 shows the bridge supported on pile foundations, the foundations were not analyzed, and with the pier height and corresponding flexibility the superstructure design and layout are not significantly affected by the choice of foundation. There may be conditions where foundation type will be significant, such as with spread footings and with unbalances during the staged construction. Foundation systems should always be addressed in consultation with geotechnical professionals.
Depending on the complexity of the structural and project requirements, the bridge could be modeled as one of the following:
• three-dimensional beam line model
• multiple beam line model with transverse beam grillage
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• multiple beam line model with transverse finite element deck elements
• finite element U-beam and deck
The prototype bridge was modeled as a three-dimensional grillage model using longitudinal beam elements to represent the U-beams and transverse beam elements to represent the concrete deck because it represents a good balance between modeling complexity and sophistication. The choice of modeling technique is left to the designer based on the requirements of the project. See chapter 5 for further discussion on the effect of radius and choice of modeling techniques. Finite element modeling is likely reserved for investigating details rather than global longitudinal effects. In any case, the model chosen must account for the staged construction during build-out, time-dependent effects of the structure, losses in post-tensioning, and potentially other items discussed in this chapter.
6.2 MATERIALS The U-beams of the prototype bridge were assumed to have a 28-day concrete compressive strength of 8.5 ksi. The cast-in-place concrete portions of the U-beams (closure placements, diaphragms, blisters, haunched bottom slab) were assumed to have a 28-day compressive strength of 6.5 ksi. The bridge deck and lid slab were assumed to have a compressive strength of 4.5 ksi. Creep and shrinkage properties were according to CEB/FIP.12 High-slump concrete was assumed for better placement in the precast concrete U-beam forms.
Reinforcing steel was assumed to be ASTM A615, Grade 60. Prestressing strand was assumed to be 0.6 in. diameter ASTM A416 Grade 270 for low-relaxation strands, and prestressing bars were assumed to be ASTM A722 Grade 150. Tendons and bars for the prototype bridge were assumed to be grouted and bonded.
Appendix A provides a more complete description of the material properties.
6.3 CONSTRUCTION SEQUENCE AND AGE AT CONSTRUCTION Figure 6.2 shows the assumed construction sequence for the prototype bridge.
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To capture the effects of creep and shrinkage and locked-in forces, the prototype bridge was modeled using a time-dependent analysis that incorporated the construction sequence, including the age of the bridge components at the time of erection. The substructure elements were assumed to be three months old when the beams were set. Table 6.1 provides a detailed description of the construction stages shown in Fig. 6.2.
Table 6.1. Construction sequence
Stage Description of work Total days
1
a Construct substructure
b Erect falsework to support girder segments
c Cast beams at casting yard, including variable bottom slab 0
d Install bracing, if needed 6
e Perform stress checks for lifting; lift beams out of forms 6
f Cast girder ends 6
g Stress and grout bottom flange post-tensioning 9
h Perform stress checks for transport; transport beams to site 33
2
a Lift bearings to substructure
b Mobilize cranes to erect girders
c Transport girders to site
d Erect beam segments on temporary supports per sequence 33
e Set and grout permanent bearings 34
3
a Cast all closures 40
b Cast interior diaphragms at integral piers and bearing piers 40
c Cast first-stage diaphragms at expansion piers 40
4 a Stress transverse post-tensioning in diaphragms if applicable 45
5 a Place stay-in-place forms 47
b Cast lid slab 49
6
a Stress continuity tendons 56
b Stress top flange tendons 56
c Grout all tendons 57
d Cast second-stage diaphragms at expansion piers 57
7
a Remove all temporary supports 57
b Install deck overhang formwork 58
c Cast deck per placement sequence (three days per placement) 72
8
a Finish deck details 76
b Cast barriers 80
c Open to traffic 120
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Variations in the construction sequence are possible. For example, the top flange or one continuity post-tensioning tendon may be installed in the U-beam before casting the lid slab to control stresses in the U-beam during casting of the lid slab. Installing post-tensioning after the lid slab is cast has the benefit of providing precompression to the lid slab, but must be weighed against the disadvantage of potentially providing less precompression to the U-beam, and the negating effects of secondary forces due to fixed piers.
6.4 SPLICE LOCATIONS AND BOUNDARY CONDITIONS Splices were provided between each precast concrete U-beam segment. For the prototype bridge, each segment was assumed to be supported on permanent piers or temporary support towers, with splices being made after the beams were erected. Alternatively, to reduce the number of temporary towers, splices between segments could be made on the ground, and longer segments could be lifted onto permanent piers or temporary supports. Ground splicing would change the design from what is shown and is not simply a change of sequence and means and methods. One effect of ground splicing is that additional bottom flange post- tensioning is generally required.
The precast concrete U-beam segments were assumed to be supported on compression-only pin supports when they were initially erected. The permanent bearings were assumed to be grouted (activated and replacing the temporary supports) before casting the closure placements (stage 2e from Table 6.1).
The superstructure was supported on pinned bearings at pier 3. At end bent 1, pier 2, pier 4, and expansion pier 5, the superstructure was supported on guided bearings. One bearing supported each precast concrete U-beam at each end bent or pier. All permanent bearings at expansion piers were released in the longitudinal direction, while the permanent bearings at expansion piers supporting the right precast concrete U-beam were fixed in the transverse direction.
The permanent piers and temporary towers were assumed to be fixed and pinned at the ground elevation, respectively. End bent 1 was modeled as a rigid point support directly below the temporary and permanent bearings.
6.5 SECTION PROPERTIES The prototype bridge was modeled using two spines, with beam elements representing each composite U-beam section. Section properties were calculated according to the member proportions, including changes in section along the length of the bridge such as the bottom flange thickening near the interior piers. Section properties were recalculated automatically by the program per user instruction at relevant stages of the construction sequence to account for the build-out.
Section properties for the spine elements were calculated for the following conditions:
• precast concrete U-beam
• precast concrete U-beam with lid slab
• precast concrete U-beam with lid slab and concrete deck
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• precast concrete U-beam with lid slab and concrete deck assuming deck has cracked
The analysis intent of the last condition in the list is to modify the flexural stiffness to redistribute negative moments to the positive moment regions once the section has cracked. Internally the moment redistribution caused by cracking is considered in the sectional design. For the prototype bridge, service stresses were enough to crack the deck, and cracked section properties were used. The section at the piers was considered cracked when the deck stress exceeded the modulus of rupture fr of 0.237 × f’c0.5 (ksi). The extent of cracking was approximately 5 ft on each side of the pier centerline.
The spine elements were connected transversely with slab elements representing the stiffness of the concrete deck by rigid links from the center of gravity of the spine to the center of gravity of the slabs. For the prototype structure, the slabs were beam elements with section properties based on the deck thickness and node and member spacing. Figure 6.3 shows a graphic of one model used for the prototype structure.
Figure 6.3 Analysis model for prototype bridge.
The gross-section properties of the permanent piers were determined according to the proportions of the piers, which were assumed to be rectangular for the prototype bridge analysis. Cracking of the piers was not considered for the prototype analysis.
Figure 6.4 shows the section properties used for the prototype bridge. Thickened bottom flange properties are not shown but were also developed and used for the prototype bridge. Torsional moment of inertia is shown as it is required for the stiffness analysis. The warping constant, required to calculate torsional stresses due to loads applied away from the shear center, is not shown. See chapter 7 for a discussion on torsion of U-beam segments.
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Cross section Section property
Precast concrete U-beam
Neutral axis = 37.6 in. (from bottom)
Area = 2428 in.2
Moment of inertia = 1,936,000 in.4
Torsion moment of inertia = 83,180 in.4
Creep-exposed perimeter = 507.7 in.
Precast concrete U-beam with lid slab
Neutral axis = 44.5 in. (from bottom)
Area = 2828 in.2
Moment of inertia = 2,745,000 in.4
Torsion moment of inertia = 3,904,000 in.4
Creep-exposed perimeter = 396.4 in.
Precast concrete U-beam with lid slab and concrete deck
Neutral axis = 60.7 in. (from bottom)
Area = 4423 in.2
Moment of inertia = 4,833,000 in.4
Torsion moment of inertia = 6,033,000 in.4
Creep-exposed perimeter = 689.9 in.
Precast concrete U-beam with lid slab and concrete deck
assuming deck has cracked
Neutral axis = 46.3 in. (from bottom)
Area = 3301 in.2
Moment of inertia = 3,444,000 in.4
Torsion moment of inertia = 3,992,000 in.4
Creep-exposed perimeter = 500.2 in.
Figure 6.4 Section properties.
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6.6 TEMPORARY WORKS Section 5.3 discusses the use and design of temporary towers. In the prototype example, temporary towers were used to support the precast concrete U-beam segments before making closure and stressing post-tensioning continuity tendons. Because the statical system of the U- beams changed from simple supports in the initial stages to continuous supports at the later stages, the stiffness of the temporary towers affected the distribution of forces in the superstructure, and the stiffness of the temporary towers was included in the time-dependent analysis. Settlement of the temporary towers should be addressed when the closure placements are made and bearings over the piers are engaged, and before significant longitudinal post-tensioning is applied. Because this window of time is generally not long, and because the change in load is small, settlement is generally not a significant concern, provided attention is given the bearing pressures of the founding materials.
Parametric studies will help to determine if shoring stiffness is a significant design condition for stresses or deflections and build-ups. If so, the proper measures to accommodate the chosen shoring stiffness should be included in the contract plans, and the specialty engineer will also need to consider these in the design of temporary works.
The stiffness of the temporary towers was approximated using spring supports with stiffness equal to the axial stiffness of typical temporary falsework.
Additionally, post-tensioning operations and casting the lid slab introduced uplift at some bearings on the temporary towers. For this reason, compression-only supports were used for the bearings on the temporary towers. The compression-only springs tracked the total force in the bearing elements through the construction stages and became inactive when the sum of forces in the bearings at a particular construction stage became negative. In the prototype example, the support towers did not lift off simultaneously; thus, compression-only springs become a convenient way to address step-wise liftoffs without adding more stages.
6.7 DISTRIBUTION FACTOR The time-dependent model for the prototype structure was a full three-dimensional structural model built using spine elements for the U-beams and slab elements representing the concrete deck. Member self-weight was calculated directly in the model. Additional dead loads were applied at locations representative of the physical structure and were distributed according to the analysis.
Calculated live-load distribution factors were not used for this analysis. Rather, live-load lanes were defined along the length of the bridge at the spine elements and slab elements representing the concrete deck. The lanes were defined with offsets to the spine elements to account for lateral distribution of the loaded lanes. The slab elements distributed the live loading to the spine elements. Several design lanes were defined to capture the envelope of live-loading force resultants.
Although the AASHTO LRFD specifications indicate horizontal curvature may be neglected if certain geometric conditions are met, experience shows that neglecting curvature may slightly to moderately underestimate shear and flexure design forces for the outside girder. In NCHRP Report 620, Development of Design Specifications and Commentary for Horizontally Curved
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Concrete Box-Girder Bridges,13 rigorous parametric studies were performed that led to the following span L over radius R ratio recommendations when:
• L/R < 0.2, designed as straight and ignore torsions;
• 0.2 < L/R < 0.8, analyzed as a curved single-spine girder; and,
• L/R > 0.8, analyzed using the finite element method or more sophisticated analysis.
Using these parameters for the prototype example with R = 750 and L = 200, L/R = 0.267, which is just above the threshold where curvature is ignored which is consistent with the AASHTO LRFD specifications. To provide an example that can be used for a moderate curvature, the prototype analysis uses dual longitudinal spine elements and transverse slab elements. The design professional may choose a more simplified analysis, using a single spine, and neglecting curvature if indicated by layout parameters.
The ratio of midspan moment determined using dual curved longitudinal spine elements and transverse slab elements and the lever rule applied to a straight, single-spine model was 7006 kip-ft (analysis)/8720 kip-ft (lever rule) = 0.80.
6.8 PIER FIXITY As discussed in section 5.6.3, the number of fixed piers affected the longitudinal force imparted on the substructure. It was desirable to distribute longitudinal forces due to longitudinal wind and braking force to as many fixed piers as possible. An efficient design introduces an optimum number of fixed piers that considers substructure forces due to temperature, creep and shrinkage, and post-tensioning, as well as the distribution of longitudinal forces from wind, braking, and friction.
For the prototype bridge, one fixed pier (pier 3) was selected. The fixed pier was chosen to support the superstructure on bearings restrained against longitudinal movement, but pier fixity could also be established using integral piers.
6.9 THREE-DIMENSIONAL MODELING – FLEXURE, SHEAR, AND TORSION The previously discussed time-dependent model discussed was analyzed using a robust platform that accommodated relevant construction stages and loading conditions. Selected results are discussed in this section.
Figure 6.5 plots service flexure in the right U-beam due to dead loads, primary and secondary post-tensioning, and the effects of creep and shrinkage at time equals infinity. The summation of these loads and effects are also plotted.
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Figure 6.5 Flexure in right U-beam from permanent loads.
Based on the results of Fig. 6.5, the post-tensioning moment counteracts the dead load moments. While the effects of creep and shrinkage are relatively small compared with dead loads, they add to the dead load moment and must be considered in the design.
Figures 6.6 through 6.8 show flexure, shear, and torsion in the right U-beam due to the permanent loads in Fig. 6.5 and live loads. Note that results due to temperature loadings not plotted because they are relatively small for the prototype bridge, but are dependent on the fixity of the structure and may be larger for differing bridge layouts. For example, temperature loads can be a concern with longer spans and shorter (more fixed) piers.
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Figure 6.6 Flexure in right girder.
Figure 6.7 Shear in right girder.
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Figure 6.8 Torsion in right girder. Section 7.2 discusses additional results of the model.
6.10 PRINCIPAL WEB STRESS Principal web stresses are the combination of axial and shear stress in the web. Excessive principal web tension can lead to cracking of the web under service conditions. Principal web stresses were computed for the prototype bridge using classical beam theory and the principles of Mohr’s circle. Many analysis programs are capable of computing principal web stresses directly or reporting concurrent axial and shear stresses, which was done for this analysis.
Figure 6.9 shows the principal web stresses for the right U-beam due to dead loads, post- tensioning, creep and shrinkage, and live loadings.
It is noted that the eighth edition AASHTO LRFD specifications do not prescriptively require principal web stresses to be checked for U-beam bridges. However, per Article 5.12.5 and other articles in the AASHTO LRFD specifications, principal web stresses may be considered at the designer’s discretion. See Section 7.3.2 and Appendix A for more discussion about principal web stress.
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6.11 TRANSVERSE DECK SLAB The transverse deck slab functions as the roadway surface. It transfers live loading transversely to the longitudinal U-beams and is part of the longitudinal and transverse structural systems. For the longitudinal system, beam elements were used to model the lateral transfer of live loading between the U-beams (Fig. 6.10). The beam element thickness was the same as the deck thickness, and the width of the beam elements was based on the tributary spacing between adjacent nodes. Beam elements were defined between the spine elements with member eccentricities representing the edge of the U-beam top flanges.
Figure 6.9 Principal web stress.
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Figure 6.10 Global longitudinal modeling of transverse section.
The design of the conventionally reinforced deck slab and contribution of web bending due to loading of the transverse deck cross section may be captured through traditional influence surfaces or by modern modeling techniques, such as finite element analysis. Section 7.2 discusses this in more detail. The prototype example focuses on the longitudinal U-beam design.
6.12 GEOMETRY CONTOL PROCEDURES As discussed in section 3.3.2, the erection plan and geometry control procedures integrate the design plans, the contractor means and methods, and the erection engineering analysis to provide horizontal and vertical controls for bridge elements through particular stages of construction. The geometry control procedures are submitted by the contractor before construction as part of the erection plan. At particular stages of construction, the locations of bridge elements are checked against the predicted locations defined in the geometry control procedures.
Predicted camber and build-up based on the erection engineering analysis are also provided in the geometry control procedures.
6.12.1 Camber Requirements Predictions of vertical deflection of the beam due to permanent loads, including dead, superimposed, and post-tensioning including long-term effects, are used to calculate the cambered position of the beam such that the beam follows the theoretical profile once these deformations take place. For prestressed girders, in contrast to U-beams, it is desirable to provide adequate prestressing such that the initial camber of the beam field section at release, including the effect of the dead load of the beam, lifts the beam off the precast concrete form. Some agencies require at least ½ in. initial midspan camber for prestressed beams.
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Because the amount of prestressing or post-tensioning in the casting bed is small for precast concrete U-beams relative to precast concrete I-beams, the requirement for initial camber is less applicable. Instead, adequate mild, or preferably prestressing, reinforcing is provided to limit stresses in the precast concrete U-beam during handling, transport, and lifting. Section 7.1 discusses handling, transport, and lifting in more detail.
Compared with precast concrete I-beams, camber growth in precast concrete U-beams is relatively small, typically ½ in. or less, due to the relatively small amount of initial prestressing and short time duration between casting and erecting the beams and ultimately the closure of the system. Deflections can be made more predictable by balancing prestress deflection against deadload deflection. This can be especially useful for unbalanced span ratios. Pretensioning of members can occur in straight parts of bridges with both straight and curved alignments. Pretensioning is usually much less expensive than post-tensioning, especially if fewer tendons can be used.
6.12.2 Rotation of U-Beam Section Cast-in-place closure placements at splices between adjacent U-beam segments provide structural continuity and accommodate geometric differences caused by rotation of the U- beam segments.
Precast concrete U-beams can be cast straight or with a curve to accommodate roadways with a curved alignment. For economy of casting beds, it is desirable to cast as many U-beams as possible with the same radius. For this reason, U-beams on a curved alignment are not concentric with the bridge radius, and the ends of adjacent U-beam segments at a splice are not parallel. Regarding the radius, the theoretical transverse sweep of the cross sections less the average radius, are typically less than half of the PCI casting tolerance for a 100 ft girder length. Similarly, the difference between ends of adjacent girders is generally so small as to be nearly imperceptible when it is due solely to casting girders on an average radius. The same is true for U-beam segments placed to accommodate a vertical curve profile.
Roadway superelevation on a bridge is normally accommodated by placing U-beams in a rotated position. In areas of the bridge with constant superelevation, the U-beam top flanges are parallel to the top of the concrete deck; however, in areas of superelevation transition, U- beams are placed at a rotation angle that differs from the bridge superelevation (Fig. 6.11). The average of the bridge superelevation along the length of the U-beam segment is a convenient rotation angle for setting the U-beam. Future advancements of forming systems will likely accommodate both camber and twist of the segments, though significant setup costs may limit variation of the camber and twist to only a few segments.
For practical considerations, the out-of-plane difference between adjacent U-beam ends should target approximately 1 in. maximum for a typical 2 or 3 ft closure placement. Limitation of the out-of-plane difference across splices cannot always be controlled or specified. Severe transitions on cross fall in short distances may require offsets greater than 1 in. While 1 in. is a desirable limit, the bridge geometry may not allow it, and the designer should consider whether additional measures to smooth the transition, such as larger closure placements, adjusting the post-tensioning profiles, or reinforcing for out-of-plane effects, are necessary.
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6.12.3 Build-Up Calculation and Deck Screeding The build-up, sometimes referred to as the haunch, makes up the difference between the bottom of the concrete deck (based on the roadway finish grade elevations) and the top of the precast concrete U-beams. The build-up is calculated for construction phases based on predicted deflections of the U-beams during the build-out, varies along the length of the U- beams, and is a function of the following:
• prescribed minimum build-up
• prescribed minimum difference in build-up between adjacent segments
• finish grade elevations
• concrete deck thickness
• U-beam segment camber due to prestressing and self-weight
• deflection of the U-beam during the build-out (may be the same or different for each web)
• rotation of the U-beams to accommodate bridge superelevation
• stiffness of temporary tower supports
Figure 6.11 shows an exaggerated view of the build-up of a representative U-beam. A case with upward beam camber is shown (build-up is less at midspan than at the ends), but, as discussed in section 6.12.1, the beam camber could be such that the build-up is greater at midspan than at the ends. For the reasons discussed in section 6.12.2, build-up is specified for both the left and right webs of the U-beam. The deck screed and formwork for the concrete deck are set based on the calculated build-up. A minimum build-up of 1 in. is recommended, and corresponds to the build-up at the left web at the beam centerline in Fig. 6.11.
Table 6.2 is a sample table that may be used for drawing production. The table shown is for the right web of the right U-beam. Similar tables are required for each web. Appendix D provides a sample calculation for build-up of a select location on the prototype bridge.
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Figure 6.11 U-beam build-up (exaggerated view).
The information presented in Table 6.2 will allow the contractor to calculate the following key elevations during construction:
• elevation of lid slabs
• final deck elevations for deck casting
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T a
b le
6 .2
. E x
a m
p le
p a
r ti
a l
U -b
e a
m b
u il
d -u
p a
n d
d e
fl e
c ti
o n
d a
ta
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The “analysis points” column in Table 6.2 is the length along the top flange at the midpoint of the top flange. The total deflection at each construction stage is the deflection at the end of each stage after all loads were applied and time-dependent effects occurred.
The theoretical deflections, elevations, and build-ups from the design phase were based on an assumed construction sequence. In the construction phase, theoretical deflections, elevations, and build-ups should be verified by the contractor and the erection engineer based on the actual construction sequence, including variations from the timeline assumed in design. Field survey and dry-run measurements are required by the contractor to confirm screed elevations before casting the concrete deck.
Deflections of spliced girders during construction are significantly less than conventional simple span prestressed girders. The inherent stiffness from continuity and the lower amounts of required prestressing force, combined with the load-balancing effect of the continuity post- tensioning, greatly reduce movements of the structure during construction and over time. Appropriate setting of deck grades is much less critical than with long-span, conventional precast concrete girder bridges.
Because actual construction schedules usually vary from what is assumed in design, the specifications typically require the specialty engineer to recalculate these values. Therefore, presentation of build-ups in the design plans for design-bid-build contract delivery may be redundant and their inclusion is a decision made by the governing agency.
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DESIGN CONSIDERATIONS This section discusses critical items for the design of U beams during temporary phases of construction and in the permanent condition. This section builds on the analysis discussion of the previous chapter and is supplemented by the sample design criteria and calculations in appendices A and D.
7.1 PLANT HANDLING, TRANSPORT, AND LIFTING OUT OF FORMS A critical aspect of precast concrete U beams relative to lifting out of forms and transport restrictions is segment weight and length. It is advantageous to omit additional dead loads such as diaphragms, slab thickening, and lid slabs in the casting yard to reduce the lifting and transport weight of the U-beam segments. Instead, additional dead loads are cast-in-place after the segments are erected at the site. An exception, which requires more consideration, is bottom slab thickening where the design strength of concrete may be critical and more predictable if accomplished in the casting yard. U-beam segments must be analyzed for the casting and construction sequence, checking stresses and providing necessary details in the plans.
For the prototype example, beam segment lengths were limited to a U-beam segment weight of approximately 250 kip (about 100 ft), which is a practical weight for most regions and road conditions. U-beam segments up to approximately 325 kip have been successfully used in regions with flat terrain and accessible roadways with few obstructions.
Precast concrete U beams are cast in special forms that are adjustable for varying radii and beam depths. With the exception of the Satus Creek Bridge in Washington state, pretensioning of curved U beams is generally not used.14 Instead, prestressing force in curved U beams is introduced by post-tensioning. Post-tensioning that is anchored within the precast concrete U beam is stressed and grouted in the casting yard before transport to the site.
As noted in section 6.12.1, it may be desirable to provide precompression for precast concrete U beams; however, in certain cases with shorter segment lengths, the crack width checks given in the AASHTO LRFD specifications2 are compliant for lifting and transport as a reinforced member. U beams have significant capacity as reinforced concrete members, which can be successfully used during construction. The preference for a minimum amount of compression or limiting crack width during plant handling, U-beam transport, and the lifting of segments at the jobsite may be advised by the governing agency or follow AASHTO guidelines.
To account for dynamic effects, a specialized load case for temporary stresses is checked during transport. Loads calculated during transport include effective prestress, permanent loads, and dynamic load allowance (impact) during transport. See section 2, appendix A, and McGormley and Lindenberg (2016)6 for discussions on dynamic load allowance during transport.
Sections 7.1.1 through 7.1.3 discuss details necessary for handling, transport, and lifting more extensively.
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7.1.1 Internal Bracing The curvature of a U-beam segment results in torsional moments along the length of the segment. Before casting the lid slab, torsion moments on the open section are resisted by a combination of St. Venant and warping torsion. The torsional stiffness is reduced by cracking of the concrete. If torsional stresses in the open section exceed the code limits, control of torsional stresses may accomplished by the early addition of the lid slab, temporary internal bracing, and/or the introduction of prestressing force. Further, the introduction of thin web cross sections may require bracing or casting of a lid slab before transport, depending on the cross section used.
The addition of the lid slab increases the torsional stiffness of the segment by as much as 50 times or more, depending on the precast concrete section used (Fig. 6.4). The actual build-up of torsional stresses is incremental. The open section is subjected to torsional stresses due to the self-weight of the U-beam. The open section also supports the weight of the lid slab. The closed section created by the lid slab and U-beam resists additional incremental loads. The connection between the lid slab and U-beam must be designed and detailed to be sufficiently strong to resist the incremental torsional stresses that occur after the connection is established. Alternatively, the engineer may choose to design and detail a more robust connection that does not account for the incremental build-up of torsional stresses. In all projects constructed to date, the lid slab to U-beam connections have performed well.
Internal bracing or concrete diaphragms may be required during some stages of construction to control deformations and stresses of an open web box system. Internal bracing spanning between the top flanges has been previously used, including:
• horizontal struts at lifting points only, discussed in more detail in section 7.1.3
• horizontal ties at regular intervals along the segment to limit web deflections when setting overhang brackets and casting the deck
• horizontal struts at regular intervals along the segment with diagonal bracing between horizontals to create a torsional “truss”
U-beam cross sections are generally sufficiently robust that internal bracing outside lifting points does not contribute greatly to load capacity. Conversely, this bracing will increase costs and create interferences and difficulties during construction. The early placement of the lid slab generally eliminates the need for internal bracing for the girders that are described.
Horizontal struts along the length of the girder do not affect torsional stresses unless they are connected by diagonals to create a truss, similar to steel tubs to control torsions. Lid slabs are more desirable as they can be incorporated into the permanent structure.
Stresses due to torsional moments may also be controlled by introducing prestressing force before casting the lid slab. Based on the recommendations of the AASHTO LRFD specifications Eq. 5.8.2.1-3, consider torsional effects when the applied torsion is greater than 0.25 times the torsion cracking moment Tcr, including the strength reduction factor. From AASHTO LRFD specifications Eq. 5.8.2.1-4, the torsional cracking moment is defined as
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cf
f
p
A fT
pc
c
cp
ccr '125.0
1'125.0
2
+= (kip-in.)
Where
c f ' = compressive strength of concrete for use in design (ksi)
cp A = total area enclosed by outside perimeter of concrete cross section (in.
2)
c p = total length of outside perimeter of concrete cross section (in.)
pc f = compressive stress in concrete after prestress losses have occurred at the centroid
of the cross section resisting transient loads (ksi)
The introduction of compressive stress due to prestress fpc increases the torsional cracking moment.
7.1.2 Overturning During plant handling and transport, the segments must be supported in such a way that the segments are prevented from rotating due to the torsional moment about the longitudinal axis of the segment. Restraint of the segment may be accomplished by a restraint system or by offsetting lifting and support points. Rotation of the girder must also be prevented once the segments are lifted onto the temporary falsework or permanent piers.
Overturning is not typically an issue and is generally controlled with proper handing and bunking rather than external bracing, which would only be necessary in unusual situations.
7.1.3 Lifting U-beam segments are generally lifted using strand lift loops or high-strength bars with sufficient embedment to develop the required strength. Lifting points can be located near the ends of the segment or away from the ends to reduce the positive moment during lifting. . For example, a significant reduction in torsional demand is realized by positioning the temporary supports inboard by 10% of the segment length (Fig. 7.1). Shifting the lifting points inboard will require stress checks for negative moment at the cantilever supports. Twenty percent of the segment length produces approximately equal positive and negative moments; however, the section moduli at the top and bottom of the U- beams are not equal, so a support point that equalizes stresses and not moments may be advisable. The optimum location of lifting points varies and is best determined based on experience and calculation.
Inboard lifting points should be evaluated for erection considerations as they require larger crane radii to swing girders into position. Lifting points at the ends of the girder are sometimes necessary to facilitate erection.
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Figure 7.1 Torsional analysis and demand.
For a given U-beam cross section, the introduction of prestressing force in the casting yard (see section 7.1.1) in combination with careful placement of supports during lifting and transport may eliminate the need for regular horizontal struts or diagonal bracing to control torsional distortion during lifting and transport.
As noted in section 7.1.2, care must be taken to prevent the U-beam segment from rotating when lifting in the plant or during girder placement. This is accomplished by offsetting the center of action of the spreader bar and U-beam segment. Figure 7.2 shows a typical spreader bar and lifting hook arrangement.
Care must be used to consider the dynamic effect discussed in section 2.2.3 when lifting, handling, and transporting segments.
Figure 7.2 Spreader bar and lifting hooks. Figure 7.3 shows analyses that were performed to determine the behavior of the U-beam segments during lifting, transporting, and placing on temporary falsework with the lid slab
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casting operation. For lifting and transporting, the midspan moment is significantly less than for the case when the beam is placed on falsework. Table 7.1 shows a comparison of midspan stresses made for four 100 ft long beams, that is, straight and with radii of 500, 750, and 1000 ft. This comparison shows that for longitudinal stresses, the behavior of the four beams is similar. In general, the curvature of the beams can be ignored for this stress check.
Figure 7.3 Lifting, transport, and falsework evaluations.
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Table 7.1. Midspan stresses for beams for lifting and transport
Beam radius Top stress, psi Bottom stress, psi
Left Right Left Right
Straight (R = infinity) -166 -166 139 136
1000 ft -172 -161 126 144
750 ft -174 -158 126 151
500 ft -177 -154 120 151
Classical Beam Theory
-173 140
Additional evaluations were made for beams supported at their ends and with lid slab loads applied. Figure 7.4 shows transverse stress conditions that exist in the bottom slab and webs for an 84 in. deep × 100 ft long × 500 ft radius U-beam. Applying the beam dead weight and lid slab load of 0.66 kip/ft, the longitudinal moment demand at mid-span is estimated to be 3700 kipft, and the torque demand is estimated to be 240 kipft at the beam ends. Finite element results summarized in Table 7.2 show longitudinal stresses at midspan at the corners of the top and bottom flanges differing by approximately 200 psi from straight-beam (Mc/I) theory and 200 to 350 psi from an equivalent finite element analysis on a straight beam. Transverse stresses in the top of the bottom slab are estimated by the finite element analysis to be 145 psi maximum. These relative comparisons between finite element results and classical beam theory (using Mc/I) are performed for self-weight and do not include the effect of prestressing or impact for transport. Note that tension is positive in Tables 7.1 and 7.2.
Table 7.2. Midspan stresses for beams on falsework
Beam radius Top stress, psi Bottom stress, psi
Lt-1 Lt-2 Rt-1 Rt-2 Left Right
Straight (R = infinity) -1151 -1174 -1174 -1152 936 933
500 ft -1237 -835 -1526 -1079 720 1145
Classical Beam Theory
--1161 940
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Figure 7.4 Deformations and stress on U-beam segment.
Understanding that systems constructed with smaller radii and longer spans could increase the effects of out-of-plane behaviors, it is recommend the cut-off for more rigorous analysis be established at L/R = 0.2 as recommended by NCHRP Report 620 [7-1].13 This is implemented in the AASHTO LRFD specifications, Article 4.6.1.2.4c. Hence, the first step of analysis refinement after the cut-off is a grillage model, which is presented for the prototype beam in chapter 6. This ratio is applicable for the bridges on falsework or in their permanent configuration.
7.2 SECTIONAL DESIGN FOR ULTIMATE LIMIT STATE The design of a precast concrete U-beam bridge is very similar to conventional cast-in-place concrete box girder design. In general, sectional design is based on the requirements of the AASHTO LRFD specifications, as discussed in the following sections.
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The design checks discussed in general in the following sections and presented in more detail in appendix D are based on the results of the three-dimensional modeling discussed in section 6.9.
7.2.1 Longitudinal Reinforcing Check The design of longitudinal reinforcing balances the factored external moment against the internal moment generated between the tension reinforcing and compression block generated in the concrete section. Depending on the stage of construction and the location of the design check, the compression block may be on the composite cross section or on the precast concrete U-beam alone. A sample ultimate longitudinal reinforcing, or ultimate flexure, check is included in appendix D following the principles of the AASHTO LRFD specifications.
Continuous tendons placed in the webs of the precast concrete U-beams in varying profiles along the length of the bridge provide the primary load-resisting reinforcement. Top tendons may be placed in the flanges of the U-beams in negative moment regions to supplement the available load-resisting reinforcement. Similarly, bottom tendons installed in each segment before transport add to the available positive moment capacity, but are not effective at the splice closure placements. For this reason, it is desirable to place splices at locations within spans with lower flexural demands, such as quarter points.
The design of the prototype bridge assumes grouted and bonded post-tensioning tendons. Depending on the preference of the design team and governing agency, replaceable tendons may be incorporated. Grouted external tendons are unbonded. Stress in unbonded prestressing steel is based on the effective stress in the tendon after losses and the global displacement compatibility between bonded sections of tendons (such as anchorage points or deviators). Alternatively, the stress in unbonded tendons may be estimated using approximate equations in the AASHTO LRFD specifications.
The depth from the extreme compression fiber of the beam to the centroid of the prestressed reinforcing is adjusted to account for eccentricity in the ducts according to the AASHTO LRFD specifications, Article 5.9.1.6.
7.2.2 Transverse Web Reinforcing Transverse web reinforcing is determined using the relevant formulae and methods in the AASHTO LRFD specifications, Articles 5.8.3 and 5.8.3.4.2, using the principles of modified compression field theory.
Due to curvature and eccentric loading, transverse web reinforcing is required to resist the combined action of longitudinal shear and torsion according to the requirements of the AASHTO LRFD specifications, Article 5.8.3.6.
Depending on the judgement of the engineer and governing agency, the webs are also analyzed for the combination of longitudinal shear and transverse web bending. Historical practice is used as a basis to compute the amount of reinforcing required for each face of the webs independently under the actions of both longitudinal shear forces and transverse moments. The analysis of the web for transverse bending and shear/torsion is carried out using Podolny’s equations, where the amount of reinforcing placed on the face of the webs is chosen as the greatest of:
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• As = 1.0(Av) + 0.5(Af)
• As = 0.5(Av) + 1.0(Af)
• As = 0.7(Av + Af)
Where
Av = area of reinforcement required for longitudinal shear and torsion
Af = area of reinforcement required for transverse flexure
The width of the web effective for shear was according to the AASHTO LRFD specifications, Article 5.8.2.9, and reduced for post-tensioning ducts based on the requirements of the AASHTO LRFD specifications, Article 5.8.6.1.
7.2.3 Reinforcing Parameters The reinforcement ratio is an indicator of the economy and ductility of a concrete beam. For prestressed beams, it is defined as follows:
= Aps/bd
where
Aps = area of prestressed steel on the tension face of the beam
b = width of the compression face of the beam
d = distance from the extreme fiber in compression to the centroid of the steel on the tension side of the member
The reinforcement ratio varies along the length of the bridge due to the profile of the continuity tendons, the addition of local bottom or top tendons, and changes in the bridge cross section. The reinforcement ratio differs for positive and negative moment regions. Reinforcement ratios for key locations of the prototype bridge were calculated to provide a reference to the designer (Table 7.3). An example calculation for reinforcement ratio is included with the ultimate flexure check in appendix D.
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Table 7.3. Reinforcement ratios for prototype bridge
Location Reinforcement ratio
Positive moment region
0.0014
Negative moment region
0.0061
7.3 SECTIONAL DESIGN FOR SERVICE LIMIT STATE Design of pre- and post-tensioned structures requires checks for service level limit states as well as ultimate level limit states. In general, service design is based on the requirements of the AASHTO LRFD specifications, as discussed in the following sections.
For ultimate state checks, the service level checks discussed in general in the following sections and presented in more detail in appendix D are based on the results of the three- dimensional modeling discussed in section 6.9.
7.3.1 Longitudinal Stress Check The calculation of longitudinal stress is relatively straightforward and is the summation of axial and flexural stress at the extreme fiber of the cross section. The cross section changes throughout the construction stages, for example, after casting the lid slab or concrete deck, and stress is calculated at the extreme fiber of each cross section. Because the deck is cast after stressing the continuity post-tensioning, the deck is not precompressed and may crack under some loading conditions. For this reason, and at the discretion of the design professional and governing agency, stress on the composite section may be calculated assuming both cracked and uncracked section properties (Fig. 6.4) and for both short- and long-term creep and shrinkage results. For all projects, these criteria and the evaluation of cracked versus uncracked should be established at the beginning of the project.
Many analysis programs internally calculate and report extreme fiber stresses for the cross section. Analysis programs are also capable of enveloping and reporting extreme fiber stresses due to construction stages. Stress values calculated internally by the analysis program or externally using force results and section properties are compared with stress limits established in the design codes. An example calculation for longitudinal stress is included in appendix D. For the prototype bridge, the U- beam and lid slab are in compression under permanent loads and within allowable stress limits under service loads using both short- and long-term creep and shrinkage results with cracked section properties at the piers.
7.3.2 Principal Stress Check As discussed in section 6.10, principal stresses in the webs of U-beams may be calculated for special design cases per Article 5.12.5 of the eighth edition AASHTO LRFD specifications using classical beam theory and Mohr’s circle. Code provisions and governing authorities establish
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limits on principal stress to limit cracking in the web under service conditions, including construction stages.
Principal web stresses are generally checked for each construction stage and for the structure in the final stage for both short- and long-term creep and shrinkage results at the centroid of the cross section. An example principal web stress calculation is included in appendix D.
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DESIGN DETAILS This chapter includes design details for U-beam bridges, including the following:
• typical section and post-tensioning
• lid slab and deck details
• precast concrete tongue section
• interior haunch section
• blisters
• diaphragms
• bearings
Qualitative design discussion related to various elements is provided throughout this chapter. In-depth discussion is provided for unique elements, such as the diaphragm, over more common elements, such as the deck slab.
The prototype project that is the focus of this document is not intended to represent the most efficient and cost-effective design alternative, nor is the discussion in this chapter intended to provide a comprehensive view of all possible details and design decisions that must be included in a given project. Instead, it serves an example of one prototype project with focus on some of the more important structural design requirements. Other items that should be considered by the design professional may include, but are not limited to:
• reinforcing to resist curvature effects in webs (see bar 3B21 in Fig. 8.11)
• stressing jack access at expansion joints and intermediate tendon anchorages
• superstructure to substructure connections without bearings
- pinned connections
- integral connections
• bottom slab anchorages and blisters
• expansion joint details
• splice details
- splice length
- splice reinforcement
- shear interface between precast concrete U-beam and cast-in-place splice
- post-tensioning duct connections
• staged deck slab placement to minimize dead load stress in cast-in-place deck over the piers
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• special erection requirements
- strongback supports
- ground splicing
8.1 TYPICAL SECTION AND POST-TENSIONING The typical section for the prototype bridge has a bridge width of 45 ft 1 in. with two assumed travel lanes. Figure 8.1 shows the typical section. The cross section consists of two PCI 84 in. deep U-beams with an 8¾ in. thick concrete deck between the U- beams and 10 in. thick deck over the U-beams and at the overhangs.
Figure 8.1 Typical section of prototype bridge. Figure 8.2 shows the post-tensioning layout for the prototype bridge. The post-tensioning is composed of three types of tendons. Each segment has two nine-strand tendons in the bottom flange designed to support its self-weight. The U-beam section has four draped continuity 15- strand tendons in each web that pass through internal ducts from the beginning to the end of each unit, linking all the U-beam segments in the unit when the final stressing is complete. The geometry of tendons is arranged in a parabolic pattern, although harped arrangements are equally feasible. In general, Colorado designs have used a parabolic pattern instead of the harped pattern. Also, a top flange 12-strand tendon in each web is provided over the middle pier. These tendons were sized to limit the Service III tension and Service I compression stresses within allowable limits during all stages of construction and final service life of the bridge. Figure 8.3 shows post-tensioning coupling at a field splice using couplers (red) and heat shrink sleeves (black).
Post-tensioning ducts are spliced within cast-in-place closure placements between U-beam segments. Because the lengths of cast-in-place splices are relatively short (less than 2 ft), duct protrusions from the ends of the beam segments are very rigid and not easily moved. Therefore, mitigation of duct extension translation during beam concrete placement is paramount for field splicing success; otherwise, the integrity of this splice will be
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compromised. Means and methods of setting and holding duct profiles, particularly at the duct extensions, should be discussed before beam fabrication. Although not directly comparable, the use of a bulkhead/mandrel system similar to that used for precast concrete duct couplers can be considered, in addition to ingenious detailing at the duct-concrete beam interface. It is important to hold the free end of the duct protruding from the end of the beam at the proper location so that it aligns with its mating duct in the adjacent U-beam segment.
Figure 8.2 Post-tensioning of prototype bridge.
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Figure 8.3 Post-tensioning coupling details at field splice.
8.2 LID SLAB AND DECK DETAILS Figures 8.4 to 8.6 show the slab reinforcement details. Because the U-beams without the slab have a low torsional resistance, it is necessary to have a lid slab that increases the torsional resistance of the section before deck placement. Lid slabs are necessary in bridges where curvature is significant to increase the torsional resistance before stressing longitudinal post- tensioning, removing falsework, and casting the deck slab. Lid slabs are not used on straight sections and could be eliminated on sections with large radius and a low degree of curvature based on the judgment of the design professional.
Figure 8.4 Typical slab reinforcement.
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Figure 8.5 Typical lid slab reinforcement before main deck placement.
Figure 8.6 Typical slab reinforcement detail over top flange.
If used, the lid slabs are cast in place or installed as precast concrete elements after the beams are erected to limit the transport weight (Fig. 8.5). The design of the lid slab is recommended to account for horizontal shear forces at the interface between the lid slab and U-beam, horizontal shear forces at the interface between the lid slab and deck slab, torsional force flows via diaphragm and strut-and-tie action, longitudinal distribution reinforcing, and transverse moment capacity due to the weight of the deck placement and subsequent superimposed dead and live loads after the deck is cast.
8.3 PRECAST CONCRETE TONGUE The development and function of the precast concrete tongue is discussed in section 2.4.4. The tongue design uses both precast and cast-in-place concrete for the diaphragms. At the ends of the units where the continuity tendons are anchored, a tongue extension section allows the contractor to cast the remainder of the U-beam segment with the end diaphragms. Figures 8.7
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to 8.9 show the precast concrete U-beam segment end with a tongue extension. The tongue extension provides sufficient concrete to support the U-beam on the permanent bearings (section 8.8), before the diaphragm casting. Tongue reinforcing is designed to accommodate U- beam and diaphragm weight when placed on bearings, and also general zone reinforcing for the longitudinal post-tensioning.
Figure 8.7 Tongue extension elevation reinforcement.
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Figure 8.8 Tongue extension section reinforcement.
Figure 8.9 Tongue extension isometric view of reinforcement.
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8.4 INTERIOR HAUNCH CONNECTION As mentioned in section 8.3, a significant factor in U-beam bridge design is the precast concrete beam weight. To limit the weight of the pier segments with the bottom flange haunch, a secondary placement can be specified (Fig. 8.10). The need for thickening of the bottom flange at piers can also be reduced by using ultra-high-performance concrete for the bottom flange at and near the interior piers. Another issue, which is both a design and construction consideration related to means and methods, is the selecting of cast-in-place or precast concrete for bottom slab thickening at the pier. It may be difficult to achieve high design strengths in critical sections such as a bottom slab haunch if cast in the field, and precasting may be more desirable. If the bottom flange haunch is cast in place, it is necessary to couple the transverse reinforcement at the face of the joint (Fig. 8.11) or extend precast concrete reinforcement though the side face roughened construction joint (Fig. 2.4). These figures indicate that the joint, and therefore coupler or lap splice provided, are optional to provide flexibility so the bottom slab can be cast in the yard as one placement or in the field as two placements.
Figure 8.10 Haunch detail at piers.
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Figure 8.11 Haunch reinforcement detail (assuming construction joint).
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8.5 BLISTERS As mentioned in section 8.1, it may be necessary to have a top flange tendon in each web over the interior piers to bring tension and compression stresses within allowable limits during all stages of construction and final service life of the bridge. For the prototype design, a 12-strand tendon is anchored 18 ft 0 in. on each side of the centerline of pier 3. Figures 8.12 to 8.15 show the tendon blister details for the top tendon. Because the top flange is not large, the geometry of the tendon exiting from the top flange and reinforcement details are critical. It is appropriate to use the AASHTO LRFD specifications,2 Article 5.10.9, for the blister analysis and design. Another useful reference is a publication by Rogowky and Marti titled, Detailing for Post-Tensioning.15 Similar to the diaphragms described later, strut-and-tie models can be used for analysis and design of these blisters.
Regarding the top flange blister shown in Fig. 8.12 through 8.15, the blister extending outside the typical cross section may be cast as a secondary placement (Fig. 8.16). Also note reference to a connecting block adjacent to and between blisters in these figures. The connecting blocks are important to provide out-of-plane support to the webs.
Figure 8.12 Plan view of top blister. (Connecting block reinforcing not shown.)
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Figure 8.13 Partial elevation of top blister. (Connecting block reinforcing not shown.)
Figure 8.14 Section of top blister.
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Figure 8.15 Isometric view of top blister.
Figure 8.16 Block-out for top flange post-tensioning blister.
Appendix E gives schematic details for bottom flange blisters.
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8.6 DIAPHRAGM Diaphragms are cast at all the permanent piers to tie the two U-beams together and transmit loads to the bearings. The diaphragm carries vertical shear and torsion from the webs of the U- beam around the access opening to the bearings on the pier cap located at the centerline of each U-beam. Figure 8.17 shows the elevation view of the diaphragm at pier 3. The diaphragms at the end of the unit are similar. This section demonstrates strut-and-tie layouts that may be used to design a diaphragm for the prototype curved U-beam bridge with each U-beam supported on single bearings (See Figure 8.21).
Integral construction, or use of two bearings supporting each U-beam under the webs eliminates indirect supports. Hence, the diaphragm analysis can be simplified and reinforcing requirements reduced. Furthermore, the later details may potentially eliminate the need for a diaphragm between U-beams and facilitate skewed construction.
The interior diaphragm is 8 ft tall and approximately 32 ft wide and is 4 ft thick (Fig. 8.17). The horizontal span between bearings is approximately 23 ft, which depends on the superstructure cross slope. The assumed bearing plate at each bearing is 3 ft wide. The diaphragm includes two 3 ft diameter inspection access opening at the center of the U-beams to conform to Occupational Safety and Health Administration requirements.
Figure 8.17 Elevation view of interior diaphragm at pier 2.
Internal diaphragms are generally complex elements that must resist the introduction and transfer of various loads and reactions. Figure 8.18, adapted from Beaupre et al. (2011),16 shows an example of diaphragm cracking for a U-beam bridge that may occur if the bearing are set substantially inboard from the webs and force transfer is not accounted for by reinforcing—for example, to maintain traffic clearance by pier placement.
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Figure 8.18 Concrete box with centered bearing, similar to diaphragm for prototype.
Figures 8.19 and 8.20 show the application of diaphragm shear and torsion loadings used for the prototype bridge. In Fig. 8.20, beam action of the diaphragm is illustrated by the moment diagram (shaded orange) due to applied torques and the deflected shape shown with a dashed line. Anticipated tension and compression zones of the diaphragm are labeled. The web shear and torsion forces are assumed to be placed at the center of the transverse horizontal ties at the upper and portions of the web. Additionally, there is substantial continuity post-tensioning at the top of the section at the pier; hence, the need to provide some hanger reinforcing in the webs at this location is clear. Nonetheless, there are conflicting opinions and research regarding the placement of the resultant web shear and torsion forces, especially in the selection of the vertical level for the applied load. This is a complicated issue that partially depends on the longitudinal moment and shear-load-carrying behavior of the spans adjacent to the diaphragm. By providing some tie-up reinforcement in the web, the web cracking shown in Fig. 8.18 can be controlled. Nevertheless, the amount of tie-up reinforcing is substantial, and it is proposed to count all vertical reinforcing within d/2 of the diaphragm faces, plus the width of the diaphragm, when evaluating the demand versus the capacity of the tie-up bars. Struts from the upper portion of the tie-up reinforcing will be able to travel through the webs to nodes located at the middepth of the webs.
Figure 8.19 Diaphragm loads for shear.
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Figure 8.20 Diaphragm beam action due to applied torsional loads.
Strut-and-tie models may be used for the shear and torsion components to analyze their effects.16,17 Figure 8.21(a) shows the fan-shaped strut distribution of global longitudinal moment and shear forces. Figure 8.21(b) qualitatively shows the shear loads applied at the upper and lower portion of each web and the applied force couple resulting from pure torsion applied to one web. Ties at the upper and lower levels of the webs redirect the applied forces to the bearings. External to and between the U- beams, the diaphragm carries resultant torsional moment and shear between the two boxes via beam action.
a) Elevation view: Fan-shaped struts at intermediate diaphragm.
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b) Cross sectional view: Diaphragm transverse force flow.
Figure 8.21 Qualitative strut-and-tie models for diaphragm.
For the diaphragms at the ends of each unit where the continuity post-tensioning tendons are anchored, it is necessary to analyze and design reinforcement to resist the tensile stresses developed by the distribution of the anchorage forces into the diaphragm and U-beams. Figure 8.22 shows a simplified two-dimensional strut-and-tie model for the transfer of anchor loads from the diaphragm into the web and flanges of the U-beam. The top and bottom flange force is the equivalent force based on the section stress. The strut-and-tie model shows the controlling tie force is 0.25 to 0.30 of the factored applied post-tensioning force P. Based on this tie force, the area of steel required can be determined.
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Figure 8.22 Strut-and-tie model for tendon anchorage force distribution into the diaphragm at ends of unit.
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8.7 Bearings
The connection of the superstructure to substructure is an important design consideration. Bearings are engaged when the beams are placed or when falsework loads are released. The superstructure can be supported on bearings or made integral with the substructure assuming the piers are flexible enough to allow the necessary movements. The elimination of the bearings could result in lower initial cost and future maintenance savings. If bearings are used, pot or disk-type bearings may be an option. Figures 8.23 and 8.24 show the bearing configuration assumed for the prototype bridge. These figures show the bearing details for a fixed bearing. Bearings can be grouted at the permanent piers, which allows some translational and rotational tolerances to be built out during construction due to the room around pintles.
Figure 8.23 Transverse view of bearing.
With consideration of tolerances in the bearing design, it may be possible to erect directly on the bearings to eliminate shoring. Welded connections with steel taper plates have been used in some applications. The advantage of a welded connection is that tongue sections can be placed directly on the bearings without the use of falsework. If this detail is used, field welding must be properly detailed and executed for long-term performance and tolerances accounted for. If nonuniform bearing pressures are created, the elastomers can be overstressed and fail.
Elastomeric bearings are feasible provided they are designed with sufficient load and rotational capacities. Rotational checks must be made with code-recommended rotational setting tolerances. Furthermore, attention shall be given to all erection stages and any blocking or restraint required to prevent bearings from moving or disengaging during construction.
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Figure 8.24 Longitudinal view of grouted fixed bearing.
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REFERENCES
REFERENCES - 1 (April 2020)
REFERENCES 1. PCI Bridge Committee. 2012. Curved Precast Concrete Bridges State-of-the-Art Report. CB-
01-12. Chicago, IL: PCI.
2. AASHTO (American Association of State Highway and Transportation Officials). 2017. AASHTO LRFD Bridge Design Specifications. 8th ed., customary U.S. units. Washington, DC: AASHTO.
3. Nickas, W. N., and J. S. Dick. 2015. “Sharing New Technology Through PCI Bridge Technoquests.” Aspire 9 (3): S-1–S-15 (supplement). www.aspirebridge.com/magazine/2015Summer/ASPIRESupplementSummer2015.pdf
4. Stelmakc, T. 2016. “Design Considerations for Horizontally Curved Precast Concrete U- Girders.” Aspire 10 (1): 30–32. www.aspirebridge.com/magazine/2016Winter/CBT- DesignConsiderationforHorizontallyCurvedPrecastConcreteUGirders.pdf
5. WSDOT (Washington State Department of Transportation) Bridge and Structures Office. 2011. Bridge Design Manual (LRFD). M 23-50.05. Olympia, WA: WSDOT.
8. PTI (Post-Tensioning Institute). 2012. Guide Specification for Grouted Post-Tensioning. M50.3-12. Farmington Hills, MI: PTI.
9. Brice, R. 2018. “Designing Precast, Prestressed Concrete Bridge Girders for Lateral Stability: An Owner’s Perspective.” Aspire 12 (1): 10–12.
10. AASHTO. 2017. Guide Specification for Wind Loads During Construction. AASHTO GSWLB 1. Washington, DC: AASHTO.
11. PCI Bridge Design Manual Steering Committee. 2014. Bridge Design Manual. MNL-133. 3rd ed. Chicago, IL: PCI.
12. CEB/FIP (Euro-International Concrete Committee/International Federation for Prestressing). 1990 International System of Unified Standard Codes of Practice for Structures. Volume 2: CEB-FIP Model Code for Concrete Structures. Paris, France: CEB.
13. NCHRP (National Cooperative Highway Research Program). 2008. Development of Design Specifications and Commentary for Horizontally Curved Concrete Box-Girder Bridges. NCHRP Report 620. Washington, DC: Transportation Research Board. www.trb.org/Main/Public/Blurbs/160353.aspx
14. Bressan, M., and P. D. Kinderman. 2014. “Satus Creek Bridge.” Aspire 8 (2): 24–26.
15. Rogowsky, D. M., and P. Marti. 1991. Detailing for Post-Tensioning. VSL Report Series 3. Bern, Switzerland: VSL International. https://www.ethz.ch/content/dam/ethz/special-interest/baug/ibk/concrete-and-bridge-design- dam/lehre/masterstudium/Stahlbeton/Unterlagen/Detailing_for_post-tensioning.pdf
16. Beaupre, R. J., R. B. Anderson, and V. Bridges. 2010. Diaphragm for a Segmental Concrete Bridge. ACI Special Publication SP-273. Farmington Hills, MI: ACI.
17. Schlaich, J., K. Schafer, and M. Jennewein. 1987. “Toward a Consistent Design of Structural Concrete.” PCI Journal 32 (3): 74-150.
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REFERENCES
REFERENCES - 2 (April 2020)
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DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX A
ABBREVIATED STRUCTURAL DESIGN CRITERIA
APPENDIX A - 1 (April 2020)
APPENDIX A - ABBREVIATED STRUCTURAL DESIGN CRITERIA
A.1 INTRODUCTION TO ABBREVIATED STRUCTURAL DESIGN CRITERIA This appendix contains sample structural design criteria for curved, spliced, precast, prestressed concrete U beams. The criteria are intended to convey the design engineer’s intent to the project team. These abbreviated sample criteria highlight selected design assumptions, and are not intended to be a full and complete guide.
This sample criteria are provided for reference only. The engineer shall evaluate the appropriateness of the criteria for the intended project before their use.
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ABBREVIATED STRUCTURAL DESIGN CRITERIA
APPENDIX A - 3 (April 2020)
A1. GENERAL REQUIREMENTS
A1.1 Functional Requirements
TBD-BD (to be determined by designer): These features, related to the layout and
configuration of the bridge structure, shall be determined by the engineering design
team in accordance with the requirements specified and/or directed by the governing
agency.
A1.1.1 Bridge Classification
A1.1.2 Horizontal Alignment
A1.1.3 Vertical Alignment
A1.1.4 Typical Section
A1.1.5 Design Speed
A1.1.6 Bridge Railings
A1.1.7 Clearances – Vertical and Horizontal
A1.2 Codes, Standards, and Specifications
ACI Committee 209. 1982. Prediction of Creep, Shrinkage and Temperature Effects in
Concrete Structures. ACI 209R-82.
AASHTO LRFD Bridge Design Specifications. 2017. 8th ed., customary U.S. units.
AASHTO Guide Specifications: Thermal Effects in Concrete Bridge Superstructures. 1989.
AASHTO. Guide Specification for Design and Construction of Segmental Concrete
Bridges. 1999. 2nd ed.
AASHTO/AWS D1.5M/D1.5:2015. Bridge Welding Code. 7th ed., with Interim Revisions.
AASHTO. Construction Handbook for Bridge Temporary Works. 2017. 2nd ed.
AASHTO. Guide Design Specifications for Bridge Temporary Works. 2017. 2nd ed.
AASHTO. Manual for Bridge Evaluation. 2018. 3rd ed., with Interim Revisions.
ASTM A416/A416M-18. Standard Specification for Low-Relaxation, Seven-Wire Steel
Strand for Prestressed Concrete.
ASTM A615/A615M-18e1. Standard Specification for Deformed and Plain Carbon-Steel
Bars for Concrete Reinforcement.
ASTM A722/A722M-18. Standard Specification for High-Strength Steel Bars for
Prestressed Concrete.
CEB/FIP. 1990. International System of Unified Standard Codes of Practice for
Structures. Volume 2: CEB-FIP Model Code for Concrete Structures.
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A2. DESIGN PARAMETERS
A2.1 Reinforced Concrete Members
A2.1.1 Selected concrete mixture proportions, reinforcing type, and covers to satisfy
local practice and the anticipated exposure to environmental conditions
A2.2 Prestressed Concrete Members
a. Tolerable ranges of the assumed beam age at time of erection or closure shall be
shown in the plans.
b. The AASHTO LRFD specifications, Article 5.12.5, gives supplemental
recommendations for: thermal gradient, principal stress, and the combination of
vertical shear and transverse bending in the webs that may be used at the
discretion of the design professional.
A3. DESIGN LOADINGS
A3.1 Dead Loads
Table A3.1. Dead load – Force effects
Material Density/effect
Reinforced concrete* 150 lb/ft3
Plain concrete without reinforcement 145 lb/ft3
Post-tensioned concrete 155 lb/ft3
Structural steel 490 lb/ft3
Sacrificial deck thickness† TBD-BD
Stay-in-place (SIP) or temporary forms‡
TBD-BD
Note: TBD-BD = to be determined by designer. * Compute the concrete density accounting for concrete strength according to
AASHTO LRFD Table 3.4.1-1. † Many governing agencies require a nominal thickness of the deck to be included as a sacrificial overlay. If a sacrificial overlay is used, it shall be included in the dead load of the slab but shall be omitted from its section properties. ‡ If metal SIP forms are used, their weight shall be distributed over the projected area of the metal forms for the unit weight of metal forms and
concrete required to fill the form flutes. The governing agency shall be consulted regarding the use of metal SIP forms, SIP pretensioned concrete
deck panels, or temporary forms.
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A3.2 Superimposed Dead Loads
Table A3.2. Superimposed dead load – Force effects
Superimposed dead loads Weight
Future wearing surface TBD-BD
Traffic railing and median barriers TBD-BD
Utilities TBD-BD
Note: TBD-BD = to be determined by designer.
A3.3 Live Loads
A3.3.1 HL-93 Live Loads
Apply AASHTO LRFD specifications live-load HL93 design truck or tandem plus 0.64 kip/ft
uniform lane load.
Table A3.3. Load combinations for live-load cases
Design loads*
Load combination no.: 1 2
L o n
g it
u d
in a l
All regions,
all spans
HL93 design truck or tandem plus 0.64 kip/ft uniform lane load in all load lanes
AASHTO LRFD specifications
Articles 3.6.1.2
and 6.4.3
X
Negative moment
regions, all spans
90% of two HL93 design trucks in same lane spaced at
50 ft minimum plus 90% of 0.64 kip/ft uniform lane load
AASHTO LRFD specifications Article 3.6.1.3.1
X
* Apply vehicular dynamic load allowance IM of 33% to design truck and tandem only.
A3.3.2 Permit and Legal Loads
Permit load and legal loads shall be as defined by the governing agency.
A3.4 Wind Loads
A3.4.1 Wind loads for bridges computed in accordance with the AASHTO LRFD
specifications Article 3.8, and/or as defined by the governing agency.
A3.5 Thermal Loads
A3.5.1 Mean Temperature
TBD-BD
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APPENDIX A - 6 (April 2020)
A3.5.2 Coefficient of Thermal Expansion
Concrete: 6.0 × 10-6 per degree Fahrenheit
A3.5.3 Uniform Seasonal Temperature Rise and Fall
For structural design (concrete); see also AASHTO LRFD specifications Article 3.12:
Temperature rise TBD-BD
Temperature fall TBD-BD
Range TBD-BD
A3.5.4 Temperature Gradient
Thermal forces (longitudinal): Nonlinear temperature gradient is based on AASHTO LRFD
specifications Article 3.12.3, using the appropriate plain concrete surface for solar
radiation zone.
Thermal forces (transverse): Not considered.
Note: The AASHTO LRFD specifications Article C3.12.3 gives guidance related to the
exclusion of thermal gradient effects based on local performance experience.
A3.5.5 Deck Movements
For deck movements for design of bearings and expansion joints, per AASHTO LRFD
specifications Table 3.4.1-1, use 0.00 or 1.00 times the combined movements of creep,
shrinkage, and elastic shortening (bracketing the time-dependent behavior), plus 1.20
times the calculated movement due to temperature change.
Bearings accommodate motions that occur after girder erection; expansion joints
accommodate motions that occur after joint installation. Bearings and expansion joints
shall be designed to accommodate the full range of movement.
Bearings and expansion joints shall be adjusted based upon the temperature during the
time of installation.
A3.6 Creep and Shrinkage
A3.6.1 Strains are calculated in accordance with CEB/FIP Model Code for Concrete
Structures, 1978 or 1990, provisions developed by the American Concrete
Institute Committee 209; or AASHTO LRFD Section 5.4.2.3.
A3.6.2 Relative humidity: TBD-BD (see also the AASHTO LRFD specifications, Fig.
5.4.2.3.3-1)
A3.6.3 Permanent effects of creep and shrinkage shall be added to all AASHTO LRFD
specifications loading combinations with a load factor per Table 3.4.1-3.
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A3.7 Construction Loads
A3.7.1 TBD-BD: Minimum construction live load CLL of 10 lb/ft2 when permanent deck
slab is in place, per AASHTO LRFD Article 5.14.2.3.2. Additionally, 50 lb/ft2
loading across the width of the lid slabs and flanges during erection and 25
lb/ft2 across the full deck for falsework reactions has been used on previous
projects.
Apply construction equipment load CEQ for assumed weight of screed machine.
Apply CLL and CEQ as applicable per the load phases outlined in section A3.7.4.
A3.7.2 Wind loads on permanent and temporary components during construction shall
be considered. The design wind speed for evaluation of strength and stability
evaluations of temporary falsework may be reduced based on statistical
evaluations of the expected wind return period over the duration of the
construction. Wind loads during construction may be established by the owner.
A3.7.3 Wind load pressure coefficient:
a. Lid slab not in place: TBD-BD
b. Lid slab in place: TBD-BD
A3.7.4 Load phases during construction:
a. Lifting and hauling with beam self-weight (DC) and superimposed
dead load (DW) 20% up and 20% down of beam self-weight.
Beams supports located at lifting loops or at carrier support points denoted
on the plans or approved shop drawings.
b. Setting with beam self-weight (DC) 20% down (DC) of beam self-
weight for amplification of loads due to an abrupt placement.
Beam supports at ends.
c. Lid slab construction with beam self-weight (DC), lid slab self-weight
(DC), stay-in-place (SIP) forms between the girder webs and concrete filling
the SIP form flutes (DW) if applicable, and with construction load (CLL) over
the area of the lid slab and beam flanges.
Lid slab is noncomposite, and the beam is supported at ends before
stressing continuity post-tensioning. Lid slab is composite, and the beam is
supported as indicated by analysis after stressing continuity post-
tensioning. Temporary supports shall be removed before casting the deck
slab.
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d. Deck slab construction with beam self-weight (DC), deck slab self-
weight (DC), SIP forms and concrete filling the SIP form flutes (DW) over
the entire area of the bridge if applicable, 10 lb/ft2 construction load (CLL)
over the area of the bridge, and with construction equipment load (CEQ).
The 10 lb/ft2 construction load (CLL) and the construction equipment load
(CEQ) shall be configured in the worst location.
Deck slab is noncomposite, and the beam is supported at permanent
locations.
A3.7.5 Load combinations during construction
Table A3.4. Load factors for post-tensioned U beams during construction Load combination
Limit state (A,B,C, D)
DC DW EL CEQ CLL TU TG CR +
SH WS
Service I 1.00 1.00 1.00 1.00*
1.00 0.50† 1.00 1.00††
Service III 1.00 1.00 1.00 1.00 1.00 1.00 0.50† 1.00
Strength I 1.30 1.30 1.00 1.50 1.50 1.20 1.30
Strength III 1.30 1.30 1.00 1.50* 1.20 1.30 1.25††
Note: Differential load (DIFF), applicable to balanced cantilever construction, need not be considered. DC = dead load of structural components and nonstructural attachments; DW = dead load of wearing surfaces and utilities; EL = locked-in forces/stresses, including the primary and secondary effects of prestressing or post-tensioning; CEQ = construction
equipment; CLL = construction live load; TU = force effect due to uniform temperature; TG = force effect due to temperature gradient; CR = force effects due to creep; SH = force effects due to shrinkage; WS = wind load on structure. * For Service I and Strength III limit states, CEQ shall consider weight of screed rails and their supports along the length of the beams; however, the screed machine shall be assumed to be tied down at the pier location. † For Service I and Service III limit states, TG shall not be evaluated for lid slab before deck
casting. †† Wind speeds determined by governing agency.
A3.8 Differential Support Settlement
Differential support settlement requires the evaluation and potential monitoring of
settlement and movement of permanent and temporary foundations during erection
through post-tensioning. The contract documents shall specify limits of settlement for
temporary foundations in terms of magnitude and time.
A3.9 Load Combinations – Permanent Structure
A3.9.1 Load combinations shall be in accordance with AASHTO LRFD specifications
Tables 3.4.1-1 and 3.4.1-2.
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Table A3.5. Load factors for post-tensioned U beams for permanent structure
Load combination limit state
AASHTO LRFD specifications dead
and permanent loads
AASHTO LRFD specificationstransient loads
DC CR
SH
DW
EL w/ PS
sec.
LL WS WL FR TU TG
Service I 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.50
Service III 1.00 1.00 1.00 0.80 1.00 1.00 0.50
Strength I 1.25 1.50 1.00 1.75 1.00 0.50
Strength III 1.25 1.50 1.00 1.40 1.00 0.50
Strength V 1.25 1.50 1.00 1.35 0.40 1.00 1.00 0.50
DC = dead load of structural components and nonstructural attachments; CR = force effects due to creep; SH = force effects due to shrinkage; DW = dead load of wearing surfaces and utilities; EL = permanent effects of erection forces (for example, from erection equipment, changes in the statical system), including the secondary effects of post-tensioning; PS = secondary forces from post-tensioning for strength limit states; total prestressing forces for service limit states; LL = vehicular live load; WS = wind load on structure; FR = friction load; TU = force effect due to uniform temperature; TG = force effect due to temperature gradient; CR = force effects due to creep.
A4. MATERIALS
A4.1 Concrete
A4.1.1 All concrete properties shall be in accordance with the specified 28-day
compressive strength f’c and initial strength f’ci suggested in Table A4.1.
Table A4.1. Concrete properties
Location f’c, psi f’ci, psi
Traffic railing barrier 3400
Bridge deck and lid slabs 4500
Precast, prestressed concrete U beams 8500 6000
Prestressed concrete U beams (cast-in-place closure placements, haunched portions of bottom slabs, applicable blisters, and diaphragms)
6500 4500
Note: f’c = 28-day compressive strength; f’ci = initial strength. The concrete strengths indicated are suggested representative values and will vary based on the decision of the engineering design team and the governing agency.
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APPENDIX A - 10 (April 2020)
A4.2 Reinforcing Steel
A4.2.1 It is suggested that reinforcing steel conform to ASTM A615, Grade 60, unless
otherwise required.
A4.2.2 All reinforcing steel shall be black or epoxy as defined by the project contract
documents (plans and specifications) and the local governing agency.
A4.2.3 Mechanical couplers shall develop not less than 125% of the yield strength of
the bar.
A4.2.4 Headed reinforcing provided shall be in accordance with the project contract
documents (plans and specifications).
A4.3 Prestressing Steel
A4.3.1 Suggested Prestressing Parameters for Strand
All strands are assumed to be 0.6 in. in diameter, conforming to the requirements of ASTM
A416 Grade 270 for low-relaxation strands.
Post-tensioning:
Material properties/parameters: Tensile strength of prestressing strand fpu: 270 ksi
Yield strength of prestressing strand fpy : 243 ksi Modulus of elasticity: 28,500 ksi Anchor set: 3/8 in. Friction coefficient μ (internal tendons in polyethylene ducts): 0.23
Wobble coefficient k (internal tendons): 0.0002/ft
Allowable stresses: Maximum jacking stress at anchorage: 0.80fpu Maximum anchorage stress at anchorage immediately after anchorage: 0.70fpu
Max. anchorage stress at internal locations immediately after anchorage: 0.74fpu
A4.3.2 Suggested Prestressing Parameters for Bars
All bars shall conform to the requirements of ASTM A722 Grade 150.
Material properties/parameters: Tensile strength of prestressing bars fpu : 150 ksi Yield strength of prestressing bars fpy: 120 ksi
Modulus of elasticity: 29,700 ksi Maximum jacking stress: 0.80fpu
Maximum anchorage stress: 0.70fpu Anchor set: Zero Friction coefficient μ: 0.30 Wobble coefficient k: 0.0002/ft
Allowable stresses:
Maximum jacking stress at anchorage: 0.80fpu
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX A
ABBREVIATED STRUCTURAL DESIGN CRITERIA
APPENDIX A - 11 (April 2020)
Maximum anchorage stress at anchorage immediately after anchorage: 0.70fpu Max. anchorage stress at internal locations immediately after anchorage: 0.70fpu
A4.4 Grouting of Post-Tensioning Tendons and Bars
Grouting may be cementitious (bonded) or wax based (unbonded) as directed by the
governing agency.
A5. ALLOWABLE STRESSES
A5.1 Reinforced Concrete
Reinforced concrete shall be in accordance with the AASHTO LRFD specifications.
A5.2 Prestressed Concrete – Service Level
A5.2.1 Compression
Table A4.2. Compression stress limits
Location Design
stress limit
Temporary stresses before losses (AASHTO LRFD specifications Article 5.9.4.1)
Due to effective prestress, permanent loads, and transient loads due to shipping and handling. Estimate loads due to shipping and handling,
applied in addition of the weight of the beam, as 20%(up)/20%(down) of
the weight of the beam. See also section A3.7.4.
0.65f’ci (ksi or psi)
Stresses after losses (AASHTO LRFD specifications Table 5.9.4.2.2-1)
Due to effective prestress and permanent loads 0.45f’c (ksi or psi)
Due to effective prestress, permanent loads, and transient loads. 0.60f’c (ksi or psi)
A5.2.2 Longitudinal Tension (assuming bonded reinforcement and stress limits
to limit cracking)
Table A4.3. Tension Stress Limits
Location Design
Stress Limit
Temporary stresses before losses (AASHTO LRFD specifications Table 5.9.4.1.2-1)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX A
ABBREVIATED STRUCTURAL DESIGN CRITERIA
APPENDIX A - 12 (April 2020)
Due to effective prestress, permanent loads, and transient loads due to
shipping and handling. Estimate loads due to shipping and handling, applied in addition of the weight of the beam, as 20%(up)/20%(down) of the weight of the beam. See also section A3.7.4.
0.190∙√f’ci (ksi) 6.0∙√f’ci (psi)
Permanent condition after losses (AASHTO LRFD specifications Table 5.9.4.2.2-1)
Flexural tension: Areas outside of joints with minimum bonded auxiliary reinforcement
0.190∙√f’c (ksi) 6∙√f’c (psi)
Flexural tension: Closure joints with minimum bonded auxiliary reinforcement
0.095∙√f’c (ksi) 3∙√f’c (psi)
Principal tension: Neutral axis of web 0.110∙√f’c (ksi) 3.5∙√f’c (psi)
Construction load combinations (AASHTO LRFD specifications Table 5.14.2.3.3-1)
Flexural tension: All areas
Excluding “other loads” 0.190∙√f’c (ksi)
6∙√f’c (psi)
Including “other loads” 0.220∙√f’c (ksi)
7∙√f’c (psi)
Principal tension: Neutral axis of web
Excluding “other loads” 0.110∙√f’c (ksi) 3.5∙√f’c (psi)
Including “other loads” 0.126∙√f’c (ksi)
4∙√f’c (psi)
Design operating legal and permit limits (as defined by the governing agency)
Flexural tension: All areas TBD-BD
Principal tension: Neutral axis of web TBD-BD
A6. U-BEAM DESIGN DETAILS
A6.1 Longitudinal Tendons and Ducts
a. Minimum four tendons per web, or as specified by governing agency.
b. Horizontal and vertical spacing, the maximum of:
i. 4 in.; or,
ii. Outer duct diameter plus 1.5 times maximum aggregate size; or,
iii. Outer duct diameter plus 2 in.
c. Assumed post-tensioning duct out-to-out rib diameters:*
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX A
ABBREVIATED STRUCTURAL DESIGN CRITERIA
APPENDIX A - 13 (April 2020)
i. Twelve 0.6 in. strands: 3.58 in.
ii. Fifteen 0.6 in. strands: 3.94 in.
iii.Nineteen 0.6 in. strands: 4.57 in.
* Dimensions are for plastic duct. Revise for galvanized duct if they are allowed by
governing agency.
A6.2 Provisional Strands
Provisional strands are not required. Provisional strands may be provided at the discretion
of the governing agency. Alternatively, the jacking stress may be reduced to allow for
adjustment of post-tensioning.
A6.3 Future Post-Tensioning Strands
Future post-tensioning strands are not required.
A6.4 Average Radius for Pairs of Girders
Use same radius for pairs of girders along the length of the span.
A6.5 Maximum Girder Rotation at Kink Points
The maximum rotation shall be defined by maintaining the maximum and minimum haunch
specified in section A6.7.
A6.6 Girder Access Points
See section A7.6.
A6.7 Girder Haunch
• 6 in. maximum preferred for cast-in-place haunches; larger haunches are possible with appropriate detailing
• 1 in. minimum for cast-in-place lid slabs; 1½ in. minimum for precast concrete lid slabs
A6.8 SIP Forms
The governing agency shall be consulted regarding the use of metal SIP forms, SIP
pretensioned concrete deck panels, or temporary forms.
A7. MISCELLANEOUS
A7.1 Placement of Reinforcing Steel
A7.1.1 Concrete cover shown on the plans does not include placement or fabrication
tolerances unless noted as “minimum cover”.
A7.1.2 Dimensions shown on the plans from face of the concrete to reinforcing bars are the
clear distances, unless noted otherwise. Spacing of bars is center to center.
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX A
ABBREVIATED STRUCTURAL DESIGN CRITERIA
APPENDIX A - 14 (April 2020)
A7.1.3 Suggested minimum cover for reinforcing steel, or as specified by the governing
agency:
Superstructure:
Prestress U beams (interior and exterior) 2 in.
Prestress girders: girder top flange 1 in.
CIP, except top deck surface 2 in.
Top deck surface (including ½ in. sacrificial) 2½ in.
All other surfaces 2 in.
A7.2 Bearings
A7.2.1 Integral superstructure to substructure connections are recommended and
preferred. Multirotational disk or pot bearings may also be used to satisfy particular
project requirements and constraints.
A7.2.2 If bearing are used, it is suggested to include provisions for jacking of the
superstructure for replacement of all bearings. Bearing replacement may be
considered with a reduced live load.
A7.3 Expansion Joints
Expansion joints shall be in accordance with the project plans and specifications.
A7.4 Deck Drainage
Spread confined to shoulders and water conveyed to off-bridge drainage systems.
Optimally, drains shall be located at pier locations and drainage pipes shall be kept to the
exterior of the box girders. Consideration shall be given to force transfer for load paths
interrupted by pans for drainage systems.
A7.5 Lighting, Power, and Intelligent Traffic Systems
A7.5.1 Roadway Lighting: [TBD-BD]
A7.5.2 Aesthetic Lighting: [TBD-BD]
A7.5.3 Interior Power and Lighting: [TBD-BD]
It is suggested to provide interior lighting and electrical outlets at all ingress/egress access
openings and at midspan of each span. Only a single interior light and electrical outlet are
required if these locations coincide. Alternatively, the use of battery powered portable
lighting may be anticipated. The inclusion of interior lighting and power is generally
prescribed by the governing agency.
A7.5.4 Intelligent Traffic Systems (ITS): [TBD-BD]
A7.6 Maintenance and Inspection Access
Suggested U-beam inspection access is described below and shall comply with
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX A
ABBREVIATED STRUCTURAL DESIGN CRITERIA
APPENDIX A - 15 (April 2020)
Occupational Safety and Health Administration standards and consider confined space
entry:
A7.6.1 Provide access opening into the box through the bottom slab. Provide doors at all
bottom slab access openings.
A7.6.2 Provide access holes in diaphragms at both expansion and interior piers. Provide
doors at diaphragm access openings at expansion joints at all piers and abutments.
A7.6.3 Equip all doors at abutments and bottom flange entrances with a keyed lock and
hasp. Require that all locks on an individual bridge be keyed alike.
A7.6.4 Provide handles on either side of access holes for inspectors.
A7.6.5 Provide wooden ramps at diaphragms and bottom slab blisters to facilitate
inspection and equipment movement. Provide ramps that are continuous through
the access opening. Composite internal bottom flange build-ups used for haunched
girders may serve as ramps. For all other wood, meet the treatment requirements
of the project plans and specifications.
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX A
ABBREVIATED STRUCTURAL DESIGN CRITERIA
APPENDIX A - 16 (April 2020)
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DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX B
DESIGN DETAILS
APPENDIX B - 1 (April 2020)
APPENDIX B – DESIGN DETAILS
The illustrations and reinforcing details shown in this publication are samples from constructed projects. Local practices and requirements need to be followed.
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DESIGN DETAILS
APPENDIX B - 2 (April 2020)
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DESIGN DETAILS
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APPENDIX B - 9 (April 2020)
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APPENDIX B - 10 (April 2020)
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APPENDIX B - 11 (April 2020)
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DESIGN DETAILS
APPENDIX B - 12 (April 2020)
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APPENDIX B - 13 (April 2020)
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APPENDIX B - 14 (April 2020)
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DESIGN DETAILS
APPENDIX B - 15 (April 2020)
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DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
SAMPLE SPECIFICATIONS
APPENDIX C - 1 (April 2020)
APPENDIX C – SAMPLE SPECIFICATIONS The following sample technical specification was developed and adapted from projects constructed in Florida. Reference is given to sections of the Florida Department of Transportation (FDOT), “Standard Specifications for Road and Bridge Construction,” which are summarized below and are not intended to supersede the requirements of local jurisdictions.
DIVISION II CONSTRUCTION DETAILS
GENERAL CONSTRUCTION OPERATIONS
105 Contractor Quality Control General Requirement
STRUCTURES
346 Portland Cement Concrete
400 Concrete Structures
415 Reinforcing for Concrete
450 Precast Prestressed Concrete Construction
458 Bridge Deck Joints
462 Post-Tensioning
MATERIALS FOR PORTLAND CEMENT CONCRETE
(STRUCTURAL, PAVEMENT AND MISCELLANEOUS)
925 Curing Material for Concrete
DIVISION III MATERIALS
The most recent Florida specifications can be found at:
www.fdot.gov/programmanagement/Implemented/SpecBooks/
The following definitions are used in this sample technical specification:
FDOT – Owner Agency or Authorized Representatives
FDOT Inspector – Owner Agency’s (or Authorized Representatives) Inspection Team on site or at casting yard.
EOR – Engineer of Record responsible for U-Beam Plans and Technical Special Provision
As recommended industry practice, the following sample technical specification includes separate payment for Specialty Engineering of the Precast Prestressed Concrete Spliced U- Beams structure.
Modification of this sample technical specification is necessary for other projects, governing agencies, and delivery methods.
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SAMPLE SPECIFICATIONS
APPENDIX C - 2 (April 2020)
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SAMPLE SPECIFICATIONS
APPENDIX C - 3 (April 2020)
TECHNICAL SPECIAL PROVISION
For
PRECAST PRESTRESSED CONCRETE SPLICED U-BEAM BRIDGES
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SAMPLE SPECIFICATIONS
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SAMPLE SPECIFICATIONS
APPENDIX C - 5 (April 2020)
SECTION 450A PRECAST PRESTRESSED CONCRETE SPLICED U-BEAM BRIDGES
450A-1 Description.
Fabricate, store, transport and erect precast prestressed spliced structural U-Beam concrete superstructure segments to the established lines and grades, in accordance with the design, dimensions and details shown on the Plans and in accordance with this Technical Special Provision. Spliced U-Beams shall meet the requirements of Sections 400 and 450 of the FDOT Specifications except as appended by this Technical Special Provision.
Embedded reinforcing steel, other embedded items and all appurtenant items are included. Additionally, concrete, reinforcing and post-tensioning in cast-in-place portions of spliced U- Beams shall be in accordance with Sections 400, 415 and 462 of the FDOT Specifications, respectively.
The work in this Section 450A is applicable to longitudinally post-tensioned spliced beams upon which a concrete slab is cast-in-place.
450A-2 Qualification Requirements for Supervisory Personnel.
Meet the requirements of Section 105 of the FDOT Specifications.
Individuals filling the position of Project Engineer, Project Superintendent, and Foreman, shall have experience meeting the requirements of Section 105-8.8.6 of the FDOT Specifications.
450A-3 Quality Control Program.
Meet the requirements of Section 450-2 of the FDOT Specifications. The plant shall be certified by the Precast/Prestressed Concrete Institute (PCI). No substitutions will be accepted.
450A-4 Definitions.
The following definitions apply to precast prestressed spliced U-Beam bridge construction:
450A-4.1 U-Beam Segment: A modular section of the superstructure consisting of the U-Beam cross-section shape and length as detailed in the Plans. U-Beam pier segments may have a variable thickness bottom slab which can be cast be cast monolithically, or as a secondary pour, as detailed in the Plans.
450A-4.2 Casting Bed: A special formwork arrangement, meeting the requirements of
Section 450-6 and 5.2.2 of the FDOT Specifications, usually consisting of movable bulkheads of the cross-section shape with side and core forms capable of horizontal movement, designed and assembled into an assembly for making single or multiple superstructure spliced U-Beam segments.
450A-4.3 Lid Slab: A field cast partial depth portion of the deck slab cast between the top flanges of a single U-Beam to provide improved torsional characteristics to the spliced U-
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
SAMPLE SPECIFICATIONS
APPENDIX C - 6 (April 2020)
Beam structural system prior to application of longitudinal continuity post-tensioning and casting of the deck slab per the sequence indicated on the Plans.
450A-4.4 Closure Joints: The individual U-Beam segments are made in a casting bed. Continuous units are made when the individual segments are erected in the superstructure with a reinforced cast-in-place closure joint between each segment except at expansion joints. (During erection, all the segments of a span or multiple spans are supported by falsework, strongbacks, or other techniques until the closure joints have gained strength and the longitudinal post-tensioning installed and sequenced to make them self-supporting as indicated on the Plans.)
450A-4.5 Ground Splice: Two segments properly blocked and made into a single segment on the ground by casting a closure joint between the segments and subsequently post- tensioning. The combined segments are then incorporated as one segment into the permanent structure.
450A-4.7 Segment-By-Segment (Erection): Placing a specified number of segments on a temporary support system and permanent piers, with intermediate closure joints, aligned and post-tensioned longitudinally forming a completed unit of the superstructure from expansion joint to expansion joint.
450A-4.8 Camber: The amount by which the concrete profile at the time of erection must differ from the theoretical geometric profile grade to compensate for preceding beam build-ups, all structural dead load including that induced by the removal of falsework or temporary shoring, post-tensioning, all long term and time dependent deformations (creep and shrinkage) including all intermediate erection stages and effects. (The opposite of deflections.)
450A-4.9 Erection Elevation: The elevation at which a segment is set in the structure at the time it is erected. (This is profile grade corrected by the amount of deflection calculated to occur from that stage onwards.)
450A-5 Shop Drawings, Calculations and Manuals.
450A-5.1 General: Use methods and procedures providing adequate safety to the general public from construction/erection activities and/or falsework placed over or adjacent to traveled roadways, navigational or recreational waterways or any existing commercial, industrial or other facility.
450A-5.2 Information Required: Submit detailed shop drawings, calculations, manuals and other information, including, but not limited to, the following:
450A-5.2.1 U-Beam Segment Shop Drawings:
(1) A schedule of materials for segment fabrication including concrete, reinforcing steel, post-tensioning including ducts and hardware, prestressing steel (if applicable), grout, and other similar items.
(2) Each segment number and the direction of erection.
(3 ) Segment dimensions including widths, lengths, thicknesses, tapers, fillets, radii, working points, post-tensioning, clearances, rebar dimensions and spacing, embedded items, holes, anchorage positions, and other similar items.
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APPENDIX C - 7 (April 2020)
(4) Post-tensioning requirements as outlined in Section 462 of the FDOT Specifications. Check post-tensioning for consistency with pre-approved post-tensioning hardware and provide part numbers for FDOT pre-approved systems on the shop drawings. Substitution of parts or materials is not allowed. Profiles of post-tensioning shall be developed for each U-Beam segment, and at diaphragms and closure joints.
(5) The length of the spliced U-Beam segment, volume of concrete, weight of reinforcement and weight of post-tensioning in each precast segment and the total weight for reinforcement and post-tensioning for both the precast and cast-in-place portions of the U-Beam segments summarized and tabulated on the shop drawings.
(6) Details and calculations, as necessary, for any localized strengthening for concentrated supports and loads or reactions from any special erection equipment placed in locations not already allowed for in the Plans. Calculations and details for lifting and storage of U-Beam segments. Any effect to the Permanent Works caused or induced by the construction efforts and Temporary Works shall be evaluated.
(7) Details and supporting calculations for any modifications to segment geometry, cross-section dimensions, or segment length including any required changes to reinforcing and post-tensioning.
(8) Details of permanent and temporary embedded items including inserts, blockouts, temporary openings, holes, and other similar items; and any localized required strengthening and the materials and methods to fill and finish the holes.
(9) Detailed shop drawings shall be fully integrated depicting all information listed in (1) through (8) above.
450A-5.2.2 Casting Bed: Precaster shall provide information regarding:
(1) Procedures for spliced U-Beam segment fabrication including set-up and operation of the casting bed, movable rain and sun shades, geometry control stations, the storage and handling of rebar cages, placing and finishing concrete, curing of concrete, form stripping, and other similar items.
(2) Equipment for segment fabrication, including details of the forms for the manufacture of the segments, lifting and transportation of the segment in the yard, and other similar items.
(3) Segment storage including method of supporting the segments, placing erection marks and segment identification, and other similar items. Stacking of U-Beam segments will not be permitted.
(4) Segment transportation from the casting bed to the site.
450A-5.2.3 Erection Plan: Meet the requirements in 450A-9 of this Technical Special Provision.
450A-6 Materials.
450A-6.1 General: Use materials which conform to this Section 450A and the requirements prescribed in the FDOT Division III Specifications, Materials, for the particular kind and type of material specified.
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SAMPLE SPECIFICATIONS
APPENDIX C - 8 (April 2020)
450A-6.2 Concrete: Use concrete as specified in Section 346 except as specifically modified by this Technical Special Provision. Use No. 67 coarse aggregate in the concrete for segments with strengths as shown in the Plans. Screenings are not allowed as a substitute for silica sand for use in concrete for Precast Superstructure Segments.
450A-6.3 Reinforcing Steel: Use ASTM A615, Grade 60 reinforcing steel which meets the requirements of Section 415 of the FDOT Specifications. Field welding of reinforcing steel is not allowed.
As an alternative, the Contractor may submit to the EOR for approval alternate reinforcing details utilizing Welded Wire Fabric (WWF). If approved, WWF shall meet the requirements of ASTM A1064 deformed wire. No substitutions shall be made without prior approval of the EOR.
450A-6.4 Post-Tensioning Systems: Use post-tensioning hardware components meeting the requirements of Section 462 of the FDOT Specifications. Components are not interchangeable and must comply with the details of the approved shop drawings.
450A-7 U-Beam Segment Casting Requirements.
450A-7.1 General: Ensure that all materials, details, and procedures are as specified in this Technical Special Provision, as noted in the Plans, or as shown on the approved shop drawings.
Do not begin casting segments until the EOR approves the relevant shop drawings, calculations, casting manuals, concrete forms and concreting operations and the post-tensioning system components and layout if different from that on the Contract Plans. (Approval of post- tensioning stressing elongations and forces for field erection operations is not required at this stage but is required prior to erection.)
Give each segment an erection mark indicating its location, orientation and order in the erection sequence. Show erection marks on the erection plans or in the erection manual.
450A-7.2 Forms: The Contractor is responsible for the design and engineering of the forms as well as their construction. Exterior exposed surfaces of each element of the structure shall be formed with the same material to produce similar concrete surface textures, color, and appearance. Build the details shown on the Contract Plans or as amended by approved shop drawings into the forms.
Repair or replace worn, damaged, or otherwise unacceptable forms and obtain the Inspector's approval before casting any segment.
Where sections of forms are joined, ensure that offsets in flat surfaces do not exceed 1/16 inches and that offsets with corners and bends do not exceed 1/8 inches.
Ensure that all joints in the forms and contact points with bulkheads and existing segments have good fitting seals to prevent loss of fine material and cement grout.
Ensure forms are properly aligned to maintain cross-section and horizontal alignment shown on approved shop drawings. Check and inspect forms on a regular weekly basis to ensure proper alignment and geometric accuracy. Do not use forms which fail to meet the specified
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
SAMPLE SPECIFICATIONS
APPENDIX C - 9 (April 2020)
casting tolerances until such corrections are made to produce segments within the specified tolerances.
450A-7.3 Precast Geometry: Before commencing the casting operation, submit the proposed method of curve layout for all girder casting operations to the EOR for review. This submittal must include but is not necessarily limited to:
(1) All measuring equipment and procedures for layout of curved formwork
(2) Location of working points to be established on the forms for manufacturing the girders.
450A-7.4 Embedded Items:
450A-7.4. 1 General: Embedded items must be in accordance with specifications for prestressed, and post-tensioned construction as outlined in Sections 450 and 462 of the FDOT Specifications, respectively, and the requirements in this Technical Special Provision.
450A-7.4.2 Embedded Post-Tensioning Ducts: Ensure that embedded ducts for post-tensioning tendons and bars are positioned accurately to their required alignment. Properly fabricate and identify all ducts so that proper positioning is assured and can be verified after casting.
Utilize positive methods to ensure that ducts will not be displaced or damaged during concrete placement and consolidation. Adequately secure all embedded post-tensioning ducts to the reinforcement cage at intervals not exceeding 30 inches for steel pipes and 24 inches for plastic ducts. (Small ducts and very flexible ducts may require closer supports.) Any auxiliary ties and support bars needed for these purposes will be considered incidental and at no extra cost to the project. Prevent the concrete cover requirements from being violated by any auxiliary ties and support bars.
After installation in the forms, ensure that the ends of the ducts are sealed at all times to prevent entry of water, debris and fine material. Following each pour of concrete, demonstrate that all empty ducts are free of water and are unobstructed and undamaged. Immediately prior to installation of the prestressing steel into the ducts, again demonstrate to the satisfaction of FDOT that all ducts are unobstructed and free of water and debris.
450A-7.4.3 Anchor Plates and Castings: Prior to placing concrete in the forms either in the precast bed or the field, fix all tendon anchor plates and anchor castings in their respective position in the forms, connected to their duct and sealed to prevent mortar intrusion. Ensure that anchor plates and castings are rigidly fixed in the forms to maintain their correct alignment and position during concrete placement and consolidation.
450A-7.4.4 Reinforcing Steel: Fabricate and place reinforcing steel in accordance with the Contract Plans or as superseded by the approved shop drawings, in accordance with Section 450-9.1 of the FDOT Specifications, and as required in this Technical Special Provision.
Do not cut out or remove reinforcing steel to permit proper alignment of post-tensioning ducts except as indicated on the Plans. Replace any bar that cannot be fabricated to clear the
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SAMPLE SPECIFICATIONS
APPENDIX C - 10 (April 2020)
ducts by additional bars with adequate lap lengths and submit the details to the EOR for approval.
450A-7.5 Concrete Placement, Consolidation and Finishing:
450A-7.5 .1 General: Do not deposit concrete into the forms until the entire set- up of the forms, reinforcement, ducts, anchorages and embedded items have been thoroughly inspected and checked. Do not place concrete until FDOT is satisfied that all the above items have been properly inspected and checked, and the rate of producing and placing the concrete will be sufficient to complete the casting and finishing operations within the scheduled time, that experienced concrete finishers are available where required for finish work and that all necessary finishing tools and equipment are on hand at the site of the work and are in satisfactory condition for use.
During conveying and placement, protect concrete against undue drying, rise in temperature, and inclement weather.
450A-7.5.2 Concrete Placement Equipment: Use concrete placement equipment of a size and design which permits placing concrete within the specified time. Clean all equipment at the end of each operation or workday. Just prior to reuse, check the equipment again and clean off hardened concrete and foreign materials.
Place concrete by belt conveyors and by pumping in accordance with 400-7.6 and 400- 7.7 of the FDOT Specifications, respectively. Provide concrete with adequate slump to fill the volume of the forms with proper consolidation.
450A-7.5.3 Concrete Placement Sequence: Place concrete at the precast site in accordance with 450-10.3.2.5 of the FDOT Specifications.
450A-7 .5.4 Concrete Placement and Consolidation: Discharge individual loads of concrete into the forms, and place and consolidate in the required locations. After discharge into the forms, do not bodily move concrete from place to place within the forms by mechanical vibrators or other similar equipment.
Place and consolidate concrete with care so that post-tensioning ducts, anchorages and any other embedded items are maintained in their proper positions and are not damaged.
Consolidate all concrete using approved vibrators together with any other equipment necessary to perform the work as specified. Use internal vibrators having a minimum frequency of 8,000 vibrations per minute and sufficient amplitude to consolidate the concrete effectively. Provide at least two stand-by vibrators in working condition for emergency use in case of malfunction.
Use of external vibrators for consolidating concrete when the concrete is inaccessible for adequate consolidation by internal means. When external vibration is used, construct the forms sufficiently rigid to resist displacement or damage.
Vibrate concrete in a manner which avoids displacement or damage to reinforcement, post-tensioning ducts, anchorages and other embedded items.
No construction joints are allowed within a segment, except as detailed in the Plans.
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450A-7.5.5 Finishing: Give top surfaces of precast U-Beam components, lid slabs, or closure joints a rough surface finish of 1/4 inch amplitude.
450A-7.6 Curing:
450A-7.6. 1 General: Where casting cells are intended to operate on a short (daily) cycle and it can be demonstrated to the satisfaction of the EOR that the required initial concrete strengths for the removal of the forms, application of pre-stress, moving and handling of the segments and that the final concrete strength can be achieved in a timely and consistent manner, then steam curing will not be required. However, take precautions to promote proper curing by methods approved by the EOR and in accordance with Sections 400 and 450-10.6 of the FDOT Specifications. Such precautions must meet or exceed the following:
(a) To prevent moisture loss, cover all exposed surfaces (those not in contact with a form) as soon as possible after casting with a moisture tight covering (wet curing blankets or other approved equal systems).
(b) After stripping of the side and core forms, continue curing of the precast concrete by the application of a Type 2 (white pigmented) membrane curing compound as specified in Section 925-2 of the FDOT Specifications to all exposed surfaces (including segment exterior once exposed by removal from the form).
(c) Maintain the moisture tight covering for at least 72 hours. As an alternative, steam curing may be used.
450A-7.6.2 Steam Curing: Meet the requirements of Sections 400 and 450-10.6 of the FDOT Specifications modified by the following requirements when steam curing is used.
(1) Provide a device or devices for simultaneously recording the temperature of three widely separated locations per casting bed. Locate the three temperature sensors near the top, middle and bottom of the enclosure or as otherwise approved by the EOR. Identify the charts with the hours, dates and segment number and deliver to the FDOT inspector immediately after steam curing is completed unless otherwise approved.
450A-7.7 Removal of Forms: Prior to removing the forms, protect the plastic concrete from adverse weather effects.
Keep supporting forms in place until the concrete has reached the required strength for form removal as specified in the Plans, in this Section, or as shown on the approved shop drawings.
Provide test cylinders, made and cured in the same manner as the segment, to confirm the form release strength prior to removing form. With the approval of FDOT, a strength curve chart may be established to determine the time necessary for achieving the required form release strength, in accordance with the specifications for form removal.
Avoid damaging the segment when removing the forms. Notify the FDOT inspector of any damage which occurs and address in an approved manner.
450A-7.8 Test Samples: Provide additional test samples and testing for compressive strength on precast segments and field closure joints to control the construction activities and to ensure adequate strength of these components at various stages of their manufacture and
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assembly. Make test cylinders, in accordance with Section 346 of the FDOT Specifications, cured in the same manner as the structural components to ensure adequate compressive strength has been achieved in accordance with the plan requirements for the following conditions:
(a) Prior to release of prestressing for components which are to be pretensioned. (Note: No prestressing strands have been identified on the Plans for the curved post-tensioned U- Beams on this project.)
(b) Prior to form release and/or moving the components to storage.
(c) Prior to placing a component into position in the structure and/or stressing of longitudinal post-tensioning tendons if the component is less than 28 days old.
Determine the number of cylinders in accordance with the proposed method for casting, transporting and erecting the various components.
Provide the results of the compression testing of one or more test cylinders for controlling the time of execution of the various construction operations. Obtain FDOT's approval for meeting the specification requirements on casting, curing and testing of concrete test cylinders.
No direct payment will be made for the concrete testing. All costs for such testing will be included in the bid items for the various precast structural components.
450A-7.9 Beam Age: U-Beam component age for incorporating continuity post- tensioning shall be as shown on the Plans.
450A-7.10 Tolerances:
450A-7.10.1 General: Product dimension tolerances for spliced U-Beams shall meet the requirements outlined in Appendix B of PCI Manual MNL-116 (Manual for Quality Control for Plants and Production of Structural Precast Concrete Products) and those of Section
450-2.1 of the FDOT Specifications.
450A-7.10.2 Repairs: Identify and repair minor breakage, spalling, or honeycomb (not over 1 inch deep), and any other defects or deficiencies in accordance with Sections 450- 12, 450-13 and 450-14 of the FDOT Specifications. Repair of minor defects on joint surfaces is not required. Major breakage, spalling, or honeycomb in excess of 1 inch deep is subject to the EOR's structural review and approval. If found to be satisfactory, repair these areas using a method or procedure submitted by the Contractor and approved by the EOR. Do not perform surface finishing or repairs of minor cracking precast segments until after final erection of the segment, except as noted in this Technical Special Provision. Remove and dispose segments found to be unsatisfactory and not repairable after structural review and cast a new segment at no expense to the FDOT.
450A-8 Precast U-Beam Segment Handling, Storage and Shipment.
Handle, store and ship segments in accordance with Section 450-16 of the FDOT Specifications and details shown in the Plans. Handle segments using only the devices shown on the shop drawings for this purpose. Store all precast segments level in the upright position. Do not stack U-Beam segments one upon another.
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SAMPLE SPECIFICATIONS
APPENDIX C - 13 (April 2020)
Prior to shipment the FDOT inspector will thoroughly inspect each segment for damage. Thoroughly clean the faces of all joints of laitance, bond breaking compound and any other foreign material prior to shipment. Upon arrival at the bridge site an FDOT inspector will inspect each segment again. If in the FDOT inspector's opinion, any damage has occurred during shipment that will impair the function of the segment (structurally, aesthetically, etc.), the U- Beam segment will be referred to the EOR for further review. Replace any rejected U-Beam segment with an approved segment at no cost to FDOT. Provide firm support at bearing locations noted above.
450A-9 Erection.
450A-9.1 General: The work under this item consists of furnishing the design and erection plan for the erection of the U-Beams, including the design of any necessary falsework, shoring, bracing and cofferdams required during, or between, construction stages as detailed on the plans, shop drawings, and Specifications.
450A-9.1.1 References: The following references apply to this work and shall be used by the Contractor's Specialty Engineer when performing construction engineering and designing Temporary Works:
(1) AASHTO - LRFD Bridge Design Specifications - Customary U.S. Units,
2012 with 2013 Interims.
(2) AASHTO I AWS Dl.5/Dl. 5-2010 with 2011 and 2012 Interims - Bridge Welding Code.
(3) AASHTO - Construction Handbook for Bridge Temporary Works, 1st Edition (1995) with 2008 Interims.
(5) AASHTO - Guide Design Specifications for Bridge Temporary Works, 1st Edition (1995) with 2008 Interims.
(6) FDOT - Structures Design Manual effective date January 1, 2014.
450A-9.1.2 Qualifications: The Contractor's Specialty Engineer charged with preparing the erection drawings, calculations and manuals shall have a minimum of 5-years' experience in the design and erection of spliced precast concrete structures and shall be a Registered Professional Engineer in the State of Florida. The Contractor shall furnish the resume of its Specialty Engineer, which shall include a detailed description of projects worked on, the Specialty Engineer's role in these projects and owner references, which can verify the experience.
In addition to the above, the Specialty Engineer shall be qualified in accordance with Rule 1 4-75 Florida Administrative Code, Work Group 4.2.3: Major Bridge Design - Segmental.
450A-9.1.3 Construction Equipment: The Contractor shall furnish and maintain, at its own cost and risk, all tools, apparatus and appliances, equipment, and power for same, scaffolding, runways, ladders, temporary supports and bracing, and all other similar work or materials necessary to ensure speed, convenience, and safety in the execution of the work. All such items shall comply with OSHA regulations and other applicable codes and standards.
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450A-9.2 Construction Methods: The schematic construction sequence shown on the plans is not mandatory. The Contractor shall prepare a complete erection sequence based either on the construction sequence shown or a different erection sequence of its own choice. The contractor shall submit the proposed to the engineering for review. If the Engineer determines that the contractor's proposed erection sequence will significantly affect the performance of the permanent structure, the Contractor shall submit design calculations and detailed drawings to the EOR for review and approval. Any additional materials required by the contractors erection scheme shall all be at no cost to FDOT and coordinated with the Contractor's accepted Traffic Control Plan.
The furnishing of such plans, methods and calculations pertaining to the Contractor's erection sequence and their approval by the EOR shall not serve to relieve the Contractor of its responsibility for the safety of the work and the successful completion of the Project. The Contractor's erection methods must meet all requirements established in regulatory permits for the Project and must also conform to the requirements of the project criteria defined in the Plans-General Notes. The contactor's erection plan shall be signed and sealed by a Registered Professional Engineer in the State of Florida.
450A-9.3 Erection Plan: Before commencing erection operations, submit proposals for all U-Beam segment erection operations to the EOR for review. This submittal must be in the form of an "Erection Plan" and include but not necessarily be limited to:
(1) A detailed step-by-step sequence for the erection of each U-Beam segment including all intermediate procedures relating to erection equipment, temporary and permanent post-tensioning and making of closures between U-Beam segments, spans and/or cantilevers and other required sequencing.
(2) Positioning, use and sequencing of falsework, jacking and/or releasing of falsework, temporary towers, supports, tie-downs, counterweights, closure devices and the like.
(3) Positioning, use and sequencing of erection equipment, falsework, temporary bracing and the like, both on and off the structure, including the movement introduction and/or removal of any supports onto or connections with the structure. Include drawings and calculations for the structural effects of erection equipment on the structure.
(4) Scheduling of all temporary and permanent post-tensioning operations.
(5) Stressing forces and elongations for post-tensioning.
(6) Sequencing of grouting operations.
(7) Geometry control procedures for erection of the curved precast girders including but not limited to:
(a) Erection elevations for setting girders at temporary and permanent supports in order to achieve the deck elevations shown in the Plans, including calculations and/or test results to indicate estimated movement due to settlement, elastic shortening of falsework under load, etc.
(b) Procedures for monitoring elevations of erected girders throughout the construction process. Elevations shall be reported to the EOR for review.
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APPENDIX C - 15 (April 2020)
(c) U-beam build-ups at each web to be set in the field which include the theoretical geometric horizontal alignment, profile grade and superelevation appropriately combined with the camber.
(d) Proposed methods to make adjustments to erected girder elevations if required due to excessive movement/settlement after girders have been erected.
(8) Any other relevant operations as required and applicable to the structure type and construction method.
(9) Geotechnical information: The Contractor is responsible to obtain recommendations for: a) soil bearing or pile capacities; and, b) soil pressures induced on temporary shoring. These recommendations shall be signed and sealed by a Professional Engineer registered in the State of Florida and submitted to the EOR for review.
450A-9.4 Other Miscellaneous Erection Requirements:
450A-9.4.1 Closure Joints, Diaphragms, and Built-Up Bottom Slab Haunches: Ensure that concrete reaches the minimum required strength as shown in the Plans or in the Specifications prior to stressing the continuity post-tensioning. Ensure that the closure joint forms provide tolerances as specified under 450A-7.10 Tolerances.
450A-9.4.2 Temporary Works-Shoring, Bracing, Falsework and Formwork: The Contractor is responsible for identifying the need for and the design of any and all Temporary Works. Temporary bracing and shoring shall be designed to accommodate all loads to which the structure may be subjected during construction, including erection equipment and operation of the same. Such bracing shall be left in place as long as necessary for safety.
The Contractor shall submit plans and details for Temporary Works including shoring, falsework, bracing, blocking, and cofferdams, to the EOR for review to verify that they produce no adverse effect to the Permanent Works.
450A-9.4.3 Cranes Supported by the Permanent Structure: If the Contractor's Erection Plan requires the use of cranes supported by any permanent structure, the Contractor shall prepare and submit for review by the EOR a detailed plan, including supporting calculations, to verify that the erection method does not adversely affect any existing or new construction. Drawings shall include all details for attaching the cranes to the permanent structure including erection and removal details.
450A-9.5 Pressure Grouting of Bearings: Where designated on the Plans, pressure grout after the precast element and bearing have been set at the proper final elevation.
Submit materials and method to be used for pressure grouting the interface between the bearing and precast U-Beam to the EOR for approval.
450A-10
This section has been deleted.
450A- 11 Bridge Deck Construction and Surface.
Construct bridge deck and provide a Class 4 Floor Finish in accordance with Section 400 of the FDOT Specifications for Long Bridges subsequent to superstructure segment erection and prior
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
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to opening to traffic. Install expansion joints in accordance with Section 400 and other applicable Sections of the FDOT Specifications.
450A-12 Method of Measurement.
For Precast Prestressed Spliced U-Beams, the final lengths will be the plan quantity based on the casting lengths, as detailed on the plans along the centerline of each beam, subject to the provisions of subarticle 9-3.2 of the FDOT Specifications.
450A -13 Basis of Payment.
450A-13.1 General: Payment will be in accordance with the following:
450A-13.2 Precast Prestressed Spliced U-Beams: Payment will be made at the Contract unit price per linear foot for Precast Prestressed Spliced U-Beams, complete in place and accepted.
Such prices and payments will be full compensation for manufacture, storage, transport, assembly and erection of the segments complete and in place, including filling all concrete blockouts and similar miscellaneous details. These prices and payments will also include providing temporary and permanent segment access details, material testing, special erection equipment, temporary post-tensioning or prestressing, tools, labor and incidental items necessary for completing the work in accordance with the Plans, Specifications and approved shop drawings. All work and material for installing, maintaining, modifying or adjusting and removing shoring, falsework, bracing and cofferdams shall be incidental to the unit price (per foot) of the Precast Prestressed Spliced U-Beam.
The cost for concrete and reinforcing for haunched portions of the U-Beam bottom slab (precast or cast-in-place) shall be considered incidental to the unit price (per foot) of the Precast Prestressed Spliced U-Beam.
450A-13.3 Precast Prestressed Spliced U-Beams-Concrete: Payment for cast-in- place concrete for closure joints, diaphragm and details will be paid for under this item which also includes the cost of all formwork, closure devices and other temporary construction needed to make these closures and joints and cast-in-place segments or portions thereof as designated in the Plans.
Include the cost of providing a Class 4 floor finish on the bridge deck and approach slab surfaces in the cost of bridge deck and approach slab concrete.
The Bridge floor grooving will be measured and paid for separately.
No additional payment will be made for extra concrete necessitated by approved modifications to the segments or structure needed to accommodate the Contractor’s construction methods.
450A-13.4 Precast Prestressed Spliced U-Beams-Reinforcement: Payment for reinforcement embedded or originating in precast segments shall be considered incidental to the unit price (per foot) of the Precast Prestressed Spliced U-Beam.
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APPENDIX C - 17 (April 2020)
Payment for reinforcement in cast-in-place closure joints and other cast-in-place diaphragms and details will be at the Contract bid price per pound for reinforcing steel (prestressed spliced U-Beam closure pours and diaphragms) and will be in accordance with Section 400.
No additional payment will be made for extra reinforcement necessitated by accepted modifications to the segments or structure for the purposes of the Contractor’s construction methods.
450A-13.5 Precast Prestressed Spliced U-Beams-Post-Tensioning: Payment for permanent post-tensioning will be in accordance with Section 462.
No additional payment will be made for extra permanent or temporary post- tensioning or prestressing necessitated by accepted modifications to the segments or structure for the purposes of the Contractor’s construction methods, nor will payment be made for temporary tendons which are approved to be left in the structure, either stressed or unstressed, for the convenience of the Contractor’s operations.
450A-13.7 Precast Prestressed Spliced U-Beams-Non-Compliance: Any penalties or deductions for non-compliance with regard to concrete, reinforcement or post-tensioning will be applied to the work affected in accordance with the requirements of the respective specifications.
450A-13.8 Specialty Engineering Precast Prestressed Spliced U-Beams: Specialty Engineering required for the erection of the Precast Prestressed Spliced U-Beams structure shall be paid for separately.
450A-13.9 Payment Items:
Payment will be made under:
Item No. 400- 8-22 Class V Concrete (Closure Joint)–per cubic yard. Item No. 415- 1- 4 Reinforcing Steel (Superstructure)–per pound. Item No. 450A- 1 Precast Prestressed Spliced U-Beam, 84”–per foot. Item No. 450A- 2 Specialty Engineering for Precast Prestressed Spliced U-Beams
End of Section 450A
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
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The following sample technical specification was developed to allow the development of alternative designs in Colorado.
REVISION OF SECTION 631
ALTERNATIVE BRIDGE DESIGN & CONSTRUCTION
The Standard Specifications are hereby revised for this project to include Section 631, Alternative Bridge design & Construction, as follows:
DESCRIPTION
631.01 (a) The intent of this Special Provision is to provide to all bidders the option to submit a bid for the design and construction of an alternative bridge structure (“alternative bridge”), in lieu of submitting a bid for only the construction of the two-cell steel box girder structure shown on the Plans and referred to herein as the “default bridge”.
Bidders are not required to submit a bid for an alternative bridge; rather, that is an option, at their sole discretion. However, bidders are hereby notified that Colorado Department of Transportation (CDOT) will consider all submitted bids for the default bridge and for the alternate bridge together, and that CDOT will award to the low responsible and responsive bidder regardless of the particular type of bridge structure (default or alternative) bid by that bidder.
(b) The only alternative bridge structure type that is acceptable to CDOT under this Special Provision, and for which CDOT will consider a bid is Precast Post-tensioned horizontally curved U-Girders.
No other alternative bridge types will be considered by CDOT. Any bids submitted for alternative bridge types other than the type described above will be automatically rejected and will not be considered.
(c) The intent of this Special Provision is to provide a specification that is applicable to an alternative bridge. Any alternative bridge submitted by a bidder must be at least equivalent to the default bridge. To be considered “equivalent”, the alternative bridge:
(1) Must provide all of the architectural features, live load capacity, safety features, horizontal and vertical alignment, lateral clearance and minimum vertical clearances, as described herein and as shown on the Plans; and
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
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(2) Must include all work and materials to design and construct foundations, piers, abutments, and superstructure with all appurtenances, as described herein and as shown on the Plans.
(d) Any bid for an alternative bridge structure must strictly comply with all terms and conditions of this Special Provision, in order to be considered “responsive” and eligible for award.
DESIGN
631.02(a) General.
CDOT has not provided designs for the alternative bridge type described above. Therefore, if a bidder elects to submit a bid for the alternative bridge structure, the bid must include both the design and construction of the alternative bridge, and that bidder must provide a design for the alternative bridge (“alternative design”).
Further, the alternative design must be completed by a Professional Engineer registered in the State of Colorado. That Professional Engineer designer of the alternative bridge shall have been in responsible charge of the design of the type of structure being proposed within the past five years, and a list of successfully completed projects (which include the proposed type of structure) shall be provided as reference.
If a bidder who elects to submit a bid for the alternative bridge is the apparent low responsible bidder, that bidder shall submit the alternative design to the Award Officer for acceptance within 12 calendar days of bid opening. As part of the alternative design, the bidder shall provide to CDOT preliminary design calculations, a preliminary design and construction schedule, and preliminary drawings for the alternative bridge structure for preliminary approval. The preliminary drawings shall include a general layout, structure elevation, typical section, and girder erection scheme. Two hard copies of reproducible drawings shall also be included.
Bidders on alternative bridge should be aware that only the low bidder who gets the award will be compensated by CDOT for the design, as part of that bid; any bidders who will have performed design work before award, but do not get the award for any reason, will have performed that work at their sole cost and that design work will not be reimbursed by CDOT.
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
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If CDOT does not approve that preliminary design within 30 calendar days of bid opening (12 calendar days for bidder submittal, plus 18 calendar days for CDOT review), that bid will be rejected.
Any delay in the bidder’s submittal or CDOT’s review and approval of a proposed alternative design, or a revision thereto, shall not extend the contract time.
The Contractor shall ensure that the alternative design meets all applicable design criteria for strength and serviceability, as described herein and as shown on the Plans. The Contractor shall use the Plans, and the References and Guidelines in subsection 631.02(e), for the design criteria.
Alternative designs predicated on any errors or omissions in the Contract will be rejected. If any such error, omission or discrepancy is discovered, the Contractor shall notify the Engineer immediately. Failure to notify the Engineer will constitute a waiver of all claims for misunderstandings, ambiguities, or other situations resulting from error, omission, or discrepancy.
Experimental or demonstration-type design concepts, products, structures, or elements that have not been pre-approved by CDOT, in writing, for general use will not be permitted in the alternative design. Post-tensioned structural steel will not be permitted. Claims for design errors will not be allowed for any portion of alternative design.
The alternative design shall include an independent design check by an independent engineer registered in the State of Colorado.
(b) Final Plans and Specifications.
An alternative bridge design structure shall be identified by the same structure number as the default bridge.
On the alternative bridge design drawings, the title block shall show the Contractor’s signature in ink, the date signed, a business name, business address, and the note: “These drawings (Bxxx-Byyy) which supersede drawings (Bwww-Bzzz) were approved (insert date).”
The Contractor shall submit complete original plans and electronic files for an alternative design entirely in Auto-Cad 2000 format, and the Contractor shall make any changes in the same medium.
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
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The Contractor shall submit the final plans, the itemized quantity and cost break down, and the bridge field package, to the Engineer in accordance with the preliminary design and construction schedule. The final package for submittal shall include complete design calculations, design check calculations, and the bridge rating. Final bridge geometry, including project coordinates and dead load deflections, shall be included in the bridge field package.
For each portion of the alternative bridge, the Contractor shall submit two record sets of plans with design notes and computations to the Engineer one week prior to starting construction of that portion of the alternative bridge. The design notes and computations shall document the conclusions reached during the development of the construction plans. The plans and design computations will be reviewed by CDOT for completeness and to assure conformance with the design requirements only. However, all details of the alternative design plans, as well as the completeness and accuracy of those plans, are the Contractor’s sole responsibility. Designs and computations that are not in compliance with Design Requirements, in section 631.02(d) below, shall be corrected by the Contractor and resubmitted. The record sets shall bear the endorsement seal and signature of the Professional Engineer in responsible charge of the design and preparation of the plans.
(c) Design Computations.
The first sheet of the computations for the alternative bridge design shall contain the endorsement seal and signature of a Professional Engineer registered in the State of Colorado. Discrepancies between the design and the design check shall be resolved by the Contractor and all corrections shall be reflected in the design computations.
The complete set of design computations for the alternative bridge design shall include both substructure and superstructure and all appurtenances required. The structure shall be rated in accordance with the CDOT Bridge Rating Manual and subsection 3.2 of the CDOT Bridge Design Manual. The structure shall be designed for an HL-93 live load and the design shall conform to all AASHTO requirements as amended by the CDOT Bridge Design Manual.
In the event of a conflict or difference in interpretation of the design criteria, standards, or specifications that cannot be resolved, the decision of the Engineer shall be final.
The foundations design shall be consistent with the recommendations provided by the CDOT Geotechnical Section. In lieu of those recommendations, the Contractor may provide a foundation analysis by an independent geotechnical consultant. Costs for independent foundation analysis shall be borne by the Contractor.
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(d) Design Requirements.
The Standard Specifications shall apply to the construction of the alternative bridge.
The Contractor, in accordance with the Plans and the CDOT Bridge Design Manual, shall provide inspection and maintenance access to the alternative bridge.
The Contractor shall provide all roadway lighting attachments for the alternative bridge at the locations shown on the Plans.
All deck drains for the alternative bridge shall be placed by the Contractor at the locations, and of the same or greater hydraulic capacity, than shown on the Plans.
All earthquake restraints or pintels for the alternative bridge shall be provided by the Contractor in accordance with the CDOT Bridge Design Manual and AASHTO specifications.
The horizontal and vertical alignment for the alternative bridge shall be as shown on the Plans. All substructure locations for the alternative bridge shall be as shown on the Plans. All horizontal clearances to the traveled roadways for the alternative bridge shall be as shown on the Plans. All vertical clearances for the alternative bridge shall not be less than the minimum shown on the Plans.
All bearings, expansion devices, bridge rail and fence screening of the alternative bridge shall be in accordance with the Contract, and CDOT Staff Bridge Design Manual and Staff Bridge Design Worksheets.
The Contractor may use lightweight concrete for any portion of the alternative bridge only with written approval of the Owner or Governing Agency.
The texture finish and color scheme of the alternative bridge shall be as shown on the Plans. The pier column shape of the alternative bridge shall be as shown on the Plans. All piers shall be the same shape.
The alternative bridge shall be constant depth, or shall provide the appearance of constant depth. The girders of the alternative bridge shall be trapezoidal box shaped, and they shall be continuous. The minimum deck overhang from the edge of the deck to the face of the girder at the bottom of the deck shall be 3’-0”. The exterior webs of the boxes shall be sloped at one
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horizontal to four vertical (1:4). The Contractor shall not use intermediate hinge joints in the superstructure.
(e) Reference and Guidelines.
The following shall be applicable to the design and construction of an alternative bridge.
- Standard Specification for Road and Bridge Construction
- American Association of State Highway and Transportation Official (AASHTO) LRFD Bridge Design Specifications (1998 with 1999 and 2001 Interims)
- Colorado Department of Transportation M& S Standards (2000)
- Colorado Department of Transportation Bridge Design Manual (1992)
- Colorado Department of Transportation Bridge Rating Manual (1995)
- CDOT Staff bridge Design Worksheets
- CDOT Bridge Manual Vol. II Detailing and Checking Chapter 3
- ANSI/AASHTO/AWS Bridge Welding Code D1.5-95
- AASHTO Guide Specification for Design and Construction of Segmental Concrete Bridges
- AASHTO Guide Specification for Horizontally Curved Highway Bridges
- Colorado Department of Transportation (CDOT) Field Materials Manual
- CDOT Survey Manual
- CDOT Cost Estimates Item Book
- CDOT Cost Estimates Cost Data ( Current Addition)
- CDOT Procedural Directive 508.1 Professional Engineers Stamp
- Final Foundation Report; Structure #E-17-QJ
Future continuity reinforcement required by the AASHTO Guide specification for Precast Post- tensioned Segmental Bridges shall be external and shall be provided for with tendon blockouts, deviation blocks and anchor blocks.
MATERIALS
631.04 General: All materials used in the construction of an alternative bridge structure must meet the requirements of the applicable sections of the Standard Specifications.
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Materials that do not meet these requirements are subject to rejection or price adjustment.
CONSTRUCTION
631.07
(a) General. Construction of the alternative bridge shall strictly conform to the applicable sections of the Standard Specifications.
(b) Survey. Construction survey for the alternative bridge shall be in accordance with Section 625, as revised for this project.
(c) Traffic Control. Traffic control for the alternative bridge shall conform to the Traffic Control Plan included in the Contract.
(d) Construction Oversight and Inspection. Cost of quality assurance inspections will be the responsibility of CDOT. The Contractor shall be responsible for quality control inspections for the alternative bridge. The Contractor’s Engineer of Record shall check and approve all construction details, and records of post-tensioning and geometric control, for the alternative bridge.
The designer of a shored structure shall review and approve shoring and falsework details for construction of the proposed alternative bridge.
(e) Engineer’s Certification. The Contractor’s registered Engineer shall provide a letter certifying that the alternative bridge structure was constructed in accordance with the Contract, and that it meets all requirements of the design.
The presence of the Engineer of Record on the project shall in no way act to relieve the Contractor of the full responsibility for: conformance of the work to the requirements of the contract documents; the structural adequacy of the erection scheme he chooses; or the safety of workmen or the general public.
(f) As-constructed Plans. The Contractor shall provide copies of the as-constructed plans, shop drawings, and working drawings for the alternative bridge for informational purposes and for future maintenance. Complete as-constructed plans and electronic files for an
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
SAMPLE SPECIFICATIONS
APPENDIX C - 25 (April 2020)
alternative bridge shall be submitted by the Contractor entirely in AutoCAD 2000 format, and all changes shall be made by the Contractor in the same medium.
Falsework shall be removed prior to placement of the Type 7 Barrier.
The bottom slab and webs shall be placed monolithically. A construction joint between the bottom slab and web will not be allowed.
631.10 The alternative bridge design and construction will not be measured, but will be paid for on a lump sum basis, which basis will include all work and materials required to design and construct an alternative bridge.
The work will include, without limitation, the design, the independent design check, bridge rating, preparation of plans, details, and drawings required to fabricate and construct the alternative bridge, and the construction of the superstructure, foundations, abutments, railings and appurtenances. All discrepancies in quantities for the alternative bridge design will be the Contractor’s sole responsibility and will not be adjusted.
The completed structure shall include the following items, which will not be measured separately, but will be included in the bid price for Item 631, Alternative Bridge Design Construction:
Structure Excavation, Structure Backfill (Class 1), Structure Backfill (Class 2), Mechanical Reinforcement of Soil, Shoring, Drilled Caissons, Concrete Slope and Ditch Paving, Structural Steel, Bearing Devices, Bridge Drains, Concrete Sealer, Bridge Expansion Devices, Concrete Class D (Bridge), Structural Concrete Coating, Bridge Deck Finish (sawed Grooves), Reinforcing Steel, Reinforcing Steel (Epoxy Coated), Bridge Rail Type 7, Fence Chain Link (Special) (36 Inch), 1 Inch Electrical Conduit, 2 Inch Electrical Conduit, Prestressing Steel Wire or Strand, Prestressed Concrete Slab (Depth Less Than 6 Inches), Precast Concrete U Girder (Post-Tensioned), Mobilization and all other work and materials to complete the structure.
By submitting a bid for Alternative Bridge Design and Construction, the Contractor agrees to accept the amount of that bid, as a lump sum basis, for the complete and satisfactory performance of the work.
BASIS OF PAYMENT
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES______________APPENDIX C
SAMPLE SPECIFICATIONS
APPENDIX C - 26 (April 2020)
631.11 The accepted quantities for construction of the alternative bridge will be paid for at the contract lump sum bid as follows:
Payment will be made under:
Pay Item Pay Unit
Alternative Bridge Design & Construction Lump Sum
Lump sum Basis:
The lump sum bid price shall be full compensation for the cost of all the work, materials, tools, equipment, and incidentals required to complete the design and construction of the alternative bridge, including any modification required at bridge approaches. The work shall include design, independent design check, bridge rating, and plan preparation for the alternative bridge. Supplemental survey and foundation investigation required for alternative bridge shall also be included in the work. The Contractor’s construction oversight and quality control inspections shall be included in the work.
The Engineer will determine partial payment for the construction of the alternative bridge and include the partial payment on the monthly pay estimate.
Partial Payment and Price Reduction: The Contractor shall furnish an itemized quantity and cost break down of the Lump Sum bid to the Engineer prior to commencement of construction. The Contractor’s itemized quantity and cost break down shall reference the CDOT item numbers as provided in the CDOT Cost Estimates Item Book.
The Engineer will review the Contractor’s itemized quantity and cost break down to determine its trueness and reasonableness by using CDOT cost estimate data. The Contractor’s approved itemized quantity and cost break shall be used as a basis for calculating monthly partial payments and price adjustments for materials that do not meet specifications.
No adjustment will be made for differences in preliminary estimated quantities and final quantities.
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 1 (April 2020)
APPENDIX D - INTRODUCTION TO EXAMPLE CALCULATIONS Selected calculations are included to illustrate design concepts for curved, spliced, precast, prestressed concrete U-beams. These calculations build on the analysis and discussion presented for the prototype bridge in section 6 of this report.
These calculations are provided for reference only. The engineer shall evaluate the appropriateness of the calculations for the intended project before their use.
An example table of contents for a complete set of calculations is provided in this appendix. Calculations for a particular project will vary depending on the design opportunities and constraints, and the requirements of the project governing agency. Thus, a representative collection of abbreviated calculations related to curved U-beam design is provided, including the following:
• Flexure at service limit state
• Flexure at strength limit state
• Web design at service limit state – Principal tensile stress
• Web design at strength limit state
• Beam camber
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 2 (April 2020)
D.1 EXAMPLE TABLE OF CONTENTS FOR CALCULATIONS 1 General
1.1 General 1.2 Tender Design Layout 1.3 Design Criteria 1.4 Survey Information 1.5 Geotechnical Information 1.6 Bridge Drainage 1.7 Utilities 1.8 Traffic Data 1.9 Special Provisions
2 Geometry 2.1 Geometry Computations
2.1.1 Clearance Criteria 2.1.2 Geometry Data 2.1.3 Roadway to Bridge Horizontal Clearances (Bridge Layout) 2.1.4 Roadway to Bridge Vertical Clearances
2.2 Geometrics 2.2.1 Roadway Geometry 2.2.2 Bridge Geometry 2.2.2.1 Bridge Geometry 2.2.2.2 Girder Geometry 2.2.2.3 Beam Dimensions 2.2.2.4 Finished Grade Elevations 2.2.2.5 Beam Seat Elevations
2.2.3 End Bent Layout and Elevations 2.2.4 Top of Footing and Pile Cut Off Elevations 2.2.5 Pier Geometry and Elevations 2.2.6 Pile Group Work Point Coordinates
3 Superstructure 3.1 General
3.1.1 Material Properties 3.1.2 Section Properties
3.2 Construction Design 3.2.1 Construction Loads 3.2.2 Lifting and Transport
3.3 Loading 3.3.1 Dead Loads 3.3.2 Superimposed Dead Loads 3.3.3 Live Loads 3.3.4 Creep and Shrinkage 3.3.5 Temperature Loads 3.3.6 Post-Tensioning
3.3.6.1 General 3.3.6.2 Tendon Geometry 3.3.6.3 Jacking Analysis 3.3.6.4 Tendon Input Data
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 3 (April 2020)
3.4 Slab Design 3.4.1 Slab Design 3.4.2 Slab Pouring Sequence
3.5 Main Girder Design - Transverse 3.5.1 Model Input 3.5.2 Model Output 3.5.3 Slab & Girder Design
3.6 Main Girder Global Analysis - Longitudinal (Time Dependent Model Input) 3.6.1 Model Layout
3.6.1.1 Superstructure Element Numbering 3.6.1.2 Substructure Element Numbering 3.6.1.3 Boundary Conditions & Temporary Supports 3.6.1.4 Girder Geometry
3.6.2 Geometry Input 3.6.3 Element Properties
3.6.3.1 Material Properties 3.6.3.2 Creep & Shrinkage Properties
3.6.4 Section Properties 3.6.4.1 U-Beams 3.6.4.2 Piers 3.6.4.3 Deck Slab 3.6.4.4 Diaphragms
3.6.5 Loadings 3.6.5.1 Dead Loads 3.6.5.2 Post-Tensioning 3.6.5.3 Construction Loads 3.6.5.4 Live Loads 3.6.5.5 Temperature Loads 3.6.5.6 Load Combinations
3.6.6 Construction Schedule & Casting Dates 3.6.7 Verification Model
3.6.7.1 Model Input 3.6.7.2 Model Output 3.6.7.3 Model Comparison to Design Model
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 4 (April 2020)
3.7 Main Girder Design - Longitudinal 3.7.1 General
3.7.1.1 Section Properties 3.7.1.2 Post-Tensioning 3.7.1.3 Mild Reinforcement Data
3.7.2 Load Combinations 3.7.3 Flexure at Service Limit State <- Included
3.7.3.1 Left Girder 3.7.3.2 Right Girder
3.7.4 Flexure at Strength Limit State <- Included 3.7.4.1 Left Girder 3.7.4.2 Right Girder
3.7.5 Web Design at Service Limit State - Principal Tensile Stress <- Included 3.7.5.1 Left Girder 3.7.5.2 Right Girder
3.7.6 Web Design at Strength Limit State <- Included 3.7.6.1 Left Girder 3.7.6.2 Right Girder
3.7.7 Erection Stresses Envelopes 3.7.7.1 Left Girder 3.7.7.2 Right Girder
3.7.8 Temporary Towers Service Loads 3.8 Diaphragm Design
3.8.1 General 3.8.2 Loadings 3.8.3 Interior Pier Diaphragm 3.8.4 Expansion Diaphragm 3.8.5 Anchorage 3.8.6 Shear Friction Check 3.8.7 Spalling Reinforcement Check 3.8.8 Reinforcement Details - Interior 3.8.9 Reinforcement Details - Expansion
3.9 Closure Joint Segment Design 3.10 Blister Design
3.10.1 Intermediate Anchorage Details 3.10.1.1 Top Blister 3.10.1.2 Bottom Blister
3.10.2 U-Beam End Anchorage Details 3.11 Access Opening Design 3.12 Tendon Radial Confinement 3.13 Camber 3.13.1 Camber Design <- Included
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 5 (April 2020)
4 Substructure - End Bents 4.1 Layout and Geometry 4.2 End Bent Loads 4.3 End Bent Pile Design and Strap Forces
4.3.1 Pile Axial Loads and Strap Forces 4.3.2 Pile Lateral Analysis
4.4 End Bent Cap Design 4.4.1 Cap Design 4.4.2 Detailing Summary
5 Substructure - Piers 5.1 Pier Geometry
5.1.1 Pier Design Geometry 5.1.2 Minimum Beam Seat
5.2 Pier Loads 5.2.1 Load Combinations 5.2.2 Superstructure Loads from Design Model 5.2.3 Centrifugal Loads 5.2.4 Braking Loads 5.2.5 Wind Loads
5.3 Pier Cap Design 5.3.1 Strut and Tie Model Design 5.3.2 Beam Model Design
5.4 Pier Column Design 5.4.1 Column Design 5.4.2 Serviceability Check 5.4.3 Shear and Torsion Design
5.5 Pile Design 5.5.1 Pile Axial Load Design 5.5.2 Pile Lateral Analysis
5.6 Pile Cap Design 5.6.1 Pile Cap Design
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 6 (April 2020)
D.2 FLEXURE AT SERVICE LIMIT STATE
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 7 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 8 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 9 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 10 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 11 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 12 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 13 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 14 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 15 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 16 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 17 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 18 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 19 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 20 (April 2020)
D.3 FLEXURE AT STRENGTH LIMIT STATE
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 21 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 22 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 23 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 24 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 25 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 26 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 27 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 28 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 29 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 30 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 31 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 32 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 33 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 34 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 35 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 36 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 37 (April 2020)
D.4 WEB PRINCIPAL AT SERVICE LIMIT STATE PRINCIPAL TENSILE STRESS
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 38 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 39 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 40 (April 2020)
D.5 WEB DESIGN AT STRENGTH LIMIT STATE
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 41 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 42 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 43 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 44 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 45 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 46 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 47 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 48 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 49 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 50 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 51 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 52 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 53 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 54 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 55 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 56 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 57 (April 2020)
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EXAMPLE CALCULATIONS
APPENDIX D - 58 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 59 (April 2020)
D.6 CAMBER
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 60 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX D
EXAMPLE CALCULATIONS
APPENDIX D - 61 (April 2020)
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EXAMPLE CALCULATIONS
APPENDIX D - 62 (April 2020)
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EXAMPLE CALCULATIONS
APPENDIX D - 63 (April 2020)
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EXAMPLE CALCULATIONS
APPENDIX D - 64 (April 2020)
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DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 1 (April 2020)
APPENDIX E - PCI STANDARDS
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 2 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 3 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 4 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 5 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 6 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 7 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 8 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 9 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 10 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 11 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 12 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 13 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX E
PCI STANDARDS
APPENDIX E - 14 (April 2020)
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PCI STANDARDS
APPENDIX E - 15 (April 2020)
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PCI STANDARDS
APPENDIX E - 16 (April 2020)
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PCI STANDARDS
APPENDIX E - 17 (April 2020)
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PCI STANDARDS
APPENDIX E - 18 (April 2020)
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PCI STANDARDS
APPENDIX E - 19 (April 2020)
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PCI STANDARDS
APPENDIX E - 20 (April 2020)
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PCI STANDARDS
APPENDIX E - 21 (April 2020)
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APPENDIX E - 22 (April 2020)
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DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 1 (April 2020)
APPENDIX F - PCI-PROJECT QUESTIONNAIRE RESPONSES
The information presented on these questionnaires was collected from available plan sets and may not represent the actual as-built condition of the structure. For bridges with multiple units, only the unit containing the controlling span was recorded.
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 2 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 3 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 4 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 5 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 6 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 7 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 8 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 9 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 10 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 11 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 12 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 13 (April 2020)
DESIGN OF CURVED, SPLICED PRECAST CONCRETE U-BEAM BRIDGES_____________APPENDIX F
PROJECT QUESTIONNAIRE RESPONSES
APPENDIX F - 14 (April 2020)
A PCI Report
8770 W. Bryn Mawr Ave. | Suite 1150 | Chicago, IL 60631-3517 | 312-786-0300 | www.pci.org
- U1.0 About This Document
- U1.1 Structure of the Document
- U1.1.1 Using Links
- U1.1.2 Numbered Paragraphs
- U1.1.3 Page Header
- U1.1.4 Page Footer
- U1.1.5 Figures and Tables
- U1.2 Revisions and Registration
- U1.2.1 Registering Your Copy
- U1.2.2 Errors and Omissions
- U1.2.3 Dissemination of Corrections
- U1.3 Exchange of Suggestions
- U1.3.1 Send Your Suggestions
- U1 3.2 Our Suggestion
- TABLE OF CONTENTS
- TABLE OF FIGURES
- CHAPTER 1 - CURVED, SPLICED PRECAST CONCRETE U-BEAM CONCEPT
- 1.1 GENERAL
- 1.2 OBJECTIVE
- 1.3 LIMITS OF APLICABILITY
- 1.4 DEFINITIONS AND GLOSSARY OF TERMS
- 1.5 NOTATION
- 1.5.1 Loads
- 1.5.2 General
- 1.6 UNITS
- 1.7 REFERENCE CODE
- CHAPTER 2 - IMPLEMENTATION OF CURVED, SPLICED U-BEAM SYSTEM
- 2.1 GENERAL
- 2.1.1 Review of Projects
- 2.1.2 U-Beam Cross Section
- 2.1.3 Span-to-Depth Ratios
- 2.2 FABRICATION AND CONSTRUCTION
- 2.2.1 U-Beam Fabrication
- 2.2.2 Transportation in Yard
- 2.2.3 Transportation to and at Site
- 2.2.4 Temporary Falsework and U-Beam Placement
- 2.2.5 Lid Slabs
- 2.2.6 Closure Joints
- 2.2.7 Post-Tensioning
- 2.2.8 Deck Screeding
- CHAPTER 3 - PROJECT DELIVERY
- 3.1 DESIGNER ROLE AND STATED ASSUMPTIONS
- 3.2 SPECIALTY ENGINEER ROLE AND SUBMITTALS
- 3.3 TECHNICAL SPECIFICATIONS
- 3.3.1 Erection Plan
- 3.3.2 Geometry Control Procedures
- CHAPTER 4 -DESIGN CRITERIA
- 4.1 GENERAL
- 4.2 LIMIT STATES – CONSTRUCTION PHASE
- 4.3 TORSIONAL CHECKS
- CHAPTER 5 - PRELIMINARY DESIGN AND SPAN LAYOUT
- 5.1 USE OF STRAIGHT AND CURVED SECTIONS
- 5.2 LID SLAB AND DECK
- 5.3 FALSEWORK TOWERS
- 5.3.1 Temporary Tower Size and Configuration
- 5.3.2 Lateral Loads and Sway Bracing in Towers
- 5.4 STRONGBACKS
- 5.5 GROUND SPLICING
- 5.6 SECTIONAL DESIGN FOR SERIVE LIMIT STATE
- 5.6.1 Span-to-Depth Ratio
- 5.6.2 Parametric Data
- 5.6.3 Effect of Radius
- 5.6.4 Effect of Pier Fixity
- CHAPTER 6 - MODELING AND ANALYSIS
- 6.1 SELECTION OF PROTOTYPE BRIDGE
- 6.2 MATERIALS
- 6.3 CONSTRUCTION SEQUENCE AND AGE AT CONSTRUCTION
- 6.4 SPLICE LOCATIONS AND BOUNDARY CONDITIONS
- 6.5 SECTION PROPERTIES
- 6.6 TEMPORARY WORKS
- 6.7 DISTRIBUTION FACTOR
- 6.8 PIER FIXITY
- 6.9 THREE-DIMENSIONAL MODELING – FLEXURE, SHEAR, AND TORSION
- 6.10 PRINCIPAL WEB STRESS
- 6.11 TRANSVERSE DECK SLAB
- 6.12 GEOMETRY CONTOL PROCEDURES
- 6.12.1 Camber Requirements
- 6.12.2 Rotation of U-Beam Section
- 6.12.3 Build-Up Calculation and Deck Screeding
- CHAPTER 7 - DESIGN CONSIDERATIONS
- 7.1 PLANT HANDLING, TRANSPORT, AND LIFTING OUT OF FORMS
- 7.1.1 Internal Bracing
- 7.1.2 Overturning
- 7.1.3 Lifting
- 7.2 SECTIONAL DESIGN FOR ULTIMATE LIMIT STATE
- 7.2.1 Longitudinal Reinforcing Check
- 7.2.2 Transverse Web Reinforcing
- 7.2.3 Reinforcing Parameters
- 7.3 SECTIONAL DESIGN FOR SERVICE LIMIT STATE
- 7.3.1 Longitudinal Stress Check
- 7.3.2 Principal Stress Check
- CHAPTER 8 - DESIGN DETAILS
- 8.1 TYPICAL SECTION AND POST-TENSIONING
- 8.2 LID SLAB AND DECK DETAILS
- 8.3 PRECAST CONCRETE TONGUE
- 8.4 INTERIOR HAUNCH CONNECTION
- 8.5 BLISTERS
- 8.6 DIAPHRAGM
- REFERENCES
- APPENDIX A - INTRODUCTION TO APPREVIATED STRUCTURAL DESIGN CRITERIA
- A.1 INTRODUCTION TO ABBREVIATED STRUCTURAL DESIGN CRITERIA
- APPENDIX B - DESIGN DETAILS
- APPENDIX C - SAMPLE SPECIFICATIONS
- APPENDIX D - EXAMPLE CALCULATIONS
- D.1 EXAMPLE TABLE OF CONTENTS FOR CALCULATIONS
- D.2 FLEXURE AT SERVICE LIMIT STATE
- D.3 FLEXURE AT STRENGTH LIMIT STATE
- D.4 WEB PRINCIPAL AT SERVICE LIMIT STATE PRINCIPAL TENSILE STRESS
- D.5 WEB DESIGN AT STRENGTH LIMIT STATE
- D.6 CAMBER
- APPENDIX E - PCI STANDARDS
- APPENDIX F - PCI-PROJECT QUESTIONNAIRE RESPONSES
