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NATIONAL NCHRP REPORT 655 COOPERATIVE HIGHWAY RESEARCH PROGRAM Recommended Guide Specification for the Design of Externally Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements

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TRANSPORTATION RESEARCH BOARD 2010 EXECUTIVE COMMITTEE* OFFICERS CHAIR: Michael R. Morris, Director of Transportation, North Central Texas Council of Governments, Arlington VICE CHAIR: Neil J. Pedersen, Administrator, Maryland State Highway Administration, Baltimore EXECUTIVE DIRECTOR: Robert E. Skinner, Jr., Transportation Research Board MEMBERS J. Barry Barker, Executive Director, Transit Authority of River City, Louisville, KY Allen D. Biehler, Secretary, Pennsylvania DOT, Harrisburg Larry L. Brown, Sr., Executive Director, Mississippi DOT, Jackson Deborah H. Butler, Executive Vice President, Planning, and CIO, Norfolk Southern Corporation, Norfolk, VA William A.V. Clark, Professor, Department of Geography, University of California, Los Angeles Eugene A. Conti, Jr., Secretary of Transportation, North Carolina DOT, Raleigh Nicholas J. Garber, Henry L. Kinnier Professor, Department of Civil Engineering, and Director, Center for Transportation Studies, University of Virginia, Charlottesville Jeffrey W. Hamiel, Executive Director, Metropolitan Airports Commission, Minneapolis, MN Paula J. Hammond, Secretary, Washington State DOT, Olympia Edward A. (Ned) Helme, President, Center for Clean Air Policy, Washington, DC Adib K. Kanafani, Cahill Professor of Civil Engineering, University of California, Berkeley Susan Martinovich, Director, Nevada DOT, Carson City Debra L. Miller, Secretary, Kansas DOT, Topeka Sandra Rosenbloom, Professor of Planning, University of Arizona, Tucson Tracy L. Rosser, Vice President, Corporate Traffic, Wal-Mart Stores, Inc., Mandeville, LA Steven T. Scalzo, Chief Operating Officer, Marine Resources Group, Seattle, WA Henry G. (Gerry) Schwartz, Jr., Chairman (retired), Jacobs/Sverdrup Civil, Inc., St. Louis, MO Beverly A. Scott, General Manager and Chief Executive Officer, Metropolitan Atlanta Rapid Transit Authority, Atlanta, GA David Seltzer, Principal, Mercator Advisors LLC, Philadelphia, PA Daniel Sperling, Professor of Civil Engineering and Environmental Science and Policy; Director, Institute of Transportation Studies; and Interim Director, Energy Efficiency Center, University of California, Davis Kirk T. Steudle, Director, Michigan DOT, Lansing Douglas W. Stotlar, President and CEO, Con-Way, Inc., Ann Arbor, MI C. Michael Walton, Ernest H. Cockrell Centennial Chair in Engineering, University of Texas, Austin EX OFFICIO MEMBERS Thad Allen (Adm., U.S. Coast Guard), Commandant, U.S. Coast Guard, U.S. Department of Homeland Security, Washington, DC Peter H. Appel, Administrator, Research and Innovative Technology Administration, U.S.DOT J. Randolph Babbitt, Administrator, Federal Aviation Administration, U.S.DOT Rebecca M. Brewster, President and COO, American Transportation Research Institute, Smyrna, GA George Bugliarello, President Emeritus and University Professor, Polytechnic Institute of New York University, Brooklyn; Foreign Secretary, National Academy of Engineering, Washington, DC Anne S. Ferro, Administrator, Federal Motor Carrier Safety Administration, U.S.DOT LeRoy Gishi, Chief, Division of Transportation, Bureau of Indian Affairs, U.S. Department of the Interior, Washington, DC Edward R. Hamberger, President and CEO, Association of American Railroads, Washington, DC John C. Horsley, Executive Director, American Association of State Highway and Transportation Officials, Washington, DC David T. Matsuda, Deputy Administrator, Maritime Administration, U.S.DOT Victor M. Mendez, Administrator, Federal Highway Administration, U.S.DOT William W. Millar, President, American Public Transportation Association, Washington, DC Cynthia L. Quarterman, Administrator, Pipeline and Hazardous Materials Safety Administration, U.S.DOT Peter M. Rogoff, Administrator, Federal Transit Administration, U.S.DOT David L. Strickland, Administrator, National Highway Traffic Safety Administration, U.S.DOT Joseph C. Szabo, Administrator, Federal Railroad Administration, U.S.DOT Polly Trottenberg, Assistant Secretary for Transportation Policy, U.S.DOT Robert L. Van Antwerp (Lt. Gen., U.S. Army), Chief of Engineers and Commanding General, U.S. Army Corps of Engineers, Washington, DC *Membership as of June 2010.

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NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM NCHRP REPORT 655 Recommended Guide Specification for the Design of Externally Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements Abdul-Hamid Zureick Bruce R. Ellingwood GEORGIA INSTITUTE OF TECHNOLOGY Atlanta, GA Andrzej S. Nowak UNIVERSITY OF NEBRASKA-LINCOLN Lincoln, NE Dennis R. Mertz UNIVERSITY OF DELAWARE Newark, DE Thanasis C. Triantafillou UNIVERSITY OF PATRAS Patras, Greece Subscriber Categories Bridges and Other Structures Research sponsored by the American Association of State Highway and Transportation Officials in cooperation with the Federal Highway Administration TRANSPORTATION RESEARCH BOARD WASHINGTON, D.C. 2010 www.TRB.org

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NATIONAL COOPERATIVE HIGHWAY NCHRP REPORT 655 RESEARCH PROGRAM Systematic, well-designed research provides the most effective Project 10-73 approach to the solution of many problems facing highway ISSN 0077-5614 administrators and engineers. Often, highway problems are of local ISBN 978-0-309-15485-7 interest and can best be studied by highway departments individually Library of Congress Control Number 2010930888 or in cooperation with their state universities and others. However, the © 2010 National Academy of Sciences. All rights reserved. accelerating growth of highway transportation develops increasingly complex problems of wide interest to highway authorities. These problems are best studied through a coordinated program of COPYRIGHT INFORMATION cooperative research. Authors herein are responsible for the authenticity of their materials and for obtaining In recognition of these needs, the highway administrators of the written permissions from publishers or persons who own the copyright to any previously American Association of State Highway and Transportation Officials published or copyrighted material used herein. initiated in 1962 an objective national highway research program Cooperative Research Programs (CRP) grants permission to reproduce material in this employing modern scientific techniques. This program is supported on publication for classroom and not-for-profit purposes. Permission is given with the understanding that none of the material will be used to imply TRB, AASHTO, FAA, FHWA, a continuing basis by funds from participating member states of the FMCSA, FTA, or Transit Development Corporation endorsement of a particular product, Association and it receives the full cooperation and support of the method, or practice. It is expected that those reproducing the material in this document for Federal Highway Administration, United States Department of educational and not-for-profit uses will give appropriate acknowledgment of the source of any reprinted or reproduced material. For other uses of the material, request permission Transportation. from CRP. The Transportation Research Board of the National Academies was requested by the Association to administer the research program because of the Board's recognized objectivity and understanding of NOTICE modern research practices. The Board is uniquely suited for this purpose as it maintains an extensive committee structure from which The project that is the subject of this report was a part of the National Cooperative Highway Research Program, conducted by the Transportation Research Board with the approval of authorities on any highway transportation subject may be drawn; it the Governing Board of the National Research Council. possesses avenues of communications and cooperation with federal, The members of the technical panel selected to monitor this project and to review this state and local governmental agencies, universities, and industry; its report were chosen for their special competencies and with regard for appropriate balance. relationship to the National Research Council is an insurance of The report was reviewed by the technical panel and accepted for publication according to procedures established and overseen by the Transportation Research Board and approved objectivity; it maintains a full-time research correlation staff of by the Governing Board of the National Research Council. specialists in highway transportation matters to bring the findings of The opinions and conclusions expressed or implied in this report are those of the research directly to those who are in a position to use them. researchers who performed the research and are not necessarily those of the Transportation The program is developed on the basis of research needs identified Research Board, the National Research Council, or the program sponsors. by chief administrators of the highway and transportation departments The Transportation Research Board of the National Academies, the National Research and by committees of AASHTO. Each year, specific areas of research Council, and the sponsors of the National Cooperative Highway Research Program do not needs to be included in the program are proposed to the National endorse products or manufacturers. Trade or manufacturers' names appear herein solely because they are considered essential to the object of the report. Research Council and the Board by the American Association of State Highway and Transportation Officials. Research projects to fulfill these needs are defined by the Board, and qualified research agencies are selected from those that have submitted proposals. Administration and surveillance of research contracts are the responsibilities of the National Research Council and the Transportation Research Board. The needs for highway research are many, and the National Cooperative Highway Research Program can make significant contributions to the solution of highway transportation problems of mutual concern to many responsible groups. The program, however, is intended to complement rather than to substitute for or duplicate other highway research programs. Published reports of the NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM are available from: Transportation Research Board Business Office 500 Fifth Street, NW Washington, DC 20001 and can be ordered through the Internet at: http://www.national-academies.org/trb/bookstore Printed in the United States of America

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COOPERATIVE RESEARCH PROGRAMS CRP STAFF FOR NCHRP REPORT 655 Christopher W. Jenks, Director, Cooperative Research Programs Crawford F. Jencks, Deputy Director, Cooperative Research Programs Amir N. Hanna, Senior Program Officer Eileen P. Delaney, Director of Publications Maria Sabin Crawford, Assistant Editor NCHRP PROJECT 10-73 PANEL Field of Materials and Construction--Area of Specifications, Procedures, and Practices Paul V. Liles, Jr., Georgia DOT, Atlanta, GA (Chair) Tadeusz C. Alberski, New York State DOT, Albany, NY Jim Gutierrez, California DOT, Sacramento, CA Issam Harik, University of Kentucky, Lexington, KY Calvin E. Reed, Kansas DOT, Topeka, KS Andrew L. Thomas, Pennsylvania DOT, Harrisburg, PA Eric P. Munley, FHWA Liaison Stephen F. Maher, TRB Liaison

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FOREWORD By Amir N. Hanna Staff Officer Transportation Research Board This report presents a recommended guide specification for the design of externally bonded Fiber-Reinforced Polymer (FRP) systems for the repair and strengthening of con- crete bridge elements. This guide specification addresses the design requirements for mem- bers subjected to different loading conditions (e.g., flexure, shear and torsion, and com- bined axial force and flexure). The guide specification is supplemented by design examples to illustrate its use for different FRP strengthening applications. The guide specification is presented in AASHTO LRFD format to facilitate use and incorporation into the AASHTO LRFD Bridge Design Specification. The material contained in the report should be of imme- diate interest to state engineers and others involved in the strengthening and repair of con- crete structures using FRP composites. Use of externally bonded FRP systems for the repair and strengthening of reinforced and prestressed concrete bridge structures has become accepted practice by some state highway agencies because of their technical and economic benefits. Such FRP systems are lightweight, exhibit high tensile strength, and are easy to install; these features facilitate handling and help expedite repair or construction, enhance long-term performance, and result in cost savings. In addition, research has shown that external bonding of FRP composites improves flexural behavior of concrete members and increases the capacity of concrete bents and columns. In spite of their potential benefits, use of externally bonded FRP systems is hampered by the lack of nationally accepted design specifications for bridges. Thus, research was needed to review available information and develop a recommended guide specification for such repair and strengthening systems. Under NCHRP Project 10-73, "Guide Specification for the Design of Externally Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements," Georgia Institute of Technology conducted a review of relevant domestic and international information, identified and categorized the items necessary for developing a guide specification, and developed a reliability-based guide specification that employs Load and Resistance Factor Design (LRFD) methodology. The guide specification is accompanied by commentaries that are necessary for explaining the background, applicability, and limitations of the respective provisions. In addition, design examples are provided to illustrate use of the recommended guide specification for different strengthening requirements. The recommended guide specification will be particularly useful to highway agencies because it will facilitate consideration of FRP systems among the options available for the repair and strengthening of concrete bridge elements and help select options that are expected to yield economic and other benefits. The incorporation of the recommended guide specification into the AASHTO LRFD Bridge Design Specifications will provide an easy access to the information needed for the design of externally bonded FRP systems for the repair and strengthening of concrete bridge elements.

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CONTENTS 1 Summary 2 Chapter 1 Introduction and Research Approach 4 Chapter 2 Findings 12 Chapter 3 Interpretation, Appraisal, and Application 19 Chapter 4 Conclusions, Implementation, and Recommendations for Further Research 21 References A-i Attachment A Recommended Guide Specification for the Design of Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements B-i Attachment B Illustrative Examples

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1 SUMMARY Recommended Guide Specification for the Design of Externally Bonded FRP Systems for Repair and Strengthening of Concrete Bridge Elements Fiber-reinforced polymer (FRP) composites now are being used to strengthen or to upgrade the load-carrying capacity of a wide range of bridge structures. These materials must offer tech- nical and economical advantages in order to be successful in the highly competitive construc- tion marketplace. While FRP composites increasingly are being used in combination with traditional construction materials for rehabilitation of existing structures, codes, and standards for structural condition assessment, evaluation and rehabilitation of bridge structures using composite materials do not exist as of yet. Design information for most FRP composite materi- als has been developed mainly by the composites industry. This report summarizes the research conducted in NCHRP Project 10-73 to develop a recom- mended guide specification for the design of externally bonded FRP composite systems for repair and strengthening of reinforced and prestressed concrete highway bridge elements. This infor- mation will facilitate the use of FRP materials in strengthening reinforced concrete and pre- stressed bridge elements by providing bridge engineers with a rational basis for such use. The research produced a recommended Guide Specification for the Design of Bonded FRP Reinforce- ment Systems for Repair and Strengthening of Concrete Bridge Elements. This Guide Specification is presented in a format resembling that of the AASHTO LRFD Bridge Design Specifications, 4th Edition (2007) in order to facilitate their consideration and adoption by the AASHTO. The rec- ommended Guide Specification is accompanied by commentaries that explain the background, applicability, and limitations of the provisions contained therein. Included also are step-by-step calculations in accordance with the recommended Guide Specification for six examples of com- monly used FRP strengthening applications. These examples would serve as a tutorial on how to approach bridge strengthening projects in practice. The report concludes with suggestions for implementing the guide specification and recom- mendations for further research to support future revisions and enhancements of the recom- mended guide specification.

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2 CHAPTER 1 Introduction and Research Approach 1.1 Background portation agencies and industry organizations, and other do- mestic and foreign sources, including the American Concrete Because of the technical and economic benefits achieved by Institute "Guide for the Design and Construction of Exter- the use of externally bonded fiber-reinforced polymer (FRP) nally Bonded FRP Systems for Strengthening Concrete Struc- systems for the repair and strengthening of reinforced and tures" (ACI 2002) and similar publications. prestressed concrete bridge structures, this method of reha- Task 2. Based on the information gathered in Task 1, the bilitation of bridge structures has become accepted practice items necessary for developing the guide specification were in many state highway agencies. Such FRP systems are light- identified and categorized. These items addressed flexure, weight, exhibit high tensile strength, and are easy to install; shear, axial loading, development length, detailing, and other these features facilitate handling and help expedite repair or design considerations in a manner similar to that provided in construction, enhance long-term performance, and result in the AASHTO LRFD Bridge Design Specifications. cost savings. In addition, the external bonding of FRP com- Task 3. Based on the information obtained in Tasks 1 and posites improves flexural behavior of concrete members and 2, a tentative outline of the proposed guide specification and increases the capacity of concrete bents and columns. a work plan for developing the specification along with a com- In spite of their potential benefits, the use of externally bonded FRP systems is hampered by the lack of nationally ac- mentary and design examples were prepared. The plan de- cepted design specifications for their use in the repair and scribed the proposed approach for incorporating appropriate strengthening of concrete bridge elements. NCHRP Project resistance factors and other design criteria in the specification. 10-73 was initiated to review available information and to de- Task 4. The plan for developing the guide specification was velop a recommended guide specification for the design of ex- executed. Based on the results of this work, the guide specifi- ternally bonded FRP systems. This specification will help high- cation was developed. way agencies consider FRP systems among the options for the Task 5. Using the specification developed in Task 4, a com- repair and strengthening of concrete bridge elements and select mentary and design examples to illustrate use of the specifi- options that are expected to yield economic and other benefits. cation were prepared. Task 6. A final report that documents the entire research, including the recommended guide specification and commen- 1.2 Project Objective and Scope tary and the design examples was prepared. The objective of this project was to develop a recommended guide specification for the design of externally bonded FRP 1.3 Applicability of Results composite systems for their use in the repair and strengthen- to Highway Practice ing of reinforced and prestressed concrete highway bridge elements. FRP composite systems covered in this project The research products resulting from this project provide include thermoset polymers reinforced by carbon, glass, or a technically sound and documented basis for using FRP re- aramid fibers. To achieve this project objective, the following inforcement in bridge rehabilitation and retrofit. The use of tasks were carried out: FRP reinforcement will have a significant impact on the eco- Task 1. Information relevant to the design of FRP systems nomics of bridge maintenance and rehabilitation at state and used in repair and strengthening of concrete bridge elements national levels, and may permit them to upgrade the load- was collected and reviewed. This information was assembled carrying capacity of bridge members through easy-to-install from published and unpublished reports, contacts with trans- retrofits rather than replacement. The recommended guide

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3 specifications gives FRP manufacturers a consistent basis for tasks performed to accomplish the objective. Chapter 2 pres- reporting material properties while at the same time allows ents the findings of this study, and Chapter 3 addresses the bridge design and maintenance engineers to use such material analytical formulations and the experimental data that formed property data for conditions similar to those under which these the basis upon which the proposed Guide Specifications were properties are obtained. The guide specifications and com- developed. Chapter 4 presents the conclusions and recom- mentary presented in Attachment A are formatted to facilitate mendations for further research. Attachment A presents rec- consideration and adoption by AASHTO. ommended guide specifications and commentaries for the design of externally bonded FRP reinforcement systems for the repair and strengthening of concrete bridge elements. At- 1.4 Report Organization tachment B contains step-by-step illustrative examples that This report consists of four chapters and two attachments. serve as a tutorial on how to approach bridge strengthening Chapter 1 describes the objective and outlines the various projects in practice.

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A-40 4.5.3.3 ­ The clamping force, C , shall be determined as follows: C Avf f yf frp Afrp E frp frp (4.5.3.3-1) In which Avf = area of steel reinforcement for shear-friction; f yf = yield strength of steel reinforcement for shear-friction; Afrp = effective area of FRP reinforcement for shear-friction; E frp = effective modulus of FRP reinforcement for shear-friction; frp = strain in FRP reinforcement for shear- friction, and frp = 0.65 The strain in the FRP reinforcement for shear- friction shall be taken as 0.004 unless test data are provided to support an alternative value. 4.5.3.4 ­ The coefficient of friction, µ, shall be determined as follows: 1.4 for concrete placed monolithically; 1.0 for concrete placed against hardened concrete intentionally roughened 0.7 for concrete anchored to structural steel by studs or other mechanical devices 0.6 for concrete placed by other methods than those above in which 1.0 for normal weight concrete 0.75 for light weight concrete

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A-41 4.5.3.5 The nominal shear strength Vn shall not exceed the smaller of 0.2 f c Ac or 800 Ac , where Ac is the area of the concrete section resisting shear transfer. 4.5.3.6 Net tension across the shear plane shall be resisted by additional reinforcement. The value of fy used for design of shear-friction reinforcement shall not exceed 60 ksi. It is permitted to take permanent net compression across the shear plane as additive to the force in the shear-friction reinforcement, Avf fy, when calculating the required Avf

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A-42 REFERENCES ACI (2005). Building code requirements for structural concrete (ACI Standard 318-05). American Concrete Institute, Farmington Hills, MI. ACI Committee 440 (2002). Guide to the design and construction of externally bonded FRP systems for strengthening concrete structures (ACI 440.2R). American Concrete Institute, Farmington Hills, MI Araki, N., Matsuzaki, Y., Nakano, K., Kataoka, T., and Fukuyama, H. (1997). "Shear capacity of retrofitted rc members with continuous fiber sheets." Non-Metallic (FRP) Reinforcement for Concrete Structures, Japan Concrete Institute, 1, 515-522. Brosens, K. and Van Gemert, D. (1999), "Anchorage design for externally bonded carbon fiber reinforced polymer laminates", Proceedings of Fourth International Symposium on FRP Reinforcement for Concrete Structures, Baltimore, USA, 635-645. Carolin, A. and Taljsten, B. (2005). "Experimental study of strengthening for increased shear bearing capacity", ASCE J. Comp. Constr., 9(6), 488-496. Chajes, M. J., Januska, T. F., Mertz, D. R., Thomson, T. A., and Finch, W. W. (1995). "Shear strengthening of reinforced concrete beams using externally applied composite fabrics." ACI Struct. J., 92(3), May-June, 295-303 Deniaud, C. and Cheng, R. (2001). "Shear behaviour of reinforced concrete T-beams with externally bonded fiber-reinforced polymer sheets", ACI Struct. J., 98(3), May-June, 386-394 Holzenkämpfer,P. (1994), Ingenieurmodelle des verbundes geklebter bewehrung für betonbauteile. Dissertation, TU Braunschweig (In German). Khalifa, Ahmed, Gold, William J., Nanni, A., and Abdel Aziz, M.I. (1998). "Contribution of Externally Bonded FRP to Shear Capacity of FRP Members," ASCE Journal of Composites for Construction, Vol 2, No. 4, pp. 195-202.

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A-43 Monti, G., Santinelli, F. and Liotta, M. A. (2004a), "Shear strengthening of beams with composite materials", Proceedings of the International Conference on FRP Composites in Civil Engineering ­ CICE 2004, Ed. R. Seracino, Adelaide, Australia, 569- 577. Monti, G., Santinelli, F., and Liotta, M.A. (2004b). Mechanics of shear FRP-strengthening of RC beams. ECCM 11, Rhodes, Greece. Priestly, M. J.N., Seible, F., and Calvi, M. (1996). "Seismic design and retrofit of bridges," John Wiley and Sons, Inc, New York. Ritter, W. (1899). "Die Bauweise Hennebique," Schweizerische, Bauzeitung, Vol. 33, No. 7 pp. 59­61. Sato, Y., Ueda, T., Kakuta, Y., and Tanaka, T. (1996). "Shear reinforcing effect of carbon fiber sheet attached to side of reinforced concrete beams." Advanced Composite Materials in Bridges and Structures, M. M. El-Badry, ed., 621-627. Triantafillou, T. C. (1998), "Shear strengthening of reinforced concrete beams using epoxy-bonded FRP composites", ACI Structural Journal, 95(2), 107-115.

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A-44 SECTION 5: MEMBERS UNDER COMBINED AXIAL FORCE AND FLEXURE 5.1 GENERAL REQUIREMENTS . The factored resistance of structural members subjected to axial forces and combined axial forces and flexure shall equal or exceed the required strength at all sections calculated for the factored loads and forces in combinations stipulated by these Guide Specifications. Except where specifically provided below, all provisions of Article 6.9 of the AASHTO LRFD Bridge Design Specifications, 4th Edition (2007), shall apply. 5.2 METHODS FOR STRENGTHENING WITH FRP REINFORCEMENT 5.2.1 Columns shall be strengthened with FRP reinforcement using the complete wrapping method specified in Article 4.2. 5.3 COLUMNS IN AXIAL COMPRESSION 5.3.1 General Requirements C5.3.1 The factored axial load resistance, Pr , for a The design procedure for columns strengthened confined column shall be taken as follows: with FRP is the same as for reinforcement concrete columns without strengthening. For members with spiral reinforcement However, the concrete compressive strength f c ' Pr 0.85 0.85 f ' cc Ag Ast f y Ast is substituted by the increased confined concrete ' compressive strength f cc as calculated (5.3.1-1) according to Article 5.3.2.2. The multipliers of 0.85 and 0.80 in Equations 5.3.1-1 and 5.3.1-2 reflect the effect of minimum accidental eccentricities of axial force (0.05h and For members with tie reinforcement 0.10h, respectively, for columns with spiral or tied reinforcement) which impart small end Pr 0.80 0.85 f ' cc Ag Ast f y Ast moments to columns. Columns with eccentricities greater than these values must be (5.3.1-2) designed using the provisions of Section 5.5.to take these extra moments into account.

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A-45 where Confined circular columns sustain ultimate axial strains that are far greater than those of non- = resistance factor specified in Article 5.5.4.2 confined columns. Any gain in strength due to of the AASHTO Bridge Design Specifications, 4th strain hardening of the steel reinforcement is not Edition accounted for in the above equation, thus providing additional safety. This gain is a Ag = gross area of section (in2) function of the ultimate axial strains, unless buckling of the steel reinforcement initiates Ag = total area of longitudinal reinforcement, failure of the column. (in2). f y = specified yield strength of reinforcement (ksi) f 'cc = compressive strength of the confined concrete determined according to Article 5.3.2.2. 5.3.2 Short Columns in Compression C5.3.2 Columns in compression shall be fully wrapped The provisions in Article 5.3.2 apply to short over the entire length. columns in which second-order effects are negligible and the limit state of instability can be ignored. 5.3.2.1 Limitations C5.3.2.1 Provisions in this section shall apply to circular The limitations are similar to those in the columns in which the slenderness parameter Canadian guidelines for column strengthening lu Ddoes not exceed 8 and to rectangular (ISIS 2001). The limitation on column slenderness in this section ensures that the columns in which the aspect ratio, h b does not development of column strength not prevented exceed 1.1, the minimum radius of corners is one by column instability. inch, and the slenderness parameter, lu b, does not exceed 9, where: D = external diameter of the circular member b = smaller dimension of the rectangular member h = larger dimension of the rectangular member 5.3.2.2 Confinement in Columns C5.3.2.2

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A-46 The compressive strength of the confined The bonding of FRP sheets, where the fiber concrete, f 'cc , shall be determined from: orientation is perpendicular to the column axis to limit the circumferential strains in the column, constitutes confinement. Various confinement 2 fl f ' cc f 'c 1 models have been developed over the years and f c' comparisons among the most common models have been presented by Rocca et al. (2008). The (5.3.2.2-1) expression for the compressive strength of confined concrete adopted in these guides is The confinement pressure due to FRP similar to that of ISIS Canada due to its strengthening, f l [ksi] for circular columns shall simplicity. The stress-strain curve for concrete be determined as: confined by FRP reinforcement can be considered to be bilinear, but differs from the 2 N frp f c' 1 situation where the confinement is provided by fl frp 1 D 2 ke spiral reinforcement or steel jacketing. The secondary stiffness depends on the hoop stiffness (5.3.2.2-2) of the confining reinforcement. where The maximum value of the confinement pressure specified in Eq 5.3.2.2-2 was established to limit k e is a strength reduction factor applied for the axial compression strains in unexpected eccentricities. It shall be taken as overstrengthened columns. The minimum follows: confinement pressure of 600 psi reflects the fact that the effectiveness of the confinement k e =0.80 for tied columns, and pressure depends upon a certain level of ductility. Relevant background related the k e = 0.85 for spiral columns. maximum and minium values of confinement pressure in FRP reinforcement jackets in axially loaded columns is given by Thériault and Neale N frp = Strength per width of FRP reinforcement (2000). corresponding to a strain of 0.004. When Equation 5.3.2.2-2 is applied to frp = 0.65, rectangular columns after replacing D with the smaller dimension of the rectangular section, the The confinement pressure shall be greater or factored axial strength estimated from eqs. 5.3.1- equal to 600 psi. 1 or 5.3.1-2 errs on the conservative side. At present, this is justified owing to the limited For rectangular columns, the diameter D in Eq properly documented available test data. (5.3.2.2-2) shall be replaced with the smaller dimension of the width and depth. The gain in strength provided by the confinement of rectangular sections is very little compared to that attainable for circular sections. As a result, neither minimum nor maximum limits are specified for rectangular sections since the attainable confinement pressure, which relies on ductility development, is very limited for rectangular columns.

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A-47 5.3.3 Slender columns C5.3.3 Columns not meeting the limitations on The provisions for short columns in Article 5.3.2 slenderness in 5.3.2.1 shall be designated as are adequate for the majority of rehabilitation slender and their design shall be based on forces projects because second-order structural actions and moments determined from rational analysis. leading to instability seldom would occur. There Such an analysis shall take into account the is only limited test data to support the influence of forces, deflections and foundation development of column strength provisions in rotations, and duration of loads on member situations where this is not the case. In such stiffness and on the development of moments, situations, the required columnstrength should shears and axial forces. be determined by rational analysis, supplemented by confirmatory testing, where feasible. 5.4 COMBINED AXIAL COMPRESSION AND BENDING 5.4.1 General requirements C5.4.1 Members subjected to moment in combination The design procedure for the members with axial load shall be designed for the strengthen with FRP is the sameas for maximum moment that can accompany the axial reinforcement concrete members without strengthening. However, the concrete load. The factored axial force at given compressive strength f c' is substituted by the eccentricity shall not exceed Pr given in increased confined concrete compressive Section 5.3.1. The maximum required moment, ' Mu, shall be magnified, as appropriate, for strength fcc as calculated according to articles slenderness effects. 5.3.2.2. 5.4.2 Design Basis Design of columns subject to combinations of axial force and flexure shall be based on stress and strain compatibility. The maximum usable strain in the extreme concrete compression fiber shall be assumed to equal 0.003. Externally bonded FRP reinforcement of columns strengthened to withstand end moments due to lateral load shall be reinforced over a distance from the column ends equal to the maximum column dimension or the distance over which the moment exceeds 75% of the maximum required moment, whichever distance is larger.

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A-48 The tensile strength of the FRP reinforcement in the longitudinal direction of the column shall be determined by rational analysis. However, the strength in the longitudinal direction shall not be less than 50% of the strength in the perimeter direction. 5.4.3. Limitations C5.4.3 The contribution of the FRP reinforcement to Provisions in Article 5.4 are limited to members column capacity shall not be considered at subjected to combined axial loading and bending eccentricity ratios greater than those where failures occur by concrete crushing in corresponding to balanced strain conditions, at compression rather than reinforcement yielding which tension reinforcement reaches the strain in tension. If the eccentricity of axial force corresponding the steel yield strength and present in the member is greater than 0.10h for concrete in compression reaches an ultimate the spirally reinforced columns or 0.05h for tied strain of 0.003 at any cross section. columns, strengthening requires externally bonded FRP reinforcement to withstand force in the longitudinal direction of the columnin addition to its perimeter. 5.5 AXIAL TENSION 5.5.1 Limitation Members that are axially loaded in tension shall be reinforced symmetrically with respect to the column cross section principal axes. C5.5.2 5.5.2 General requirements The factored axial load resistance, Pr, for an FRP systems can be used to provide additional axially loaded member with externally bonded tensile strength to concrete members. The FRP reinforcement shall be tension strength provided by the FRP is limited by the design tensile strength of the FRP and the Pr 0.9 As f y frp N frp w frp ability to transfer stresses into the substrate through bond. The effective strain in the FRP In which can be determined based on the criteria given for shear strengthening. frp = 0.5 For members completely wrapped by the FRP N frp = tensile strength per unit width in the load systems, loss of the aggregate interlock of concrete occurs at fiber strain less than the direction at a strain value of 0.005. ultimate fiber strain. To preclude this mode of failure, the maximumdesign strain should be w frp = total length of FRP reinforcement along limited to 0.4%: the cross section.

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A-49 fe 0.004 0.75 fu where fe is the effective strain level in FRP reinforcement attained at failure fu is the design rupture strain of FRP reinforcement References ISIS (2001). ISIS Canada Design Manuals, "Strengthening Reinforced Concrete Structures with Externally-Bonded Fiber-Reinforced Polymers," Winnipeg, Manitoba. Mirmiran, A., Shahawy, M. (1997). "Behavior of concrete columns confined by fiber composites." J. Struct. Engrg. ASCE 123(5):583-590. Mirmiran, A., Shahawy, M., Samaan, M., El Echary, H., Mastrapa, J.C. and Pico, O. (1998) "Effect of column parameters on FRP-confined concrete." J. Composites for Construction, ASCE 2(4):175-185. Saaman, M., Mirmiran, A. and Shahawy, M. (1998). "Model of concrete confined by fiber composites." J. Struct. Engrg. ASCE 124(9):1025-1031. Rocca, S., Galati, N. and Nanni, N. (2008) ASCE Journal of Composites for Construction, Vol. 12, No. 1,February, pp.80-92. Thériault, M. and Neale, K.W. (2000). " Design equations for axially loaded reinforced concrete columns strengthened with fibre reinforced polymer wraps, Canadian Journal of Civil Engineering, 27(5): 1011.1020. Val, D. (2003). "Reliability of fiber-reinforced polymer-confined reinforced concrete columns." J. Struct. Engrg. ASCE 129(8):1122-1130.

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ATTACHMENT B Illustrative Examples The following examples are presented to illustrate calculations associated with a number of commonly used FRP strengthening techniques in accordance with the recommended Guide Specification for the Design of Bonded FRP Reinforcement Systems for Repair and Strengthening of Concrete Bridge Elements. These examples should illustrate how to approach bridge strengthening projects in practice. These examples cover the five sections of the proposed Guide Specification. Example 1: Calculation of the characteristic value of the strength of an FRP reinforcement system Example 2: Flexural strengthening of a T-beam in an unstressed condition Example 3: Flexural strengthening of a T-beam in a stressed condition Example 4: Shear strengthening of a T-beam using U-jacket FRP reinforcement Example 5: Shear strengthening of a rectangular beam using complete wrapping FRP reinforcing system Example 6: Strengthening of an axially loaded circular column.