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ACI 440.2R-17
Guide for the Design and
Construction of Externally
Bonded FRP Systems for
Strengthening Concrete
Structures
Reported by ACI Committee 440
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MCPOL Licensed to: McMaster University Library
First Printing
May 2017
ISBN: 978-1-945487-59-0
Guide for the Design and Construction of Externally Bonded FRP Systems for
Strengthening Concrete Structures
Copyright by the American Concrete Institute, Farmington Hills, MI. All rights reserved. This material
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MCPOL Licensed to: McMaster University Library
ACI 440.2R-17
Guide for the Design and Construction of Externally
Bonded FRP Systems for Strengthening Concrete
Structures
Reported by ACI Committee 440
Carol K. Shield, Chair
Tarek Alkhrdaji
Charles E. Bakis
Lawrence C. Bank
Abdeldjelil Belarbi
Brahim Benmokrane
Luke A. Bisby
Gregg J. Blaszak
Hakim Bouadi
Timothy E. Bradberry
Vicki L. Brown
John Busel
Raafat El-Hacha
Garth J. Fallis
William J. Gold, Secretary
Amir Z. Fam
Russell Gentry
Nabil F. Grace
Mark F. Green
Zareh B. Gregorian
Doug D. Gremel
Shawn P. Gross
H. R. Trey Hamilton III
Issam E. Harik
Kent A. Harries*
Mark P. Henderson
Ravindra Kanitkar
Yail Jimmy Kim
Michael W. Lee
Maria Lopez de Murphy
Ibrahim M. Mahfouz
Amir Mirmiran
John J. Myers
Antonio Nanni
Ayman M. Okeil
Carlos E. Ospina
Renato Parretti
Maria A. Polak
Max L. Porter
Andrea Prota
Hayder A. Rasheed
Sami H. Rizkalla
Rajan Sen
Rudolf Seracino
Venkatesh Seshappa
Pedro F. Silva
Samuel A. Steere, III
Jennifer E. Tanner
Jay Thomas
Houssam A. Toutanji
J. Gustavo Tumialan
Milan Vatovec
David White
Sarah E. Witt*
*Co-chairs of the subcommittee that prepared this document.
Consulting Members
P. N. Balaguru
Craig A. Ballinger
Harald G. F. Budelmann
C. J. Burgoyne
Rami M. Elhassan
David M. Gale
Srinivasa L. Iyer
Koichi Kishitani
Howard S. Kliger
Kyuichi Maruyama
Antoine E. Naaman
Hajime Okamura
Fiber-reinforced polymer (FRP) systems for strengthening concrete
structures are an alternative to traditional strengthening techniques
such as steel plate bonding, section enlargement, and external
post-tensioning. FRP strengthening systems use FRP composite
materials as supplemental externally-bonded or near-surfacemounted reinforcement. FRP systems offer advantages over traditional strengthening techniques: they are lightweight, relatively
ACI Committee Reports, Guides, and Commentaries are
intended for guidance in planning, designing, executing, and
inspecting construction. This document is intended for the use
RILQGLYLGXDOVZKRDUHFRPSHWHQWWRHYDOXDWHWKHVLJQL¿FDQFH
and limitations of its content and recommendations and who
will accept responsibility for the application of the material it
contains. The American Concrete Institute disclaims any and
all responsibility for the stated principles. The Institute shall
not be liable for any loss or damage arising therefrom.
Reference to this document shall not be made in contract
documents. If items found in this document are desired by
the Architect/Engineer to be a part of the contract documents,
they shall be restated in mandatory language for incorporation
by the Architect/Engineer.
Mark A. Postma
Ferdinand S. Rostasy
Mohsen Shahawy
Surendra P. Shah
Yasuhisa Sonobe
Minoru Sugita
Luc R. Taerwe
Ralejs Tepfers
Taketo Uomoto
Paul Zia
easy to install, and noncorroding. Due to the characteristics of
FRP materials as well as the behavior of members strengthened
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This guide offers general information on the history and use of FRP
strengthening systems; a description of the material properties of
FRP; and recommendations on the engineering, construction, and
inspection of FRP systems used to strengthen concrete structures.
This guide is based on the knowledge gained from experimental
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used to strengthen concrete structures.
Keywords: DUDPLG ¿EHUV EULGJHV EXLOGLQJV FDUERQ ¿EHUV FRUURVLRQ
FUDFNLQJGHYHORSPHQWOHQJWKHDUWKTXDNHUHVLVWDQFH¿EHUUHLQIRUFHGSRO\PHUVVWUXFWXUDOGHVLJQ
ACI 440.2R-17 supersedes ACI 440.2R-08 and was adopted and published May 2017.
Copyright © 2017, American Concrete Institute
All rights reserved including rights of reproduction and use in any form or by
any means, including the making of copies by any photo process, or by electronic
or mechanical device, printed, written, or oral, or recording for sound or visual
reproduction or for use in any knowledge or retrieval system or device, unless
permission in writing is obtained from the copyright proprietors.
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1
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2
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
CONTENTS
CHAPTER 1—INTRODUCTION AND SCOPE, p. 3
1.1—Introduction, p. 3
1.2—Scope, p. 4
CHAPTER 2—NOTATION AND DEFINITIONS, p. 6
2.1—Notation, p. 6
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CHAPTER 3—BACKGROUND INFORMATION, p. 10
3.1—Historical development, p. 10
3.2—Commercially available externally bonded FRP
systems, p. 10
CHAPTER 4—CONSTITUENT MATERIALS AND
PROPERTIES, p. 11
4.1—Constituent materials, p. 11
4.2—Physical properties, p. 12
4.3—Mechanical properties, p. 12
4.4—Time-dependent behavior, p. 13
4.5—Durability, p. 14
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CHAPTER 5—SHIPPING, STORAGE, AND
HANDLING, p. 15
5.1—Shipping, p. 15
5.2—Storage, p. 15
5.3—Handling, p. 15
CHAPTER 6—INSTALLATION, p. 15
6.1—Contractor competency, p. 16
6.2—Temperature, humidity, and moisture considerations,
p. 16
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6.4—Substrate repair and surface preparation, p. 16
6.5—Mixing of resins, p. 17
6.6—Application of FRP systems, p. 17
6.7—Alignment of FRP materials, p. 18
6.8—Multiple plies and lap splices, p. 18
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CHAPTER 7—INSPECTION, EVALUATION, AND
ACCEPTANCE, p. 19
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CHAPTER 8—MAINTENANCE AND REPAIR, p. 20
8.1—General, p. 20
8.2—Inspection and assessment, p. 20
8.3—Repair of strengthening system, p. 21
8.4—Repair of surface coating, p. 21
CHAPTER 9—GENERAL DESIGN
CONSIDERATIONS, p. 21
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CHAPTER 10—FLEXURAL STRENGTHENING, p. 24
10.1—Nominal strength, p. 24
10.2—Reinforced concrete members, p. 24
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10.4—Moment redistribution, p. 31
CHAPTER 11—SHEAR STRENGTHENING, p. 31
11.1—General considerations, p. 32
11.2—Wrapping schemes, p. 32
11.3—Nominal shear strength, p. 32
CHAPTER 12—STRENGTHENING OF MEMBERS
SUBJECTED TO AXIAL FORCE OR COMBINED
AXIAL AND BENDING FORCES, p. 34
12.1—Pure axial compression, p. 34
12.2—Combined axial compression and bending, p. 36
12.3—Ductility enhancement, p. 36
12.4—Pure axial tension, p. 37
CHAPTER 13—SEISMIC STRENGTHENING, p. 37
13.1—Background, p. 38
13.2—FRP properties for seismic design, p. 38
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13.4—Flexural strengthening, p. 40
13.5—Shear strengthening, p. 41
13.6—Beam-column joints, p. 41
13.7—Strengthening reinforced concrete shear walls, p. 41
CHAPTER 14—FIBER-REINFORCED POLYMER
REINFORCEMENT DETAILS, p. 43
14.1—Bond and delamination, p. 43
14.2—Detailing of laps and splices, p. 44
14.3—Bond of near-surface-mounted systems, p. 45
CHAPTER 15—DRAWINGS, SPECIFICATIONS,
AND SUBMITTALS, p. 46
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15.3—Submittals, p. 46
CHAPTER 16—DESIGN EXAMPLES, p. 47
16.1—Calculation of FRP system tensile properties, p. 47
16.3—Flexural strengthening of an interior reinforced
concrete beam with FRP laminates, p. 50
16.4—Flexural strengthening of an interior reinforced
concrete beam with near-surface-mounted FRP bars, p. 56
16.5—Flexural strengthening of an interior prestressed
concrete beam with FRP laminates, p. 62
16.6—Shear strengthening of an interior T-beam, p. 68
16.7—Shear strengthening of an exterior column, p. 71
16.8—Strengthening of a noncircular concrete column for
axial load increase, p. 73
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increase in axial and bending forces, p. 76
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MCPOL Licensed to: McMaster University Library
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.11—Lap-splice clamping for seismic strengthening,
p. 86
16.12—Seismic shear strengthening, p. 88
16.13—Flexural and shear seismic strengthening of shear
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CHAPTER 17—REFERENCES, p. 97
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APPENDIX A—MATERIAL PROPERTIES OF
CARBON, GLASS, AND ARAMID FIBERS, p. 105
APPENDIX B—SUMMARY OF STANDARD TEST
METHODS, p. 107
APPENDIX C—AREAS OF FUTURE RESEARCH,
p. 108
APPENDIX D—METHODOLOGY FOR
COMPUTATION OF SIMPLIFIED P-M INTERACTION
DIAGRAM FOR NONCIRCULAR COLUMNS, p. 109
CHAPTER 1—INTRODUCTION AND SCOPE
1.1—Introduction
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structures to resist higher design loads, correct strength loss
GXHWRGHWHULRUDWLRQFRUUHFWGHVLJQRUFRQVWUXFWLRQGH¿FLHQcies, or increase ductility has historically been accomplished
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Externally bonded steel plates, steel or concrete jackets, and
external post-tensioning are some of the many traditional
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emerged as a viable option for repair and rehabilitation. For
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applicable resins used to bond it to the concrete substrate,
and all applied coatings used to protect the constituent materials. Coatings used exclusively for aesthetic reasons are not
considered part of an FRP system.
FRP materials are lightweight, noncorroding, and exhibit
high tensile strength. These materials are readily available in
several forms, ranging from factory-produced pultruded lamiQDWHVWRGU\¿EHUVKHHWVWKDWFDQEHZUDSSHGWRFRQIRUPWRWKH
geometry of a structure before adding the polymer resin. The
UHODWLYHO\WKLQSUR¿OHVRIFXUHG)53V\VWHPVDUHRIWHQGHVLUable in applications where aesthetics or access is a concern.
FRP systems can also be used in areas with limited access
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The basis for this document is the knowledge gained from
a comprehensive review of experimental research, analytical
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Areas where further research is needed are highlighted in
this document and compiled in Appendix C.
1.1.1 Use of FRP systems—This document refers to
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through material characterization and structural testing.
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an unexpected range of properties as well as potential material incompatibilities. Any FRP system considered for use
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performance of the entire system in similar applications,
including its method of installation. ACI 440.8 provides a
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The use of FRP systems developed through material
characterization and structural testing, including welldocumented proprietary systems, is recommended. The
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avoided. A comprehensive set of test standards and guides
for FRP systems has been developed by several organizations, including ASTM, ACI, ICRI, and ICC.
1.1.2 Sustainability—Sustainability of FRP materials may
be evaluated considering environmental, economic, and
social goals. These should be considered not only throughout
the construction phase, but also through the service life
of the structure in terms of maintenance and preservation,
and for the end-of-life phase. This represents the basis for
DOLIHF\FOHDSSURDFKWRVXVWDLQDELOLW\ Menna et al. 2013 /LIH F\FOH DVVHVVPHQW /&$ WDNHV LQWR DFFRXQW WKH HQYLronmental impact of a product, starting with raw material
extraction, followed by production, distribution, transportation, installation, use, and end of life. LCA for FRP composites depends on the product and market application, and
results vary. FRP composite materials used to strengthen
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which are derived from fossil fuels or minerals, respectively,
and therefore have impacts related to raw material extracWLRQ$OWKRXJKFDUERQDQGJODVV¿EHUVKDYHKLJKHPERGLHG
energies associated with production, on the order of 86,000
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environmental impact of resin and adhesive systems are less
studied, although the volume used is also small in comparison with conventional construction materials. In distribution
and transportation, FRP composites’ lower weight leads to
less impact from transportation, and easier material handling
DOORZV VPDOOHU HTXLSPHQW GXULQJ LQVWDOODWLRQ )RU LQVWDOODtion and use, FRP composites are characterized as having a
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less maintenance than conventional materials. The end-oflife options for FRP composites are more complex.
Although less than 1 percent of FRP composites are
currently recycled, composites can be recycled in many
ways, including mechanical grinding, incineration, and
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KRZHYHUWRVHSDUDWHWKHPDWHULDOV¿EHUVDQGUHVLQVZLWKRXW
some degradation of the resulting recycled materials. The
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4
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
market for recycled composite materials is small, although
aircraft manufacturers in particular are considering methods
and programs to recycle and repurpose composite materials
at the end of an aircraft’s life cycle.
Apart from the FRP materials and systems, their use in
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decommissioned or demolished is inherently sustainable.
In many cases, FRP composites permit extending the life or
enhancing the safety or performance of existing infrastructure at a monetary and environmental cost of only a fracWLRQ RI UHSODFHPHQW$GGLWLRQDOO\ GXH WR WKH KLJK VSHFL¿F
strength and stiffness of FRP composites, an FRP-based
repair of an existing concrete structure will often represent a
less energy-intensive option than a cementitious or metallicbased repair.
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design for strengthening and rehabilitation of existing structures. The environmental advantages of FRP, as evaluated
by LCA investigations, have been enumerated by Napolano
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, and 'DV .
1.2—Scope
This document provides guidance for the selection,
design, and installation of FRP systems for externally
strengthening concrete structures. Information on material
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presented. This information can be used to select an FRP
system for increasing the strength, stiffness, or both, of reinforced concrete beams or the ductility of columns and other
applications.
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applications of FRP strengthening systems. Based on the
available research, the design procedures outlined herein are
considered conservative.
The durability and long-term performance of FRP mateULDOV KDV EHHQ WKH VXEMHFW RI PXFK UHVHDUFK KRZHYHU WKLV
research remains ongoing. The design guidelines in this
guide account for environmental degradation and long-term
durability by providing reduction factors for various environments. Long-term fatigue and creep are also addressed
by stress limitations indicated in this document. These
factors and limitations are considered conservative. As more
research becomes available, however, these factors may be
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loading conditions to which they should apply will be better
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Caution is advised in applications where the FRP system
is subjected simultaneously to extreme environmental and
stress conditions. The factors associated with the long-term
durability of the FRP system may also affect the tensile
modulus of elasticity of the material used for design.
Many issues regarding bond of the FRP system to the
substrate remain the focus of a great deal of research.
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different modes of debonding failure that can govern the
strength of an FRP-strengthened member. While most of
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more accurate methods of predicting debonding are still
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for debonding failure modes. Future development of these
design procedures should include more thorough methods of
predicting debonding.
This document gives guidance on proper detailing
and installation of FRP systems to prevent many types of
debonding failure modes. Steps related to the surface preparation and proper termination of the FRP system are vital
in achieving the levels of strength predicted by the procedures in this document. Research has been conducted on
various methods of anchoring FRP strengthening systems,
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U-anchors. Because no anchorage design guidelines are
currently available, the performance of any anchorage
system should be substantiated through representative
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installation procedure, surface preparation, and expected
environmental conditions.
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of research primarily conducted on moderately sized and
proportioned members fabricated of normalweight concrete.
Caution should be given to applications involving strengthening of very large or lightweight concrete members or
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members such as deep beams, corbels, and dapped beam
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members and the state of stress are given herein.
This guide applies only to FRP strengthening systems used
as additional tensile reinforcement. These systems should
not be used as compressive reinforcement. While FRP materials can support compressive stresses, there are numerous
issues surrounding the use of FRP for compression. MicroEXFNOLQJRI¿EHUVFDQRFFXULIDQ\UHVLQYRLGVDUHSUHVHQWLQ
the laminate. Laminates themselves can buckle if not properly adhered or anchored to the substrate, and highly unreOLDEOHFRPSUHVVLYHVWUHQJWKVUHVXOWIURPPLVDOLJQLQJ¿EHUV
LQ WKH ¿HOG7KLV GRFXPHQW GRHV QRW DGGUHVV WKH FRQVWUXFWLRQ TXDOLW\ FRQWURO DQG PDLQWHQDQFH LVVXHV WKDW ZRXOG
be involved with the use of the material for this purpose,
nor does it address the design concerns surrounding such
applications.
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including masonry walls. Information on the repair of unreinforced masonry using FRP can be found in ACI 440.7R.
1.2.1 Applications and use—FRP systems can be used to
rehabilitate or restore the strength of a deteriorated structural
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
PHPEHUUHWUR¿WRUVWUHQJWKHQDVRXQGVWUXFWXUDOPHPEHUWR
resist increased loads due to changes in use of the structure,
or address design or construction errors. The licensed design
professional should determine if an FRP system is a suitable
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system.
To assess the suitability of an FRP system for a particular application, the licensed design professional should
perform a condition assessment of the existing structure
that includes establishing its existing load-carrying capacity,
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the condition of the concrete substrate. The overall evaluaWLRQVKRXOGLQFOXGHDWKRURXJK¿HOGLQVSHFWLRQDUHYLHZRI
existing design or as-built documents, and a structural analysis in accordance with ACI 364.1R. Existing construction
documents for the structure should be reviewed, including
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maintenance history documentation. The licensed design
SURIHVVLRQDO VKRXOG FRQGXFW D WKRURXJK ¿HOG LQYHVWLJDWLRQ
of the existing structure in accordance with ACI 437R, ACI
562, $&, 5, and other applicable ACI documents. As
D PLQLPXP WKH ¿HOG LQYHVWLJDWLRQ VKRXOG GHWHUPLQH WKH
following:
D ([LVWLQJGLPHQVLRQVRIWKHVWUXFWXUDOPHPEHUV
E /RFDWLRQVL]HDQGFDXVHRIFUDFNVDQGVSDOOV
F 4XDQWLW\DQGORFDWLRQRIH[LVWLQJUHLQIRUFLQJVWHHO
G /RFDWLRQDQGH[WHQWRIFRUURVLRQRIUHLQIRUFLQJVWHHO
H 3UHVHQFHRIDFWLYHFRUURVLRQ
I ,QSODFHFRPSUHVVLYHVWUHQJWKRIFRQFUHWH
J 6RXQGQHVV RI WKH FRQFUHWH HVSHFLDOO\ WKH FRQFUHWH
cover, in all areas where the FRP system is to be bonded to
the concrete
The tensile strength of the concrete on surfaces where
the FRP system may be installed should be determined
by conducting a pull-off adhesion test in accordance with
ASTM C1583/C1583M. The in-place compressive strength
of concrete should be determined using cores in accordance
ZLWK$&, UHTXLUHPHQWV7KH ORDGFDUU\LQJ FDSDFLW\ RI
the existing structure should be based on the information
JDWKHUHG LQ WKH ¿HOG LQYHVWLJDWLRQ WKH UHYLHZ RI GHVLJQ
calculations and drawings, and as determined by analytical
methods. Load tests or other methods can be incorporated
into the overall evaluation process if deemed appropriate.
FRP systems used to increase the strength of an existing
member should be designed in accordance with &KDSWHUV
through 15, which include a comprehensive discussion of
load limitations, rational load paths, effects of temperature
and environment on FRP systems, loading considerations,
and effects of reinforcing steel corrosion on FRP system
integrity.
1.2.1.1 Strengthening limits—In general, to prevent
sudden failure of the member in case the FRP system is
damaged, strengthening limits are imposed such that the
increase in the load-carrying capacity of a member strengthened with an FRP system is limited. The philosophy is that a
loss of FRP reinforcement should not cause member failure.
6SHFL¿FJXLGDQFHLQFOXGLQJORDGFRPELQDWLRQVIRUDVVHVVLQJ
5
member integrity after loss of the FRP system, is provided
LQ&KDSWHU
1.2.1.2 Fire and life safety—FRP-strengthened strucWXUHV VKRXOG FRPSO\ ZLWK DSSOLFDEOH EXLOGLQJ DQG ¿UH
FRGHV6PRNHJHQHUDWLRQDQGÀDPHVSUHDGUDWLQJVLQDFFRUdance with ASTM E84VKRXOGEHVDWLV¿HGIRUWKHLQVWDOODtion according to applicable building codes, depending on
WKH FODVVL¿FDWLRQ RI WKH EXLOGLQJ &RDWLQJV Apicella and
,PEURJQR DQG LQVXODWLRQ V\VWHPV Williams et al.
2006 FDQEHXVHGWROLPLWVPRNHDQGÀDPHVSUHDG
Because of the degradation of most FRP materials at
high temperature, the strength of externally bonded FRP
V\VWHPV LV DVVXPHG WR EH ORVW FRPSOHWHO\ LQ D ¿UH XQOHVV
it can be demonstrated that the FRP will remain effective
IRU WKH UHTXLUHG GXUDWLRQ RI WKH ¿UH7KH ¿UH UHVLVWDQFH RI
FRP-strengthened concrete members may be improved
through the use of certain resins, coatings, insulation
V\VWHPV RU RWKHU PHWKRGV RI ¿UH SURWHFWLRQ Bisby et al.
2005b 6SHFL¿FJXLGDQFHLQFOXGLQJORDGFRPELQDWLRQVDQG
DUDWLRQDODSSURDFKWRFDOFXODWLQJVWUXFWXUDO¿UHUHVLVWDQFH
is given in .
1.2.1.3 Maximum service temperature—The physical
and mechanical properties of the resin components of FRP
V\VWHPVDUHLQÀXHQFHGE\WHPSHUDWXUHDQGGHJUDGHDWWHPSHUatures close to or above their glass-transition temperature
Tg Bisby et al. 2005b 7KHTg for commercially available,
ambient temperature-cured FRP systems typically ranges
IURP WR ƒ) WR ƒ& 7KH Tg for a particular
FRP system can be obtained from the system manufacturer
RUWKURXJKWHVWLQJE\G\QDPLFPHFKDQLFDODQDO\VLV '0$ according to ASTM E1640. Reported Tg values should be
DFFRPSDQLHG E\ GHVFULSWLRQV RI WKH WHVW FRQ¿JXUDWLRQ
VDPSOH SUHSDUDWLRQ FXULQJ FRQGLWLRQV WLPH WHPSHUDWXUH
DQG KXPLGLW\ DQG VL]H KHDWLQJ UDWH DQG IUHTXHQF\ XVHG
The Tg GH¿QHG E\ WKLV PHWKRG UHSUHVHQWV WKH H[WUDSRODWHG
onset temperature for the sigmoidal change in the storage
modulus observed in going from a hard and brittle state to a
soft and rubbery state of the material under test. This transition occurs over a temperature range of approximately 54°F
ƒ& FHQWHUHGRQWKHTg. This change in state will adversely
affect the mechanical and bond properties of the cured laminates. For a dry environment, it is generally recommended
that the anticipated service temperature of an FRP system
not exceed Tg±ƒ) Tg±ƒ& Xian and Karbhari 2007 where Tg is taken as the lowest Tg of the components of the
system comprising the load path. This recommendation is
for elevated service temperatures such as those found in hot
regions or certain industrial environments. In cases where
the FRP will be exposed to a moist environment, the wet
glass-transition temperature Tgw VKRXOG EH XVHG Luo and
Wong 2002 7HVWLQJPD\EHUHTXLUHGWRGHWHUPLQHWKHFULWical service temperature for FRP in other environments. The
VSHFL¿FFDVHRI¿UHLVGHVFULEHGLQPRUHGHWDLOLQ
1.2.1.4 Minimum concrete substrate strength—FRP
systems need to be bonded to a sound concrete substrate
and should not be considered for applications on structural members containing corroded reinforcing steel or
deteriorated concrete unless the substrate is repaired using
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6
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
the recommendations in 6.4. Concrete distress, deterioration, and corrosion of existing reinforcing steel should be
evaluated and addressed before the application of the FRP
system. Concrete deterioration concerns include, but are not
limited to, alkali-silica reactions, delayed ettringite formation, carbonation, longitudinal cracking around corroded
reinforcing steel, and laminar cracking at the location of the
steel reinforcement.
The strength of the existing concrete substrate is an important parameter for bond-critical applications, including
ÀH[XUHRUVKHDUVWUHQJWKHQLQJ7KHVXEVWUDWHVKRXOGSRVVHVV
the necessary strength to develop the design stresses of the
FRP system through bond. The substrate, including all bond
surfaces between repaired areas and the original concrete,
VKRXOG KDYH VXI¿FLHQW GLUHFW WHQVLOH DQG VKHDU VWUHQJWK WR
transfer force to the FRP system. For bond-critical appliFDWLRQVWKHWHQVLOHVWUHQJWKVKRXOGEHDWOHDVWSVL 03D GHWHUPLQHGE\XVLQJDSXOORIIW\SHDGKHVLRQWHVWSHU
ICRI 210.3R or ASTM C1583/C1583M. FRP systems should
not be used when the concrete substrate has a compressive
strength fcƍ OHVV WKDQ SVL 03D &RQWDFWFULWLFDO
DSSOLFDWLRQVVXFKDVFROXPQZUDSSLQJIRUFRQ¿QHPHQWWKDW
rely only on intimate contact between the FRP system and
the concrete, are not governed by these minimum values.
Design stresses in the FRP system are developed by deformation or dilation of the concrete section in contact-critical
applications.
The application of FRP systems will not stop the ongoing
FRUURVLRQ RI H[LVWLQJ UHLQIRUFLQJ VWHHO El-Maaddawy et
al. 2006 ,I VWHHO FRUURVLRQ LV HYLGHQW RU LV GHJUDGLQJ WKH
concrete substrate, placement of FRP reinforcement is not
recommended without arresting the ongoing corrosion and
repairing any degradation of the substrate.
CHAPTER 2—NOTATION AND DEFINITIONS
2.1—Notation
Ac = cross-sectional area of concrete in compression
member, in.2 PP2
Acw = area of concrete section of individual vertical wall,
in.2 PP2
Ae FURVVVHFWLRQDODUHDRIHIIHFWLYHO\FRQ¿QHGFRQFUHWH
section, in.2 PP2
Af = area of FRP external reinforcement, in.2 PP2
Afanchor = area of transverse FRP U-wrap for anchorage of
ÀH[XUDO)53UHLQIRUFHPHQWLQ2 PP2
Afv = area of FRP shear reinforcement with spacing s, in.2
PP2
Ag = gross area of concrete section, in.2 PP2
Ap = area of prestressed reinforcement in tension zone,
in.2 PP2
As = area of nonprestressed steel reinforcement, in.2
PP2
Asc = area of the longitudinal reinforcement within a
distance of wf in the compression region, in.2 PP2
Asi = area of i-th layer of longitudinal steel reinforcement, in.2 PP2
Ast = total area of longitudinal reinforcement, in.2 PP2
Asw =
a
ab
=
b
=
bb
=
bw CE =
Csc =
c
cy
D
=
d
dƍ
dƍƍ
dEƐ
df
dfv =
di
=
dp
E2 =
Ec Ef Eps =
Es es =
em =
fc
fcƍ
fccƍ
fcoƍ
fc,s =
ff
area of longitudinal reinforcement in the central
area of the wall, in.2 PP2
GHSWK RI WKH HTXLYDOHQW FRQFUHWH FRPSUHVVLRQ
EORFNLQ PP
smaller cross-sectional dimension for rectangular
)53EDUVLQ PP
ZLGWKRIFRPSUHVVLRQIDFHRIPHPEHULQ PP
short side dimension of compression member of
SULVPDWLFFURVVVHFWLRQLQ PP
larger cross-sectional dimension for rectangular
)53EDUVLQ PP
ZHEZLGWKRUGLDPHWHURIFLUFXODUVHFWLRQLQ PP
environmental reduction factor
compressive force in AscOE 1
GLVWDQFH IURP H[WUHPH FRPSUHVVLRQ ¿EHU WR WKH
QHXWUDOD[LVLQ PP
GLVWDQFH IURP H[WUHPH FRPSUHVVLRQ ¿EHU WR WKH
QHXWUDOD[LVDWVWHHO\LHOGLQJLQ PP
diameter of compression member for circular cross
VHFWLRQVRUGLDJRQDOGLVWDQFHHTXDOWR b 2 + h 2 for
SULVPDWLF FURVV VHFWLRQ GLDPHWHU RI HTXLYDOHQW
FLUFXODUFROXPQ LQ PP
GLVWDQFHIURPH[WUHPHFRPSUHVVLRQ¿EHUWRFHQWURLG
RIWHQVLRQUHLQIRUFHPHQWLQ PP
GLVWDQFHIURPWKHH[WUHPHFRPSUHVVLRQ¿EHUWRWKH
center of AscLQ PP
GLVWDQFHIURPWKHH[WUHPHWHQVLRQ¿EHUWRWKHFHQWHU
of AstLQ PP
GLDPHWHU RI ORQJLWXGLQDO VWHHO LQ FRQ¿QHG SODVWLF
KLQJHLQ PP
HIIHFWLYH GHSWK RI )53 ÀH[XUDO UHLQIRUFHPHQW LQ
PP
effective depth of FRP shear reinforcement, in.
PP
distance from centroid of i-th layer of longitudinal
steel reinforcement to geometric centroid of cross
VHFWLRQLQ PP
GLVWDQFHIURPH[WUHPHFRPSUHVVLRQ¿EHUWRFHQWURLG
RISUHVWUHVVHGUHLQIRUFHPHQWLQ PP
slope of linear portion of stress-strain model for
)53FRQ¿QHGFRQFUHWHSVL 03D
PRGXOXVRIHODVWLFLW\RIFRQFUHWHSVL 03D
WHQVLOHPRGXOXVRIHODVWLFLW\RI)53SVL 03D
modulus of elasticity of prestressing steel, psi
03D
PRGXOXVRIHODVWLFLW\RIVWHHOSVL 03D
eccentricity of prestressing steel with respect to
FHQWURLGDOD[LVRIPHPEHUDWVXSSRUWLQ PP
eccentricity of prestressing steel with respect to
FHQWURLGDOD[LVRIPHPEHUDWPLGVSDQLQ PP
FRPSUHVVLYHVWUHVVLQFRQFUHWHSVL 03D
VSHFL¿HGFRPSUHVVLYHVWUHQJWKRIFRQFUHWHSVL 03D
FRPSUHVVLYHVWUHQJWKRIFRQ¿QHGFRQFUHWHSVL 03D
FRPSUHVVLYHVWUHQJWKRIXQFRQ¿QHGFRQFUHWHDOVR
HTXDOWRfcƍSVL 03D
compressive stress in concrete at service condition,
SVL 03D
VWUHVVLQ)53UHLQIRUFHPHQWSVL 03D
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
ffd
=
ffe
ff,s =
ffu ffu* =
fl
fps =
fps,s =
fpu
fs
=
fsc
=
fsi
=
fs,s =
fst
=
fsw =
fy
g
=
h
=
hf hw =
Icr =
Itr
=
K
=
k1
k2
kf
=
Le Lp Lw Ɛdb =
design stress of externally bonded FRP reinforcePHQWSVL 03D
HIIHFWLYHVWUHVVLQWKH)53VWUHVVDWWDLQHGDWVHFWLRQ
IDLOXUHSVL 03D
stress in FRP caused by a moment within elastic
UDQJHRIPHPEHUSVL 03D
GHVLJQXOWLPDWHWHQVLOHVWUHQJWKRI)53SVL 03D
ultimate tensile strength of the FRP material as
UHSRUWHGE\WKHPDQXIDFWXUHUSVL 03D
PD[LPXPFRQ¿QLQJSUHVVXUHGXHWR)53MDFNHWSVL
03D
stress in prestressed reinforcement at nominal
VWUHQJWKSVL 03D
stress in prestressed reinforcement at service load,
SVL 03D
VSHFL¿HG WHQVLOH VWUHQJWK RI SUHVWUHVVLQJ WHQGRQV
SVL 03D
stress in nonprestressed steel reinforcement, psi
03D
stress in the longitudinal reinforcement corresponding to AscSVL 03D
stress in the i-th layer of longitudinal steel reinIRUFHPHQWSVL 03D
stress in nonprestressed steel reinforcement at
VHUYLFHORDGVSVL 03D
stress in the longitudinal reinforcement corresponding to AstSVL 03D
stress in the longitudinal reinforcement corresponding to AswSVL 03D
VSHFL¿HG \LHOG VWUHQJWK RI QRQSUHVWUHVVHG VWHHO
UHLQIRUFHPHQWSVL 03D
clear gap between the FRP jacket and adjacent
PHPEHUVLQ PP
RYHUDOOWKLFNQHVVRUKHLJKWRIDPHPEHULQ PP
long side cross-sectional dimension of rectangular
FRPSUHVVLRQPHPEHULQ PP
PHPEHUÀDQJHWKLFNQHVVLQ PP
height of entire wall from base to top, or clear
height of wall segment or wall pier considered, in.
PP
moment of inertia of cracked section transformed
to concrete, in.4 PP4
moment of inertia of uncracked section transformed
to concrete, in.4 PP4
ratio of depth of neutral axis to reinforcement depth
PHDVXUHGIURPH[WUHPHFRPSUHVVLRQ¿EHU
PRGL¿FDWLRQ IDFWRU DSSOLHG WR țv to account for
concrete strength
PRGL¿FDWLRQ IDFWRU DSSOLHG WR țv to account for
wrapping scheme
stiffness per unit width per ply of the FRP reinIRUFHPHQWOELQ 1PP kf = Eftf
DFWLYHERQGOHQJWKRI)53ODPLQDWHLQ PP
SODVWLFKLQJHOHQJWKLQ PP
OHQJWKRIWKHVKHDUZDOOLQ PP
development length of near-surface-mounted FRP
EDULQ PP
Ɛd,E =
Ɛdf Ɛo =
Ɛprov
Mcr
Mn
Mnf
Mnp =
Mns Ms Msnet=
M u N =
nf =
ns
=
Pe
Pn =
Pu p fu =
pfu* =
Rn =
Rnࢥ =
R
rc
SDL =
SLL =
sf
Tf T g Tgw Tps Tst =
Tsw =
tf =
tw
=
Vc =
Ve
=
Vf
=
7
length over which the FRP anchorage wraps are
SURYLGHGLQ PP
GHYHORSPHQWOHQJWKRI)53V\VWHPLQ PP
length, measured along the member axis from the
face of the joint, over which special transverse reinIRUFHPHQWPXVWEHSURYLGHGLQ PP
OHQJWKRIVWHHOODSVSOLFHLQ PP
FUDFNLQJPRPHQWLQOE 1PP
QRPLQDOÀH[XUDOVWUHQJWKLQOE 1PP
FRQWULEXWLRQRI)53UHLQIRUFHPHQWWRQRPLQDOÀH[XUDOVWUHQJWKOELQ 1PP
contribution of prestressing reinforcement to
QRPLQDOÀH[XUDOVWUHQJWKOELQ 1PP
FRQWULEXWLRQRIVWHHOUHLQIRUFHPHQWWRQRPLQDOÀH[XUDOVWUHQJWKOELQ 1PP
VHUYLFHPRPHQWDWVHFWLRQLQOE 1PP
service moment at section beyond decompression,
LQOE 1PP
IDFWRUHGPRPHQWDWDVHFWLRQLQOE 1PP
number of plies of FRP reinforcement
modular ratio of elasticity between FRP and
concrete = Ef/Ec
modular ratio of elasticity between steel and
concrete = Es/Ec
HIIHFWLYHIRUFHLQSUHVWUHVVLQJUHLQIRUFHPHQW DIWHU
DOORZDQFHIRUDOOSUHVWUHVVORVVHV OE 1
nominal axial compressive strength of a concrete
VHFWLRQOE 1
IDFWRUHGD[LDOORDGOE 1
mean tensile strength per unit width per ply of FRP
UHLQIRUFHPHQWOELQ 1PP
ultimate tensile strength per unit width per ply of
)53UHLQIRUFHPHQWOELQ 1PP pfu* = ffu*tf
nominal strength of a member
nominal strength of a member subjected to elevated
WHPSHUDWXUHVDVVRFLDWHGZLWKD¿UH
UDGLXVRIJ\UDWLRQRIDVHFWLRQLQ PP
UDGLXVRIHGJHVRIDSULVPDWLFFURVVVHFWLRQFRQ¿QHG
ZLWK)53LQ PP
dead load effects
live load effects
FHQWHUWRFHQWHUVSDFLQJRI)53VWULSVLQ PP
WHQVLOHIRUFHLQ)53OE 1
JODVVWUDQVLWLRQWHPSHUDWXUHƒ) ƒ&
ZHWJODVVWUDQVLWLRQWHPSHUDWXUHƒ) ƒ&
WHQVLOHIRUFHLQSUHVWUHVVLQJVWHHOOE 1
tensile force in AstOE 1
tensile force in AswOE 1
nominal thickness of one ply of FRP reinforcement,
LQ PP
thickness of the existing concrete shear wall, in.
PP
nominal shear strength provided by concrete with
VWHHOÀH[XUDOUHLQIRUFHPHQWOE 1
design shear force for load combinations including
HDUWKTXDNHHIIHFWVOE 1
nominal shear strength provided by FRP stirrups,
OE 1
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8
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Vn QRPLQDOVKHDUVWUHQJWKOE 1
Vn* VKHDUVWUHQJWKRIH[LVWLQJPHPEHUOE 1
Vs = nominal shear strength provided by steel stirrups,
OE 1
wf ZLGWKRI)53UHLQIRUFLQJSOLHVLQ PP
yb = distance from centroidal axis of gross section,
QHJOHFWLQJUHLQIRUFHPHQWWRH[WUHPHERWWRP¿EHU
LQLQ PPPP
yt = vertical coordinate within compression region
measured from neutral axis position. It corresponds
WRWUDQVLWLRQVWUDLQİtƍLQ PP
Į
DQJOHRIDSSOLFDWLRQRISULPDU\)53UHLQIRUFHPHQW
direction relative to longitudinal axis of member
Į1 = multiplier on fcƍWRGHWHUPLQHLQWHQVLW\RIDQHTXLYDlent rectangular stress distribution for concrete
ĮL ORQJLWXGLQDO FRHI¿FLHQW RI WKHUPDO H[SDQVLRQ LQ
LQƒ) PPPPƒ&
ĮT WUDQVYHUVH FRHI¿FLHQW RI WKHUPDO H[SDQVLRQ LQ
LQƒ) PPPPƒ&
ȕ1 UDWLRRIGHSWKRIHTXLYDOHQWUHFWDQJXODUVWUHVVEORFN
to depth of the neutral axis
İb = strain in concrete substrate developed by a given
EHQGLQJPRPHQW WHQVLRQLVSRVLWLYH LQLQ PP
PP
İbi = strain in concrete substrate at time of FRP installaWLRQ WHQVLRQLVSRVLWLYH LQLQ PPPP
İc VWUDLQLQFRQFUHWHLQLQ PPPP
İcƍ FRPSUHVVLYH VWUDLQ RI XQFRQ¿QHG FRQFUHWH FRUUHsponding to fcƍLQLQ PPPP PD\EHWDNHQDV
0.002
İccu XOWLPDWH D[LDO FRPSUHVVLYH VWUDLQ RI FRQ¿QHG
concrete corresponding to 0.85fccƍ LQ D OLJKWO\
FRQ¿QHG PHPEHU PHPEHU FRQ¿QHG WR UHVWRUH LWV
FRQFUHWHGHVLJQFRPSUHVVLYHVWUHQJWK RUXOWLPDWH
D[LDOFRPSUHVVLYHVWUDLQRIFRQ¿QHGFRQFUHWHFRUUHVSRQGLQJWRIDLOXUHLQDKHDYLO\FRQ¿QHGPHPEHU
İc,s VWUDLQLQFRQFUHWHDWVHUYLFHLQLQ PPPP
İct = concrete tensile strain at level of tensile force resulWDQW LQ SRVWWHQVLRQHG ÀH[XUDO PHPEHUV LQLQ
PPPP
İcu XOWLPDWHD[LDOVWUDLQRIXQFRQ¿QHGFRQFUHWHFRUUHsponding to 0.85fcoƍ RU PD[LPXP XVDEOH VWUDLQ RI
XQFRQ¿QHG FRQFUHWH LQLQ PPPP ZKLFK FDQ
occur at fc = 0.85fcƍRUİc = 0.003, depending on the
obtained stress-strain curve
VWUDLQLQWKH)53UHLQIRUFHPHQWLQLQ PPPP
İf
İfd = debonding strain of externally bonded FRP reinIRUFHPHQWLQLQ PPPP
İfe = effective strain in FRP reinforcement attained at
IDLOXUHLQLQ PPPP
İfu = design rupture strain of FRP reinforcement, in./in.
PPPP
ε fu = mean rupture strain of FRP reinforcement based on
a population of 20 or more tensile tests per ASTM
''0LQLQ PPPP
İfu* = ultimate rupture strain of FRP reinforcement, in./in.
PPPP
İpe =
İpi =
İpnet İpnet,s=
İps =
İps,s =
İs
=
İsy =
İt
=
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ࢥ
ࢥ D ࢥy,frp ța
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=
=
=
ȡl
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ı
IJb
=
=
=
ȥe =
ȥf
=
ȥs =
ȥt
=
effective strain in prestressing steel after losses, in./
LQ PPPP
initial strain in prestressed steel reinforcement, in./
LQ PPPP
QHW VWUDLQ LQ ÀH[XUDO SUHVWUHVVLQJ VWHHO DW OLPLW
VWDWHDIWHUSUHVWUHVVIRUFHLVGLVFRXQWHG H[FOXGLQJ
VWUDLQVGXHWRHIIHFWLYHSUHVWUHVVIRUFHDIWHUORVVHV LQLQ PPPP
net strain in prestressing steel beyond decompresVLRQDWVHUYLFHLQLQ PPPP
strain in prestressed reinforcement at nominal
VWUHQJWKLQLQ PPPP
strain in prestressing steel at service load, in./in.
PPPP
strain in nonprestessed steel reinforcement, in./in.
PPPP
strain corresponding to yield strength of nonpreVWUHVVHGVWHHOUHLQIRUFHPHQWLQLQ PPPP
net tensile strain in extreme tension steel at nominal
VWUHQJWKLQLQ PPPP
WUDQVLWLRQ VWUDLQ LQ VWUHVVVWUDLQ FXUYH RI )53
FRQ¿QHGFRQFUHWHLQLQ PPPP
VWUHQJWKUHGXFWLRQIDFWRU
GHVLJQFXUYDWXUHIRUDFRQ¿QHGFRQFUHWHVHFWLRQ
FXUYDWXUH RI WKH )53 FRQ¿QHG VHFWLRQ DW VWHHO
yielding
HI¿FLHQF\IDFWRUIRU)53UHLQIRUFHPHQWLQGHWHUPLnation of fccƍ EDVHGRQJHRPHWU\RIFURVVVHFWLRQ
HI¿FLHQF\IDFWRUIRU)53UHLQIRUFHPHQWLQGHWHUPLQDWLRQRIİccu EDVHGRQJHRPHWU\RIFURVVVHFWLRQ
ERQGGHSHQGHQWFRHI¿FLHQWIRUVKHDU
HI¿FLHQF\ IDFWRU HTXDO WR IRU )53 VWUDLQ WR
account for the difference between observed rupture
VWUDLQLQFRQ¿QHPHQWDQGUXSWXUHVWUDLQGHWHUPLQHG
from tensile tests
plastic hinge rotation demand
FRP reinforcement ratio
ratio of area of longitudinal steel reinforcement to
FURVVVHFWLRQDODUHDRIDFRPSUHVVLRQPHPEHU As/bh
longitudinal reinforcement ratio
ratio of nonprestressed reinforcement
VWDQGDUGGHYLDWLRQ
average bond strength for near-surface-mounted
)53EDUVSVL 03D
factor used to modify development length based on
reinforcement coating
FRP strength reduction factor
IRUÀH[XUH FDOLEUDWHGEDVHGRQGHVLJQPDWHULDOSURSHUWLHV
IRU VKHDU EDVHG RQ UHOLDELOLW\ DQDO\VLV IRU
three-sided FRP U-wrap or two sided strengthening
schemes
IRUVKHDUIXOO\ZUDSSHGVHFWLRQV
factor used to modify development length based on
reinforcement size
factor used to modify development length based on
reinforcement location
@Seismicisolation
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American Concrete Institute – Copyrighted © Material – www.concrete.org
MCPOL Licensed to: McMaster University Library
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
2.2—Definitions
$&,SURYLGHVDFRPSUHKHQVLYHOLVWRIGH¿QLWLRQVWKURXJK
an online resource, “ACI Concrete Terminology,” https://
www.concrete.org/store/productdetail.aspx?ItemID=CT13.
'H¿QLWLRQVSURYLGHGKHUHLQFRPSOHPHQWWKDWVRXUFH
DUDPLG ¿EHU²¿EHU LQ ZKLFK FKDLQV RI DURPDWLF SRO\DPLGHPROHFXOHVDUHRULHQWHGDORQJWKH¿EHUD[LVWRH[SORLW
the strength of the chemical bond.
DUDPLG ¿EHUUHLQIRUFHG SRO\PHU—composite material
FRPSULVLQJ D SRO\PHU PDWUL[ UHLQIRUFHG ZLWK DUDPLG ¿EHU
cloth, mat, or strands.
FDUERQ¿EHU²¿EHUSURGXFHGE\KHDWLQJRUJDQLFSUHFXUVRU
materials containing a substantial amount of carbon, such as
rayon, polyacrylonitrile, or pitch in an inert environment.
FDUERQ ¿EHUUHLQIRUFHG SRO\PHU—composite material
FRPSULVLQJ D SRO\PHU PDWUL[ UHLQIRUFHG ZLWK FDUERQ ¿EHU
cloth, mat, or strands.
FDWDO\VW—substance that accelerates a chemical reaction and enables it to proceed under conditions more mild
WKDQRWKHUZLVHUHTXLUHGDQGWKDWLVQRWLWVHOISHUPDQHQWO\
changed by the reaction.
FRQWDFWFULWLFDO DSSOLFDWLRQ—strengthening or repair
system that relies on load transfer from the substrate to the
system material achieved through contact or bearing at the
interface.
FUHHS UXSWXUH—breakage of a material under sustained
loading at stresses less than the tensile strength.
FURVVOLQNLQJ—formation of covalent bonds linking one
polymer molecule to another.
(JODVV²IDPLO\ RI JODVV ¿EHUV XVHG LQ UHLQIRUFHG SRO\mers with a calcium alumina borosilicate composition and a
maximum alkali content of 2.0 percent.
IDEULF—two-dimensional network of woven, nonwoven,
NQLWWHGRUVWLWFKHG¿EHUV\DUQVRUWRZV
¿EHUFRQWHQW²WKHDPRXQWRI¿EHUSUHVHQWLQDFRPSRVLWH
expressed as a percentage volume fraction or mass fraction
of the composite.
¿EHUÀ\²VKRUW¿ODPHQWVWKDWEUHDNRIIGU\¿EHUWRZVRU
yarns during handling and become airborne.
¿UHUHWDUGDQW—additive to the resin or a surface coating
used to reduce the tendency of a resin to burn.
¿EHU YROXPH IUDFWLRQ²UDWLR RI WKH YROXPH RI ¿EHUV WR
WKHYROXPHRIWKHFRPSRVLWHFRQWDLQLQJWKH¿EHUV
IXOOFXUH—period at which components of a thermosetting
UHVLQKDYHUHDFWHGVXI¿FLHQWO\IRUWKHUHVLQWRSURGXFHVSHFL¿HGSURSHUWLHV
JODVV ¿EHU²¿ODPHQW GUDZQ IURP DQ LQRUJDQLF IXVLRQ
typically comprising silica-based material that has cooled
without crystallizing.
JODVV ¿EHUUHLQIRUFHG SRO\PHU—composite material
FRPSULVLQJ D SRO\PHU PDWUL[ UHLQIRUFHG ZLWK JODVV ¿EHU
cloth, mat, or strands.
JODVVWUDQVLWLRQ WHPSHUDWXUH—representative temperature of the temperature range over which an amorphous
PDWHULDO VXFKDVJODVVRUDKLJKSRO\PHU FKDQJHVIURP RU
WR DEULWWOHYLWUHRXVVWDWHWR RUIURP DSODVWLFVWDWH
LPSUHJQDWH²WRVDWXUDWH¿EHUVZLWKUHVLQRUELQGHU
9
initiator—chemical used to start the curing process for
unsaturated polyester and vinyl ester resins.
interlaminar shear—force tending to produce a relative
displacement along the plane of the interface between two
laminae.
LQWXPHVFHQW FRDWLQJ—covering that swells, increasing
YROXPH DQG GHFUHDVLQJ GHQVLW\ ZKHQ H[SRVHG WR ¿UH
LPSDUWLQJDGHJUHHRISDVVLYH¿UHSURWHFWLRQ
lamina²VLQJOHOD\HURI¿EHUUHLQIRUFHPHQW
laminate—multiple plies or lamina molded together.
OD\XS—process of placing reinforcing material and resin
system in position for molding.
monomer—organic molecule of low molecular weight
that creates a solid polymer by reacting with itself or other
compounds of low molecular weight.
SKHQROLF UHVLQ—thermosetting resin produced by the
condensation reaction of an aromatic alcohol with an aldeK\GH XVXDOO\DSKHQROZLWKIRUPDOGHK\GH SLWFK—viscid substance obtained as a residue of petroleum or coal tar for use as a precursor in the manufacture of
VRPHFDUERQ¿EHUV
SRO\DFU\ORQLWULOH²synthetic semi-chrystalline organic
SRO\PHUEDVHGPDWHULDOWKDWLVVSXQLQWRD¿EHUIRUPIRUXVH
DVDSUHFXUVRULQWKHPDQXIDFWXUHURIVRPHFDUERQ¿EHUV
SRO\HVWHU—one of a large group of synthetic resins,
mainly produced by reaction of dibasic acids with dihydroxy
alcohols.
SRVWFXULQJ—application of elevated temperature to material containing thermosetting resin to increase the degree of
SRO\PHUFURVVOLQNLQJDQGHQKDQFHWKH¿QDOPDWHULDOSURSHUWLHV
SUHSUHJ—sheet of fabric or mat preimpregnated with
UHVLQ RU ELQGHU WKDW LV SDUWLDOO\ FXUHG DQG UHDG\ IRU ¿QDO
forming and curing.
SXOWUXVLRQ²FRQWLQXRXVSURFHVVIRUPDQXIDFWXULQJ¿EHU
reinforced polymer composites in which resin-impregnated
¿EHU UHLQIRUFHPHQWV URYLQJ RU PDWV DUH SXOOHG WKURXJK D
shaping and curing die to produce composites with uniform
cross sections.
SXWW\—thickened polymer-based resin used to prepare the
concrete substrate.
UHVLQ FRQWHQW²DPRXQW RI UHVLQ LQ D ¿EHUUHLQIRUFHG
polymer composite laminate, expressed as either a percentage
of total mass or total volume.
URYLQJ—parallel bundle of continuous yarns, tows, or
¿EHUVZLWKOLWWOHRUQRWZLVW
saturating resins (or saturants)—polymer-based resin
XVHGWRLPSUHJQDWHWKHUHLQIRUFLQJ¿EHUV¿[WKHPLQSODFH
DQGWUDQVIHUORDGEHWZHHQ¿EHUV
VKHOI OLIH²length of time packaged materials can be
VWRUHGXQGHUVSHFL¿HGFRQGLWLRQVDQGUHPDLQXVDEOH
sizing²VXUIDFH WUHDWPHQW DSSOLHG WR ¿ODPHQWV WR LPSDUW
desired processing, durability, and bond attributes.
storage modulus—measure of the stored energy in a
viscoelastic material undergoing cyclic deformation during
dynamic mechanical analysis.
tow²XQWZLVWHGEXQGOHRIFRQWLQXRXV¿ODPHQWV
YLQ\OHVWHUUHVLQ²thermosetting reaction product of epoxy
UHVLQZLWKDSRO\PHUL]DEOHXQVDWXUDWHGDFLG XVXDOO\PHWK-
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MCPOL Licensed to: McMaster University Library
10
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
DFU\OLF DFLG WKDW LV WKHQ GLOXWHG ZLWK D UHDFWLYH PRQRPHU
XVXDOO\VW\UHQH YRODWLOH RUJDQLF FRPSRXQG—organic compound that
vaporizes under normal atmospheric conditions.
ZHWOD\XS²PDQXIDFWXULQJSURFHVVZKHUHGU\IDEULF¿EHU
reinforcement is impregnated on site with a saturating resin
matrix and then cured in place.
ZHWRXW—process of coating or impregnating roving,
\DUQRUIDEULFWR¿OOWKHYRLGVEHWZHHQWKHVWUDQGVDQG¿ODPHQWVZLWKUHVLQLWLVDOVRWKHFRQGLWLRQDWZKLFKWKLVVWDWH
is achieved.
ZLWQHVV SDQHO—small mockup manufactured under
FRQGLWLRQV UHSUHVHQWDWLYH RI ¿HOG DSSOLFDWLRQ WR FRQ¿UP
WKDWSUHVFULEHGSURFHGXUHVDQGPDWHULDOVZLOO\LHOGVSHFL¿HG
mechanical and physical properties.
yarn²WZLVWHGEXQGOHRIFRQWLQXRXV¿ODPHQWV
CHAPTER 3—BACKGROUND INFORMATION
([WHUQDOO\ ERQGHG ¿EHUUHLQIRUFHG SRO\PHU )53 V\VWHPV KDYH EHHQ XVHG WR VWUHQJWKHQ DQG UHWUR¿W H[LVWLQJ
FRQFUHWH VWUXFWXUHV DURXQG WKH ZRUOG VLQFH WKH PLGV
The number of projects using FRP systems worldwide has
LQFUHDVHG GUDPDWLFDOO\ IURP D IHZ LQ WKH V WR PDQ\
thousands today. Structural elements strengthened with
externally bonded FRP systems include beams, slabs,
columns, walls, joints/connections, chimneys and smokestacks, vaults, domes, tunnels, silos, pipes, and trusses.
Externally bonded FRP systems have also been used to
strengthen masonry, timber, steel, and cast-iron structures.
Externally bonded FRP systems were developed as alternaWLYHV WR WUDGLWLRQDO H[WHUQDO UHLQIRUFLQJ WHFKQLTXHV VXFK DV
steel plate bonding and steel or concrete column jacketing.
The initial development of externally bonded FRP systems
IRUWKHUHWUR¿WRIFRQFUHWHVWUXFWXUHVRFFXUUHGLQWKHV
in Europe and Japan.
3.1—Historical development
In Europe, FRP systems were developed as alternates to
steel plate bonding. Bonding steel plates to the tension zones
of concrete members with adhesive resins was shown to be
DYLDEOHWHFKQLTXHIRULQFUHDVLQJÀH[XUDOVWUHQJWK Fleming
DQG.LQJ 7KLVWHFKQLTXHKDVEHHQXVHGWRVWUHQJWKHQ
many bridges and buildings around the world. Because steel
plates can corrode, leading to a deterioration of the bond
EHWZHHQWKHVWHHODQGFRQFUHWHDQGEHFDXVHWKH\DUHGLI¿FXOW
WRLQVWDOOUHTXLULQJWKHXVHRIKHDY\HTXLSPHQWUHVHDUFKHUV
looked to FRP materials as an alternative to steel. ExperiPHQWDO ZRUN XVLQJ )53 PDWHULDOV IRU UHWUR¿WWLQJ FRQFUHWH
VWUXFWXUHVZDVUHSRUWHGDVHDUO\DVLQ*HUPDQ\ Wolf
DQG0LHVVOHU 5HVHDUFKLQ6ZLW]HUODQGOHGWRWKH¿UVW
applications of externally bonded FRP systems to reinforced
FRQFUHWH EULGJHV IRU ÀH[XUDO VWUHQJWKHQLQJ 0HLHU 5RVWDV\ )53V\VWHPVZHUH¿UVWDSSOLHGWRUHLQIRUFHGFRQFUHWHFROXPQV
IRU SURYLGLQJ DGGLWLRQDO FRQ¿QHPHQW LQ -DSDQ LQ WKH V
)DUGLV DQG .KDOLOL .DWVXPDWD HW DO $ VXGGHQ
increase in the use of FRPs in Japan was observed following
WKH+\RJRNHQ1DQEXHDUWKTXDNH 1DQQL Researchers in the United States have had a continuous
LQWHUHVWLQ¿EHUEDVHGUHLQIRUFHPHQWIRUFRQFUHWHVWUXFWXUHV
VLQFHWKHV'HYHORSPHQWDQGUHVHDUFKLQWRWKHXVHRI
WKHVHPDWHULDOVIRUUHWUR¿WWLQJFRQFUHWHVWUXFWXUHVKRZHYHU
VWDUWHG LQ WKH V WKURXJK WKH LQLWLDWLYHV RI WKH 1DWLRQDO
6FLHQFH )RXQGDWLRQ 16) DQG WKH )HGHUDO +LJKZD\
$GPLQLVWUDWLRQ )+:$ 7KH UHVHDUFK DFWLYLWLHV OHG WR WKH
FRQVWUXFWLRQ RI PDQ\ ¿HOG SURMHFWV WKDW HQFRPSDVVHG D
wide variety of environmental conditions. Previous research
DQG ¿HOG DSSOLFDWLRQV IRU )53 UHKDELOLWDWLRQ DQG VWUHQJWKening are described in ACI 440R and conference proceedings, including those of the Fiber Reinforced Polymers for
5HLQIRUFHG &RQFUHWH 6WUXFWXUHV )535&6 &RPSRVLWHV LQ
&LYLO(QJLQHHULQJ &,&( DQG&RQIHUHQFHRQ'XUDELOLW\RI
&RPSRVLWHVIRU&RQVWUXFWLRQ &'&& VHULHV
The development of codes and standards for externally
bonded FRP systems is ongoing in Europe, Japan, Canada,
DQGWKH8QLWHG6WDWHV7KH¿UVWSXEOLVKHGFRGHVDQGVWDQGDUGV
DSSHDUHGLQ-DSDQ Japan Society of Civil Engineers 2001 DQG(XURSH International Federation for Structural Concrete
2001 ,Q WKH 8QLWHG 6WDWHVACI 440.8, ICC AC125, and
1&+535HSRUW Zureick et al. 2010 SURYLGHFULWHULDIRU
evaluating FRP systems.
3.2—Commercially available externally bonded
FRP systems
FRP systems come in a variety of forms, including wet
layup systems and precured systems. FRP system forms
can be categorized based on how they are delivered to the
site and installed. The FRP system and its form should be
selected based on the acceptable transfer of structural loads
and the ease and simplicity of application. Common FRP
system forms suitable for the strengthening of structural
members are listed in 3.2.1 through 3.2.4.
3.2.1 Wet layup systems—Wet layup FRP systems consist
RIGU\XQLGLUHFWLRQDORUPXOWLGLUHFWLRQDO¿EHUVKHHWVRUIDEULFV
impregnated with a saturating resin on site. The saturating
resin, along with the compatible primer and putty, bonds the
FRP sheets to the concrete surface. Wet layup systems are
saturated on site and cured in place and, in this sense, are
analogous to cast-in-place concrete. Three common types of
wet layup systems are listed as follows:
'U\ XQLGLUHFWLRQDO ¿EHU VKHHWV ZKHUH WKH ¿EHUV UXQ
predominantly in one planar direction. ACI 440.8 provides
VSHFL¿FDWLRQV IRU XQLGLUHFWLRQDO FDUERQ ¿EHUUHLQIRUFHG
SRO\PHU &)53 DQGJODVV¿EHUUHLQIRUFHGSRO\PHU *)53 wet layup systems.
'U\ PXOWLGLUHFWLRQDO ¿EHU VKHHWV RU IDEULFV ZKHUH WKH
¿EHUVDUHRULHQWHGLQDWOHDVWWZRSODQDUGLUHFWLRQV
'U\ ¿EHU WRZV WKDW DUH ZRXQG RU RWKHUZLVH PHFKDQLFDOO\DSSOLHGWRWKHFRQFUHWHVXUIDFH7KHGU\¿EHUWRZVDUH
impregnated with resin on site during the winding operation.
3.2.2 Prepreg systems—Prepreg FRP systems consist of
SDUWLDOO\FXUHGXQLGLUHFWLRQDORUPXOWLGLUHFWLRQDO¿EHUVKHHWV
or fabrics that are preimpregnated with a saturating resin
in the manufacturer’s facility. Prepreg systems are bonded
to the concrete surface with or without an additional resin
DSSOLFDWLRQ GHSHQGLQJ RQ VSHFL¿F V\VWHP UHTXLUHPHQWV
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MCPOL Licensed to: McMaster University Library
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Prepreg systems are saturated off site and, like wet layup
V\VWHPV FXUHG LQ SODFH 3UHSUHJ V\VWHPV XVXDOO\ UHTXLUH
additional heating for curing. Prepreg system manufacturers
should be consulted for storage and shelf-life recommendations and curing procedures. Three common types of prepreg
FRP systems are:
3UHLPSUHJQDWHG XQLGLUHFWLRQDO ¿EHU VKHHWV ZKHUH WKH
¿EHUVUXQSUHGRPLQDQWO\LQRQHSODQDUGLUHFWLRQ
3UHLPSUHJQDWHGPXOWLGLUHFWLRQDO¿EHUVKHHWVRUIDEULFV
ZKHUHWKH¿EHUVDUHRULHQWHGLQDWOHDVWWZRSODQDUGLUHFWLRQV
3UHLPSUHJQDWHG¿EHUWRZVWKDWDUHZRXQGRURWKHUZLVH
mechanically applied to the concrete surface
3.2.3 Precured systems—Precured FRP systems consist of
a wide variety of composite shapes manufactured off site.
Typically, an adhesive, along with the primer and putty, is
used to bond the precured shapes to the concrete surface.
The system manufacturer should be consulted for recommended installation procedures. Precured systems are analogous to precast concrete. Three common types of precured
systems are:
1. Precured unidirectional laminate sheets typically delivHUHGWRWKHVLWHLQWKHIRUPRIODUJHÀDWVWRFNRUDVWKLQULEERQ
strips coiled on a roll
2. Precured multidirectional grids, typically delivered to
the site coiled on a roll
3. Precured shells, typically delivered to the site in
the form of shell segments cut longitudinally so they can
EH RSHQHG DQG ¿WWHG DURXQG FROXPQV RU RWKHU PHPEHUV
multiple shell layers are bonded to the concrete and to each
RWKHUWRSURYLGHFRQ¿QHPHQW
3.2.4 Near-surface-mounted (NSM) systems—Surfaceembedded NSM FRP systems consist of circular or rectangular bars or plates installed and bonded into grooves made
on the concrete surface. A suitable adhesive is used to bond
the FRP bar into the groove, and is cured in-place. The NSM
system manufacturer should be consulted for recommended
adhesives. Two common FRP bar types used for NSM applications are:
1. Round bars usually manufactured using pultrusion
processes, typically delivered to the site in the form of single
bars or in a roll, depending on bar diameter
2. Rectangular bars and plates usually manufactured using
pultrusion processes, typically delivered to the site in a roll
CHAPTER 4—CONSTITUENT MATERIALS AND
PROPERTIES
7KHSK\VLFDODQGPHFKDQLFDOSURSHUWLHVRI¿EHUUHLQIRUFHG
SRO\PHU )53 PDWHULDOV SUHVHQWHG LQ WKLV FKDSWHU H[SODLQ
the behavior and properties affecting their use in concrete
structures. The effects of factors such as loading history and
duration, temperature, and moisture on the properties of FRP
are discussed.
FRP strengthening systems come in a variety of forms
ZHW OD\XS SUHSUHJ DQG SUHFXUHG )DFWRUV VXFK DV ¿EHU
YROXPH W\SH RI ¿EHU W\SH RI UHVLQ ¿EHU RULHQWDWLRQ
GLPHQVLRQDO HIIHFWV DQG TXDOLW\ FRQWURO GXULQJ PDQXIDFturing all play a role in establishing the characteristics of
an FRP material. The material characteristics described in
11
this chapter are generic and do not apply to all commercially
available products. Standard test methods are available to
FKDUDFWHUL]H FHUWDLQ )53 SURGXFWV UHIHU WR Appendix B ACI 440.8SURYLGHVDVSHFL¿FDWLRQIRUXQLGLUHFWLRQDOFDUERQ
)53 &)53 DQGJODVV)53 *)53 PDWHULDOVPDGHXVLQJ
the wet layup process. The licensed design professional
should consult with the FRP system manufacturer to obtain
WKH UHOHYDQW FKDUDFWHULVWLFV IRU D VSHFL¿F SURGXFW DQG WKH
applicability of those characteristics.
4.1—Constituent materials
The constituent materials used in commercially available
FRP repair systems, including all resins, primers, putties,
VDWXUDQWV DGKHVLYHV DQG ¿EHUV KDYH EHHQ GHYHORSHG IRU
the strengthening of structural concrete members based on
materials and structural testing.
4.1.1 Resins—A wide range of polymeric resins, including
SULPHUVSXWW\¿OOHUVVDWXUDQWVDQGDGKHVLYHVDUHXVHGZLWK
FRP systems. Commonly used resin types, including epoxy,
vinyl esters, and polyesters, have been formulated for use
in a wide range of environmental conditions. FRP system
manufacturers use resins that have:
D &RPSDWLELOLW\ ZLWK DQG DGKHVLRQ WR WKH FRQFUHWH
substrate
E &RPSDWLELOLW\ZLWKDQGDGKHVLRQWRWKH)53FRPSRVLWH
system
F &RPSDWLELOLW\ZLWKDQGDGKHVLRQWRWKHUHLQIRUFLQJ¿EHU
G 5HVLVWDQFHWRHQYLURQPHQWDOHIIHFWVLQFOXGLQJEXWQRW
limited to, moisture, salt water, temperature extremes, and
chemicals normally associated with exposed concrete
H )LOOLQJDELOLW\
I :RUNDELOLW\
J 3RWOLIHFRQVLVWHQWZLWKWKHDSSOLFDWLRQ
K 'HYHORSPHQWRIDSSURSULDWHPHFKDQLFDOSURSHUWLHVIRU
the FRP composite
4.1.1.1 Primer—Primer is used to penetrate the surface of
the concrete, providing an improved adhesive bond for the
saturating resin or adhesive.
4.1.1.2 3XWW\ ¿OOHUV²3XWW\ LV XVHG WR ¿OO VPDOO VXUIDFH
voids in the substrate, such as bug holes, and to provide a
smooth surface to which the FRP system can bond. Filled
surface voids also prevent bubbles from forming during
curing of the saturating resin.
4.1.1.3 Saturating resin—Saturating resin is used to
LPSUHJQDWH WKH UHLQIRUFLQJ ¿EHUV ¿[ WKHP LQ SODFH DQG
provide a shear load path to effectively transfer load between
¿EHUV7KH VDWXUDWLQJ UHVLQ DOVR VHUYHV DV WKH DGKHVLYH IRU
wet layup systems, providing a shear load path between the
previously primed concrete substrate and the FRP system.
4.1.1.4 Adhesives—Adhesives are used to bond precured
)53ODPLQDWHDQGQHDUVXUIDFHPRXQWHG 160 V\VWHPVWR
the concrete substrate. The adhesive provides a shear load
path between the concrete substrate and the FRP reinforcing
system. Adhesives are also used to bond together multiple
layers of precured FRP laminates.
4.1.2 Fibers²&RQWLQXRXVJODVVDUDPLGDQGFDUERQ¿EHUV
DUHFRPPRQUHLQIRUFHPHQWVXVHGLQ)53V\VWHPV7KH¿EHUV
give the FRP system its strength and stiffness. Typical ranges
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MCPOL Licensed to: McMaster University Library
12
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
RIWKHWHQVLOHSURSHUWLHVRI¿EHUVDUHJLYHQLQAppendix A.
$ PRUH GHWDLOHG GHVFULSWLRQ RI ¿EHU W\SHV LV JLYHQ LQACI
440R.
4.1.3 Protective coatings—The protective coating protects
the bonded FRP reinforcement from potentially damaging
environmental and mechanical effects. Coatings are typically applied to the exterior surface of the FRP system after
some prescribed degree of adhesive or saturating resin cure.
The protection systems are available in a variety of forms.
These include:
D 3RO\PHUFRDWLQJVWKDWDUHJHQHUDOO\HSR[\RUSRO\XUHWKDQHV
E $FU\OLF FRDWLQJV WKDW FDQ EH HLWKHU VWUDLJKW DFU\OLF
systems or acrylic cement-based systems. The acrylic
systems can also come in different textures.
F &HPHQWLWLRXVV\VWHPVWKDWPD\UHTXLUHURXJKHQLQJRI
WKH)53VXUIDFH VXFKDVEURDGFDVWLQJVDQGLQWRZHWUHVLQ and can be installed in the same manner as they would be
installed on a concrete surface.
G ,QWXPHVFHQWFRDWLQJVWKDWDUHSRO\PHUEDVHGFRDWLQJV
XVHGWRSURYLGHDGHJUHHRISDVVLYH¿UHSURWHFWLRQDQGFRQWURO
ÀDPHVSUHDGDQGVPRNHJHQHUDWLRQSHUFRGHUHTXLUHPHQWV
There are several reasons why protection systems are used
to protect FRP systems that have been installed on concrete
surfaces. These include:
D Ultraviolet light protection—The epoxy used as part
of the FRP strengthening system will be affected over time
by exposure to ultraviolet light. There are many available
methods used to protect the system from ultraviolet light.
These include acrylic coatings, cementitious surfacing,
aliphatic polyurethane coatings, and others. Certain types of
vinylester resins have higher ultraviolet light durability than
epoxy resins.
E Fire protection—Fire protection systems are discussed
in 1.2.1.2 and .
F Vandalism—Protective systems that are to resist
vandalism should be hard and durable. There are different
levels of vandalism protection, ranging from polyurethane
coatings that will resist cutting and scraping to cementitious
overlays that provide greater protection.
G Impact, abrasion, and wear—Protection systems
for impact, abrasion, and wear are similar to those used
IRU YDQGDOLVP SURWHFWLRQ KRZHYHU DEUDVLRQ DQG ZHDU DUH
different than vandalism in that they result from repeated
exposure rather than a one-time event, and their protection
systems are usually chosen for their hardness and durability.
H Aesthetics—Protective topcoats may be used to conceal
the FRP system. These may be acrylic latex coatings that are
gray in color to match concrete, or they may be various other
colors and textures to match the existing structure.
I Chemical resistance—Exposure to harsh chemicals,
such as strong acids, may damage the FRP system. In such
environments, coatings with better chemical resistance, such
as urethanes and novolac epoxies, may be used.
J Submersion in potable water—In applications where
the FRP system is to be submerged in potable water, the FRP
system may leach compounds into the water supply. Protective coatings that do not leach harmful chemicals into the
water may be used as a barrier between the FRP system and
the potable water supply.
4.2—Physical properties
4.2.1 Density—FRP materials have densities ranging from
75 to 130 lb/ft3 WRJFP3 ZKLFKLVIRXUWRVL[WLPHV
ORZHUWKDQWKDWRIVWHHO 7DEOH Table 4.2.1—Typical densities of FRP materials,
lb/ft3 (g/cm3)
Steel
Glass FRP
(GFRP)
Carbon FRP
(CFRP)
Aramid FRP
(AFRP)
75 to 130
WR
WR
WR
WR
WR
4.2.2 &RHI¿FLHQWRIWKHUPDOH[SDQVLRQ²7KHFRHI¿FLHQWV
of thermal expansion of unidirectional FRP materials differ in
the longitudinal and transverse directions, depending on the
W\SHVRI¿EHUUHVLQDQGYROXPHIUDFWLRQRI¿EHU7DEOH
OLVWV WKH ORQJLWXGLQDO DQG WUDQVYHUVH FRHI¿FLHQWV RI WKHUPDO
expansion for typical unidirectional FRP materials. Note that
DQHJDWLYHFRHI¿FLHQWRIWKHUPDOH[SDQVLRQLQGLFDWHVWKDWWKH
material contracts with increased temperature and expands
with decreased temperature. For reference, the isotropic
YDOXHVRIFRHI¿FLHQWRIWKHUPDOH[SDQVLRQIRUFRQFUHWHDQG
steel are also provided in Table 4.2.2. Refer to for
design considerations regarding thermal expansion.
4.2.3 Effects of high temperatures—Above the glass transition temperature Tg, the elastic modulus of a polymer is
VLJQL¿FDQWO\UHGXFHGGXHWRFKDQJHVLQLWVPROHFXODUVWUXFture. The value of Tg depends on the type of resin and is
QRUPDOO\LQWKHUHJLRQRIWRƒ) WRƒ& ,QDQ
)53 FRPSRVLWH PDWHULDO WKH ¿EHUV ZKLFK H[KLELW EHWWHU
thermal properties than the resin, can continue to support
some load in the longitudinal direction until the temperature
WKUHVKROGRIWKH¿EHUVLVUHDFKHG7KLVFDQRFFXUDWWHPSHUDWXUHV H[FHHGLQJ ƒ) ƒ& IRU FDUERQ ¿EHUV ƒ)
ƒ& IRU JODVV ¿EHUV DQG ƒ) ƒ& IRU DUDPLG
¿EHUV 'XH WR D UHGXFWLRQ LQ IRUFH WUDQVIHU EHWZHHQ ¿EHUV
through bond to the resin, however, the tensile properties
of the overall composite are reduced. Test results have indiFDWHG WKDW WHPSHUDWXUHV RI ƒ) ƒ& ²PXFK KLJKHU
than the resin Tg—will reduce the tensile strength of GFRP
DQG&)53PDWHULDOVH[FHHGLQJSHUFHQW Kumahara et al.
2WKHUSURSHUWLHVDIIHFWHGE\WKHVKHDUWUDQVIHUWKURXJK
WKHUHVLQVXFKDVEHQGLQJVWUHQJWKDUHUHGXFHGVLJQL¿FDQWO\
DWORZHUWHPSHUDWXUHV :DQJDQG(YDQV For bond-critical applications of FRP systems, the properties
RI WKH SRO\PHU DW WKH ¿EHUFRQFUHWH LQWHUIDFH DUH HVVHQWLDO LQ
maintaining the bond between FRP and concrete. At a temperature close to its Tg, the mechanical properties of the polymer are
VLJQL¿FDQWO\UHGXFHGDQGWKHSRO\PHUEHJLQVWRORVHLWVDELOLW\
WRWUDQVIHUVWUHVVHVIURPWKHFRQFUHWHWRWKH¿EHUV
4.3—Mechanical properties
4.3.1 Tensile behavior—When loaded in direct tension,
XQLGLUHFWLRQDO ¿EHUUHLQIRUFHG SRO\PHU )53 PDWHULDOV GR
QRW H[KLELW DQ\ SODVWLF EHKDYLRU \LHOGLQJ EHIRUH UXSWXUH
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
13
Table 4.2.2—Typical coefficients of thermal expansion for FRP materials*
&RHI¿FLHQWRIWKHUPDOH[SDQVLRQî–6ƒ) î–6/°C)
'LUHFWLRQ
&RQFUHWH
Steel
GFRP
CFRP
AFRP
/RQJLWXGLQDOĮL
WR WR
WR WR
±WR ±WR
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7UDQYHUVHĮT
WR WR
WR WR
WR WR
WR WR
*
7\SLFDOYDOXHVIRU¿EHUYROXPHIUDFWLRQVUDQJLQJIURPWR
The tensile behavior of FRP materials consisting of a single
W\SHRI¿EHUPDWHULDOLVFKDUDFWHUL]HGE\DOLQHDUHODVWLFVWUHVV
strain relationship until failure, which is sudden and brittle.
The tensile strength and stiffness of an FRP material is
GHSHQGHQWRQVHYHUDOIDFWRUV%HFDXVHWKH¿EHUVLQDQ)53
material are the main load-carrying constituents, the type
RI¿EHUWKHRULHQWDWLRQRI¿EHUVWKHTXDQWLW\RI¿EHUVDQG
method and conditions in which the composite is produced
affect the tensile properties of the FRP material. Due to the
SULPDU\ UROH RI WKH ¿EHUV DQG PHWKRGV RI DSSOLFDWLRQ WKH
properties of an FRP repair system are sometimes reported
EDVHG RQ WKH QHW¿EHU DUHD ,Q RWKHU LQVWDQFHV VXFK DV LQ
precured laminates, the reported properties are based on the
gross-laminate area.
The gross-laminate area of an FRP system is calculated
using the total cross-sectional area of the cured FRP system,
LQFOXGLQJDOO¿EHUVDQGUHVLQ7KHJURVVODPLQDWHDUHDLVW\SLcally used for reporting precured laminate properties where
the cured thickness is constant and the relative proportion of
¿EHUDQGUHVLQLVFRQWUROOHG
7KH QHW¿EHU DUHD RI DQ )53 V\VWHP LV FDOFXODWHG XVLQJ
WKHNQRZQDUHDRI¿EHUQHJOHFWLQJWKHWRWDOZLGWKDQGWKLFNQHVVRIWKHFXUHGV\VWHPWKXVUHVLQLVH[FOXGHG7KHQHW
¿EHU DUHD LV W\SLFDOO\ XVHG IRU UHSRUWLQJ SURSHUWLHV RI ZHW
OD\XSV\VWHPVWKDWXVHPDQXIDFWXUHG¿EHUVKHHWVDQG¿HOG
installed resins. The wet layup installation process leads to
FRQWUROOHG¿EHUFRQWHQWDQGYDULDEOHUHVLQFRQWHQW$PHWKRG
VLPLODUWRQHW¿EHUDUHDUHSRUWLQJLVWRUHSRUWWKHWHQVLOHIRUFH
RUVWLIIQHVVSHUXQLWZLGWKRIWKH)53V\VWHPDVUHTXLUHGE\
ASTM D7565/D7565M.
System properties reported using the gross laminate area
have higher relative thickness dimensions and lower relative strength and modulus values, whereas system properties
UHSRUWHGXVLQJWKHQHW¿EHUDUHDKDYHORZHUUHODWLYHWKLFNness dimensions and higher relative strength and modulus
values. Regardless of the basis for the reported values, the
ORDGFDUU\LQJVWUHQJWK ffuAf DQGD[LDOVWLIIQHVV AfEf RIWKH
composite remain constant. Properties reported based on the
QHW¿EHUDUHDDUHQRWWKHSURSHUWLHVRIWKHEDUH¿EHUV:KHQ
tested as a part of a cured composite, the measured tensile
VWUHQJWKDQGXOWLPDWHUXSWXUHVWUDLQRIWKHQHW¿EHUDUHW\SLFDOO\ ORZHU WKDQ WKRVH PHDVXUHG EDVHG RQ D GU\ ¿EHU WHVW
The properties of an FRP system should be characterized
as a composite, recognizing not just the material properties
RIWKHLQGLYLGXDO¿EHUVEXWDOVRWKHHI¿FLHQF\RIWKH¿EHU
resin system, the fabric architecture, and the method used to
create the composite. The mechanical properties of all FRP
systems, regardless of form, should be based on the testing
RIODPLQDWHVDPSOHVZLWKNQRZQ¿EHUFRQWHQW
The tensile properties of some commercially available
FRP strengthening systems are given in Appendix A. The
tensile properties of a particular FRP system, however,
should be obtained from the FRP system manufacturer
or using the appropriate test method described in ASTM
''0, D7205/D7205M, or D7565/D7565M.
Manufacturers should report an ultimate tensile strength,
ZKLFKLVGH¿QHGDVWKHPHDQWHQVLOHVWUHQJWKRIDVDPSOHRI
WHVWVSHFLPHQVPLQXVWKUHHWLPHVWKHVWDQGDUGGHYLDWLRQ ffu*
= f fu ±ı DQGVLPLODUO\UHSRUWDQXOWLPDWHUXSWXUHVWUDLQ
İfu* = ε fu – ı 7KLV DSSURDFK SURYLGHV D SHUFHQW
probability that the actual ultimate tensile properties will
exceed these statistically-based design values for a standard
VDPSOH GLVWULEXWLRQ 0XWVX\RVKL HW DO 7KH HODVWLF
modulus should be calculated in accordance with ASTM
''0 ''0 RU ''0 $
minimum number of 20 replicate test specimens should be
used to determine the ultimate tensile properties. The manufacturer should provide a description of the method used to
obtain the reported tensile properties, including the number
of tests, mean values, and standard deviations.
4.3.2 Compressive behavior—Externally bonded FRP
systems should not be used as compression reinforcement
GXHWRLQVXI¿FLHQWWHVWLQJWRYDOLGDWHLWVXVHLQWKLVW\SHRI
application. The mode of failure for FRP laminates subjected
to longitudinal compression can include transverse tensile
IDLOXUH ¿EHU PLFUREXFNOLQJ RU VKHDU IDLOXUH7KH PRGH RI
IDLOXUHGHSHQGVRQWKHW\SHRI¿EHUWKH¿EHUYROXPHIUDFtion, and the type of resin. In general, compressive strengths
are higher for materials with higher tensile strengths, except
LQWKHFDVHRIDUDPLG)53 $)53 ZKHUHWKH¿EHUVH[KLELW
nonlinear behavior in compression at a relatively low level
RIVWUHVV :X 7KHFRPSUHVVLYHPRGXOXVRIHODVWLFLW\
is usually smaller than the tensile modulus of elasticity of
)53PDWHULDOV (KVDQL 4.4—Time-dependent behavior
4.4.1 Creep rupture—FRP materials subjected to a
sustained load can suddenly fail after a time period referred
to as the endurance time. This type of failure is known as
creep rupture. As the ratio of the sustained tensile stress to
the short-term strength of the FRP laminate increases, endurance time decreases. The endurance time also decreases
under adverse environmental conditions, such as high
temperature, ultraviolet-radiation exposure, high alkalinity,
wet and dry cycles, or freezing-and-thawing cycles.
,QJHQHUDOFDUERQ¿EHUVDUHWKHOHDVWVXVFHSWLEOHWRFUHHS
UXSWXUHDUDPLG¿EHUVDUHPRGHUDWHO\VXVFHSWLEOHDQGJODVV
¿EHUV DUH PRVW VXVFHSWLEOH &UHHS UXSWXUH WHVWV KDYH EHHQ
FRQGXFWHGRQLQ PP GLDPHWHU)53EDUVUHLQIRUFHG
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American Concrete Institute – Copyrighted © Material – www.concrete.org
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14
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
ZLWK JODVV DUDPLG DQG FDUERQ ¿EHUV 7KH )53 EDUV ZHUH
tested at different load levels at room temperature. Results
indicated that a linear relationship exists between creep
rupture strength and the logarithm of time for all load levels.
The ratios of stress to cause creep rupture after 500,000
KRXUV DSSUR[LPDWHO\ \HDUV WR WKH VKRUWWHUP XOWLPDWH
strength of the GFRP, AFRP, and CFRP bars were extrapRODWHG WR EH DSSUR[LPDWHO\ DQG UHVSHFWLYHO\
<DPDJXFKL HW DO 0DOYDU 5HFRPPHQGDWLRQV
on sustained stress limits imposed to avoid creep rupture
are given &KDSWHU through 15. As long as the sustained
stress in the FRP is below the creep rupture stress limits, the
strength of the FRP is available for nonsustained loads.
4.4.2 Fatigue—A substantial amount of data for fatigue
behavior and life prediction of stand-alone FRP materials is
DYDLODEOH 1DWLRQDO 5HVHDUFK &RXQFLO 0RVW RI WKHVH
data were generated from materials typically used by the
DHURVSDFH LQGXVWU\ 'HVSLWH WKH GLIIHUHQFHV LQ TXDOLW\ DQG
consistency between aerospace and commercial-grade FRP
materials, some general observations on the fatigue behavior
RI )53 PDWHULDOV FDQ EH PDGH 8QOHVV VSHFL¿FDOO\ VWDWHG
otherwise, the following cases are based on a unidirectional
PDWHULDOZLWKDSSUR[LPDWHO\SHUFHQW¿EHUYROXPHIUDFWLRQ
and subjected to tension-tension sinusoidal cyclic loading at:
D $IUHTXHQF\ORZHQRXJKWRQRWFDXVHVHOIKHDWLQJ
E $PELHQWODERUDWRU\HQYLURQPHQWV
F $ VWUHVV UDWLR UDWLR RI PLQLPXP DSSOLHG VWUHVV WR
PD[LPXPDSSOLHGVWUHVV RI
G $GLUHFWLRQSDUDOOHOWRWKHSULQFLSDO¿EHUDOLJQPHQW
Test conditions that raise the temperature and moisture
content of FRP materials generally degrade the ambient
environment fatigue behavior.
Of all types of FRP composites for infrastructure applications, CFRP is the least prone to fatigue failure. An endurance
limit of 60 to 70 percent of the initial static ultimate strength
of CFRP is typical. On a plot of stress versus the logarithm
RI WKH QXPEHU RI F\FOHV DW IDLOXUH 61 FXUYH WKH GRZQward slope for CFRP is usually approximately 5 percent of
the initial static ultimate strength per decade of logarithmic
OLIH &XUWLV $WPLOOLRQF\FOHVWKHIDWLJXHVWUHQJWK
is generally between 60 and 70 percent of the initial static
ultimate strength and is relatively unaffected by the moisture
and temperature exposures of concrete structures unless the
UHVLQRU¿EHUUHVLQLQWHUIDFHLVVXEVWDQWLDOO\GHJUDGHGE\WKH
environment.
,Q DPELHQWHQYLURQPHQW ODERUDWRU\ WHVWV Mandell and
0HLHU LQGLYLGXDO JODVV ¿EHUV GHPRQVWUDWHG GHOD\HG
rupture caused by stress corrosion, which had been induced
E\ WKH JURZWK RI VXUIDFH ÀDZV LQ WKH SUHVHQFH RI HYHQ
PLQXWHTXDQWLWLHVRIPRLVWXUH:KHQPDQ\JODVV¿EHUVZHUH
embedded into a matrix to form an FRP composite, a cyclic
tensile fatigue effect of approximately 10 percent loss in the
initial static strength per decade of logarithmic lifetime was
REVHUYHG 0DQGHOO 7KLV IDWLJXH HIIHFW LV WKRXJKW WR
EHGXHWR¿EHU¿EHULQWHUDFWLRQVDQGLVQRWGHSHQGHQWRQWKH
VWUHVVFRUURVLRQPHFKDQLVPGHVFULEHGIRULQGLYLGXDO¿EHUV
8VXDOO\QRFOHDUIDWLJXHOLPLWFDQEHGH¿QHG(QYLURQPHQWDO
factors can play an important role in the fatigue behavior of
JODVV¿EHUVGXHWRWKHLUVXVFHSWLELOLW\WRPRLVWXUHDONDOLQH
or acidic solutions.
$UDPLG¿EHUVIRUZKLFKVXEVWDQWLDOGXUDELOLW\GDWDDUHDYDLOable, appear to behave reasonably well in fatigue. Neglecting
LQWKLVFRQWH[WWKHUDWKHUSRRUGXUDELOLW\RIDOODUDPLG¿EHUV
in compression, the tension-tension fatigue behavior of an
LPSUHJQDWHGDUDPLG¿EHUVWUDQGLVH[FHOOHQW6WUHQJWKGHJUDdation per decade of logarithmic lifetime is approximately 5
WRSHUFHQW 5R\ODQFHDQG5R\ODQFH :KLOHQRGLVWLQFW
endurance limit is known for AFRP, 2-million-cycle endurance limits of commercial AFRP tendons for concrete applications have been reported in the range of 54 to 73 percent
RIWKHXOWLPDWHWHQVLOHVWUHQJWK 2GDJLULHWDO %HFDXVH
the slope of the applied stress versus logarithmic endurance
time of AFRP is similar to the slope of the stress versus logaULWKPLF F\FOLF OLIHWLPH GDWD WKH LQGLYLGXDO ¿EHUV DSSHDU WR
fail by a strain-limited creep rupture process. This lifetimelimiting mechanism in commercial AFRP bars is accelerated
E\H[SRVXUHWRPRLVWXUHDQGHOHYDWHGWHPSHUDWXUH 5R\ODQFH
DQG5R\ODQFH5RVWDV\ 4.5—Durability
Many FRP systems exhibit reduced mechanical properties
after exposure to certain environmental factors, including
high temperature, humidity, and chemical exposure. The
exposure environment, duration of exposure, resin type
DQG IRUPXODWLRQ ¿EHU W\SH DQG UHVLQFXULQJ PHWKRG DUH
VRPH RI WKH IDFWRUV WKDW LQÀXHQFH WKH H[WHQW RI WKH UHGXFtion in mechanical properties. These factors are discussed
in more detail in . The tensile properties reported by the
manufacturer are based on testing conducted in a laboratory
HQYLURQPHQWDQGGRQRWUHÀHFWWKHHIIHFWVRIHQYLURQPHQWDO
exposure. These properties should be adjusted in accordance
with the recommendations in to account for the anticipated service environment to which the FRP system may be
exposed during its service life.
4.6—FRP systems qualification
)53V\VWHPVVKRXOGEHTXDOL¿HGIRUXVHRQDSURMHFWEDVHG
on independent laboratory test data of the FRP-constituent
materials and the laminates made with them, structural test
data for the type of application being considered, and durability data representative of the anticipated environment.
Test data provided by the FRP system manufacturer demonstrating the proposed FRP system should meet all mechanLFDO DQG SK\VLFDO GHVLJQ UHTXLUHPHQWV LQFOXGLQJ WHQVLOH
strength, durability, resistance to creep, bond to substrate,
and Tg, should be considered. ACI 440.8 provides a speci¿FDWLRQ IRU XQLGLUHFWLRQDO FDUERQ DQG JODVV )53 PDWHULDOV
made using the wet layup process.
FRP composite systems that have not been fully tested
should not be considered for use. Mechanical properties of
FRP systems should be determined from tests on laminates
PDQXIDFWXUHGLQDSURFHVVUHSUHVHQWDWLYHRIWKHLU¿HOGLQVWDOlation. Mechanical properties should be tested in general
conformance with the procedures listed in Appendix B. Modi¿FDWLRQVRIVWDQGDUGWHVWLQJSURFHGXUHVPD\EHSHUPLWWHGWR
HPXODWH¿HOGDVVHPEOLHV
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American Concrete Institute – Copyrighted © Material – www.concrete.org
MCPOL Licensed to: McMaster University Library
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
7KH VSHFL¿HG PDWHULDOTXDOL¿FDWLRQ SURJUDPV VKRXOG
UHTXLUH VXI¿FLHQW ODERUDWRU\ WHVWLQJ WR PHDVXUH WKH UHSHDWability and reliability of critical properties. Testing of
multiple batches of FRP materials is recommended. Independent structural testing can be used to evaluate a system’s
SHUIRUPDQFHIRUWKHVSHFL¿FDSSOLFDWLRQ
CHAPTER 5—SHIPPING, STORAGE, AND
HANDLING
5.1—Shipping
)LEHUUHLQIRUFHGSRO\PHU )53 V\VWHPFRQVWLWXHQWPDWHrials should be packaged and shipped in a manner that
conforms to all applicable federal and state packaging and
shipping codes and regulations. Packaging, labeling, and
shipping for thermosetting resin materials are controlled by
&)5.
5.2—Storage
5.2.1 Storage conditions—To preserve the properties and
maintain safety in the storage of FRP system constituent
materials, the materials should be stored in accordance with
the manufacturer’s recommendations. Certain constituent
materials, such as reactive curing agents, hardeners, initiators, catalysts, and cleaning solvents, have safety-related
UHTXLUHPHQWV DQG VKRXOG EH VWRUHG LQ D PDQQHU DV UHFRPmended by the manufacturer and OSHA. Catalysts and initiDWRUV XVXDOO\SHUR[LGHV VKRXOGEHVWRUHGVHSDUDWHO\
5.2.2 Shelf life—The properties of the uncured resin
components can change with time, temperature, or humidity.
Such conditions can affect the reactivity of the mixed system
and the uncured and cured properties. The manufacturer sets
a recommended shelf life within which the properties of the
resin-based materials should continue to meet or exceed
stated performance criteria. Any component material that
has exceeded its shelf life, has deteriorated, or has been
contaminated should not be used. FRP materials deemed
XQXVDEOHVKRXOGEHGLVSRVHGRILQDPDQQHUVSHFL¿HGE\WKH
manufacturer and acceptable to state and federal environmental control regulations.
5.3—Handling
5.3.1 Safety data sheet—6DIHW\ GDWD VKHHWV 6'6V IRU
all FRP-constituent materials and components should be
obtained from the manufacturers, and should be accessible
at the job site.
5.3.2 Information sources—Detailed information on the
handling and potential hazards of FRP-constituent materials can be found in company literature and guides, OSHA
guidelines, and other government informational documents.
5.3.3 General handling hazards—Thermosetting resins
describe a generic family of products that includes unsaturated polyesters, vinyl esters, epoxy, and polyurethane resins.
The materials used with them are generally described as
hardeners, curing agents, peroxide initiators, isocyanates,
¿OOHUV DQG ÀH[LELOL]HUV 7KHUH DUH SUHFDXWLRQV WKDW VKRXOG
be observed when handling thermosetting resins and their
component materials. Some general hazards that may be
15
encountered when handling thermosetting resins are listed as
follows:
D 6NLQLUULWDWLRQVXFKDVEXUQVUDVKHVDQGLWFKLQJ
E 6NLQVHQVLWL]DWLRQZKLFKLVDQDOOHUJLFUHDFWLRQVLPLODUWR
that caused by poison ivy, building insulation, or other allergens
F %UHDWKLQJ RUJDQLF YDSRUV IURP FOHDQLQJ VROYHQWV
monomers, and dilutents
G :LWKDVXI¿FLHQWFRQFHQWUDWLRQLQDLUH[SORVLRQRU¿UH
RIÀDPPDEOHPDWHULDOVZKHQH[SRVHGWRKHDWÀDPHVSLORW
lights, sparks, static electricity, cigarettes, or other sources
of ignition
H ([RWKHUPLFUHDFWLRQVRIPL[WXUHVRIPDWHULDOVFDXVLQJ
¿UHVRUSHUVRQDOLQMXU\
I 1XLVDQFH GXVW FDXVHG E\ JULQGLQJ RU KDQGOLQJ RI WKH
FXUHG )53 PDWHULDOV PDQXIDFWXUHU¶V OLWHUDWXUH VKRXOG EH
FRQVXOWHGIRUVSHFL¿FKD]DUGV
The complexity of thermosetting resins and associated
materials makes it essential that labels and the SDS are read
and understood by those working with these products. CFR
16 Part 1500 regulates the labeling of hazardous substances
and includes thermosetting-resin materials. ANSI Z400.1/
=SURYLGHVIXUWKHUJXLGDQFHUHJDUGLQJFODVVL¿FDtion and precautions.
5.3.4 Personnel safe handling and clothing—Disposable
VXLWV DQG JORYHV DUH VXLWDEOH IRU KDQGOLQJ ¿EHU DQG UHVLQ
materials. Disposable rubber or plastic gloves are recommended and should be discarded after each use. Gloves
should be resistant to resins and solvents. Safety glasses or
goggles should be used when handling resin components
and solvents. Respiratory protection, such as dust masks or
UHVSLUDWRUVVKRXOGEHXVHGZKHQ¿EHUÀ\GXVWRURUJDQLF
vapors are present, or during mixing and placing of resins if
UHTXLUHGE\WKH)53V\VWHPPDQXIDFWXUHU
5.3.5 Workplace safe handling—The workplace should
be well ventilated. Surfaces should be covered as needed
to protect against contamination and resin spills. Each
FRP system constituent material has different handling
DQG VWRUDJH UHTXLUHPHQWV WR SUHYHQW GDPDJH 7KH PDWHrial manufacturer should be consulted for guidance. Some
resin systems are potentially dangerous during mixing of
the components. The manufacturer’s literature should be
consulted for proper mixing procedures, and the SDS for
VSHFL¿F KDQGOLQJ KD]DUGV $PELHQW FXUH UHVLQ IRUPXODtions produce heat when curing, which in turn accelerates
WKHUHDFWLRQ8QFRQWUROOHGUHDFWLRQVLQFOXGLQJIXPLQJ¿UH
or violent boiling, may occur in containers holding a mixed
PDVVRIUHVLQWKHUHIRUHFRQWDLQHUVVKRXOGEHPRQLWRUHG
5.3.6 Cleanup and disposal—Cleanup can involve use
RI ÀDPPDEOH VROYHQWV DQG DSSURSULDWH SUHFDXWLRQV VKRXOG
be observed. Cleanup solvents are available that do not
SUHVHQW ÀDPPDELOLW\ FRQFHUQV$OO ZDVWH PDWHULDOV VKRXOG
be contained and disposed of as prescribed by the prevailing
environmental authority.
CHAPTER 6—INSTALLATION
3URFHGXUHVIRULQVWDOOLQJ¿EHUUHLQIRUFHGSRO\PHU )53 systems have been developed by the system manufacturers
and often differ between systems. In addition, installation
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American Concrete Institute – Copyrighted © Material – www.concrete.org
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16
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
procedures can vary within a system, depending on the type
and condition of the structure. This chapter presents general
guidelines for the installation of FRP systems. Contractors trained in accordance with the installation procedures
developed by the system manufacturer should install FRP
systems. Deviations from the procedures developed by the
FRP system manufacturer should not be allowed without
consulting with the manufacturer.
6.1—Contractor competency
The FRP system installation contractor should demonstrate
competency for surface preparation and application of the FRP
system to be installed. Contractor competency can be demonstrated by providing evidence of training and documentation
of related work previously completed by the contractor or by
actual surface preparation and installation of the FRP system
on portions of the structure. The FRP system manufacturer
or its authorized agent should train the contractor’s application personnel in the installation procedures of its system and
ensure they are competent to install the system.
6.2—Temperature, humidity, and moisture
considerations
Temperature, relative humidity, and surface moisture at
the time of installation can affect the performance of the
FRP system. Conditions to be observed before and during
installation include surface temperature and moisture condition of the concrete, air temperature, relative humidity, and
corresponding dew point.
Primers, saturating resins, and adhesives should generally
not be applied to cold or frozen surfaces. When the surface
temperature of the concrete surface falls below a minimum
OHYHODVVSHFL¿HGE\WKH)53V\VWHPPDQXIDFWXUHULPSURSHU
VDWXUDWLRQ RI WKH ¿EHUV DQG LPSURSHU FXULQJ RI WKH UHVLQ
constituent materials can occur, compromising the integrity
of the FRP system. An auxiliary heat source can be used to
raise the ambient and surface temperature during installation
and maintain proper temperatures during curing. The heat
source should be clean and not contaminate the surface or
the uncured FRP system.
Resins and adhesives should generally not be applied to
damp or wet surfaces unless they have been formulated for
such applications. FRP systems should not be applied to
concrete surfaces that are subject to moisture vapor transmission. The transmission of moisture vapor from a concrete
surface through the uncured resin materials typically appears
as surface bubbles and can compromise the bond between
the FRP system and the substrate.
6.3—Equipment
6RPH )53 V\VWHPV KDYH XQLTXH RIWHQ V\VWHPVSHFL¿F
HTXLSPHQW GHVLJQHG VSHFL¿FDOO\ IRU WKHLU DSSOLFDWLRQ 7KLV
HTXLSPHQW FDQ LQFOXGH UHVLQ LPSUHJQDWRUV VSUD\HUV OLIWLQJ
SRVLWLRQLQJ GHYLFHV DQG ZLQGLQJ PDFKLQHV $OO HTXLSment should be clean and in good operating condition. The
contractor should have personnel trained in the operation of
DOOHTXLSPHQW3HUVRQDOSURWHFWLYHHTXLSPHQWVXFKDVJORYHV
masks, eye guards, and coveralls, should be chosen and worn
IRU HDFK HPSOR\HH¶V IXQFWLRQ $OO VXSSOLHV DQG HTXLSPHQW
VKRXOGEHDYDLODEOHLQVXI¿FLHQWTXDQWLWLHVWRDOORZFRQWLQXLW\
LQWKHLQVWDOODWLRQSURMHFWDQGTXDOLW\DVVXUDQFH
6.4—Substrate repair and surface preparation
The behavior of concrete members strengthened or retro¿WWHG ZLWK )53 V\VWHPV LV KLJKO\ GHSHQGHQW RQ D VRXQG
FRQFUHWH VXEVWUDWH DQG SURSHU SUHSDUDWLRQ DQG SUR¿OLQJ RI
the concrete surface. An improperly prepared surface can
result in debonding or delamination of the FRP system
before achieving the design load transfer. The general
guidelines presented in this chapter should be applicable to
DOOH[WHUQDOO\ERQGHG)53V\VWHPV6SHFL¿FJXLGHOLQHVIRU
a particular FRP system should be obtained from the FRP
system manufacturer.
6.4.1 Substrate repair—All problems associated with the
condition of the original concrete and the concrete substrate
that can compromise the integrity of the FRP system should
be addressed before surface preparation begins. ACI 546R
and ICRI 310.2R detail methods for the repair and surface
preparation of concrete. All concrete repairs should meet the
UHTXLUHPHQWVRIWKHGHVLJQGUDZLQJVDQGSURMHFWVSHFL¿FDtions. The FRP system manufacturer should be consulted on
the compatibility of the FRP system with materials used for
repairing the substrate.
6.4.1.1 Corrosion-related deterioration—Externally
bonded FRP systems should not be applied to concrete
substrates suspected of containing actively corroding reinforcing steel. The expansive forces associated with the corroVLRQSURFHVVDUHGLI¿FXOWWRGHWHUPLQHDQGFRXOGFRPSURPLVH
the structural integrity of the externally applied FRP system.
7KHFDXVH V RIWKHFRUURVLRQVKRXOGEHDGGUHVVHGDQGWKH
corrosion-related deterioration should be repaired before the
application of any externally bonded FRP system.
6.4.1.2 Injection of cracks—Cracks that are 0.010 in.
PP DQG ZLGHU FDQ DIIHFW WKH SHUIRUPDQFH RI WKH
H[WHUQDOO\ ERQGHG )53 V\VWHPV &RQVHTXHQWO\ FUDFNV
ZLGHU WKDQ LQ PP VKRXOG EH SUHVVXUHLQMHFWHG
with epoxy before FRP installation in accordance with ACI
224.1R. Smaller cracks exposed to aggressive environments
PD\UHTXLUHUHVLQLQMHFWLRQRUVHDOLQJWRSUHYHQWFRUURVLRQRI
existing steel reinforcement. Crack-width criteria for various
exposure conditions are given in ACI 224.1R.
6.4.2 Surface preparation—6XUIDFH SUHSDUDWLRQ UHTXLUHments should be based on the intended application of the FRP
system. Applications can be categorized as bond-critical or
FRQWDFWFULWLFDO%RQGFULWLFDODSSOLFDWLRQVVXFKDVÀH[XUDO
or shear strengthening of beams, slabs, columns, or walls,
UHTXLUHDQDGKHVLYHERQGEHWZHHQWKH)53V\VWHPDQGWKH
FRQFUHWH&RQWDFWFULWLFDODSSOLFDWLRQVVXFKDVFRQ¿QHPHQW
RIFROXPQVRQO\UHTXLUHLQWLPDWHFRQWDFWEHWZHHQWKH)53
system and the concrete. Contact-critical applications do
QRWUHTXLUHDQDGKHVLYHERQGEHWZHHQWKH)53V\VWHPDQG
the concrete substrate, although one is typically provided to
facilitate installation.
6.4.2.1 Bond-critical applications—Surface preparation for bond-critical applications should be in accordance
with recommendations of ACI 546R and ICRI 310.2R. The
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
concrete or repaired surfaces to which the FRP system is to
be applied should be freshly exposed and free of loose or
XQVRXQG PDWHULDOV :KHUH ¿EHUV ZUDS DURXQG FRUQHUV WKH
FRUQHUV VKRXOG EH URXQGHG WR D PLQLPXP LQ PP radius to reduce stress concentrations in the FRP system and
voids between the FRP system and the concrete. Roughened corners should be smoothed with putty. Obstructions,
inside corners, concave surfaces, and embedded objects can
affect the performance of the FRP system and should be
addressed. Obstructions and embedded objects may need to
be removed before installing the FRP system. Inside corners
DQGFRQFDYHVXUIDFHVPD\UHTXLUHVSHFLDOGHWDLOLQJWRHQVXUH
that the bond of the FRP system to the substrate is maintained. Surface preparation can be accomplished using abraVLYHRUZDWHUEODVWLQJWHFKQLTXHV$OOODLWDQFHGXVWGLUWRLO
curing compound, existing coatings, and any other matter
that could interfere with the bond of the FRP system to the
concrete should be removed. Bug holes and other small
surface voids should be completely exposed during surface
SUR¿OLQJ $IWHU WKH SUR¿OLQJ RSHUDWLRQV DUH FRPSOHWH WKH
surface should be cleaned and protected before FRP installation so that no materials that can interfere with bond are
redeposited on the surface.
The concrete surface should be prepared to a surface
SUR¿OH QRW OHVV WKDQ &63 DV GH¿QHG E\ ICRI 310.2R or
to the tolerances recommended by the FRP system manufacturer. Localized out-of-plane variations, including form
OLQHV VKRXOG QRW H[FHHG LQ PP RU WKH WROHUDQFHV
recommended by the FRP system manufacturer. Localized
out-of-plane variations can be removed by grinding, before
abrasive or water blasting, or can be smoothed over using
resin-based putty if the variations are very small. Bug holes
DQGYRLGVVKRXOGEH¿OOHGZLWKUHVLQEDVHGSXWW\
All surfaces to receive the strengthening system should
be as dry as recommended by the FRP system manufacturer.
Water in the pores can inhibit resin penetration and reduce
mechanical interlock. Moisture content should be evaluated
LQDFFRUGDQFHZLWKWKHUHTXLUHPHQWVRIACI 503.4.
6.4.2.2 Contact-critical applications—In applications
LQYROYLQJ FRQ¿QHPHQW RI VWUXFWXUDO FRQFUHWH PHPEHUV
surface preparation should promote continuous intimate
contact between the concrete surface and the FRP system.
6XUIDFHV WR EH ZUDSSHG VKRXOG DW D PLQLPXP EH ÀDW RU
convex to promote proper loading of the FRP system. Large
voids in the surface should be patched with a repair material
compatible with the existing concrete. Materials with low
compressive strength and elastic modulus, such as plaster,
can reduce the effectiveness of the FRP system and should
be removed.
6.4.3 Near-surface mounted (NSM) systems—NSM systems
are typically installed in grooves cut onto the concrete surface.
The existing steel reinforcement should not be damaged while
cutting the groove. The soundness of the concrete surface
should be checked before installing the bar. The inside faces
RIWKHJURRYHVKRXOGEHFOHDQHGWRHQVXUHDGHTXDWHERQGZLWK
concrete. The resulting groove should be free of laitance or
other compounds that may interfere with bond. The moisture
content of the parent concrete should be controlled to suit the
17
bonding properties of the adhesive. The grooves should be
FRPSOHWHO\¿OOHGZLWKWKHDGKHVLYH7KHDGKHVLYHVKRXOGEH
VSHFL¿HGE\WKH160V\VWHPPDQXIDFWXUHU
6.5—Mixing of resins
Mixing of resins should be done in accordance with
the FRP system manufacturer’s recommended procedure.
All resin components should be at the proper temperature
and mixed in the correct ratio until there is a uniform and
complete mixing of components. Resin components are
often contrasting colors, so full mixing is achieved when
color streaks are eliminated. Resins should be mixed for the
prescribed mixing time and visually inspected for uniformity of color. The material manufacturer should supply
recommended batch sizes, mixture ratios, mixing methods,
and mixing times.
0L[LQJHTXLSPHQWFDQLQFOXGHVPDOOHOHFWULFDOO\SRZHUHG
mixing blades or specialty units, or resins can be mixed by
KDQGVWLUULQJLIQHHGHG5HVLQPL[LQJVKRXOGEHLQTXDQWLWLHV
VXI¿FLHQWO\VPDOOWRHQVXUHWKDWDOOPL[HGUHVLQFDQEHXVHG
within the resin’s pot life. Mixed resin that exceeds its pot
life should not be used because the viscosity will continue
to increase and will adversely affect the resin’s ability to
SHQHWUDWHWKHVXUIDFHRUVDWXUDWHWKH¿EHUVKHHW
6.6—Application of FRP systems
Fumes can accompany the application of some FRP resins.
FRP systems should be selected with consideration for their
impact on the environment, including emission of volatile
organic compounds and toxicology.
6.6.1 Primer and putty²:KHUH UHTXLUHG SULPHU VKRXOG
be applied to all areas on the concrete surface where the FRP
system is to be placed. The primer should be placed uniformly
RQWKHSUHSDUHGVXUIDFHDWWKHPDQXIDFWXUHU¶VVSHFL¿HGUDWH
of coverage. The applied primer should be protected from
dust, moisture, and other contaminants before applying the
FRP system.
Putty should be used in an appropriate thickness and
VHTXHQFHZLWKWKHSULPHUDVUHFRPPHQGHGE\WKH)53PDQXfacturer. The system-compatible putty, which is typically a
WKLFNHQHGUHVLQEDVHGSDVWHVKRXOGEHXVHGRQO\WR¿OOYRLGV
and smooth surface discontinuities before the application of
other materials. Rough edges or trowel lines of cured putty
should be ground smooth before continuing the installation.
Before applying the saturating resin or adhesive, the
SULPHUDQGSXWW\VKRXOGEHDOORZHGWRFXUHDVVSHFL¿HGE\
the FRP system manufacturer. If the putty and primer are
IXOO\FXUHGDGGLWLRQDOVXUIDFHSUHSDUDWLRQPD\EHUHTXLUHG
before the application of the saturating resin or adhesive.
6XUIDFH SUHSDUDWLRQ UHTXLUHPHQWV VKRXOG EH REWDLQHG IURP
the FRP system manufacturer.
6.6.2 Wet layup systems—Wet layup FRP systems are
W\SLFDOO\LQVWDOOHGE\KDQGXVLQJGU\¿EHUVKHHWVDQGDVDWXrating resin, typically per the manufacturer’s recommendations. The saturating resin should be applied uniformly to
all prepared surfaces where the system is to be placed. The
¿EHUV FDQ DOVR EH LPSUHJQDWHG LQ D VHSDUDWH SURFHVV XVLQJ
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18
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
a resin-impregnating machine before placement on the
concrete surface.
7KH UHLQIRUFLQJ ¿EHUV VKRXOG EH JHQWO\ SUHVVHG LQWR WKH
uncured saturating resin in a manner recommended by the
FRP system manufacturer. Entrapped air between layers
VKRXOGEHUHOHDVHGRUUROOHGRXWEHIRUHWKHUHVLQVHWV6XI¿cient saturating resin should be applied to achieve full satuUDWLRQRIWKH¿EHUV
6XFFHVVLYH OD\HUV RI VDWXUDWLQJ UHVLQ DQG ¿EHU PDWHULDOV
should be placed before the complete cure of the previous
layer of resin. If previous layers are cured, interlayer surface
preparation, such as light sanding or solvent application as
UHFRPPHQGHGE\WKHV\VWHPPDQXIDFWXUHUPD\EHUHTXLUHG
6.6.3 Machine-applied systems—Machine-applied systems
FDQXVHUHVLQSUHLPSUHJQDWHGWRZVRUGU\¿EHUWRZV3UHSUHJ
tows are impregnated with saturating resin off site and delivHUHGWRWKHMREVLWHDVVSRROVRISUHSUHJWRZPDWHULDO'U\¿EHUV
are impregnated at the jobsite during the winding process.
Wrapping machines are primarily used for the automated
wrapping of concrete columns. The tows can be wound either
KRUL]RQWDOO\RUDWDVSHFL¿HGDQJOH7KHZUDSSLQJPDFKLQHLV
placed around the column and automatically wraps the tow
material around the perimeter of the column while moving
up and down the column.
After wrapping, prepreg systems should be cured at
an elevated temperature. Usually, a heat source is placed
around the column for a predetermined temperature and time
schedule in accordance with the manufacturer’s recommendations. Temperatures are controlled to ensure consistent
TXDOLW\7KHUHVXOWLQJ)53MDFNHWVGRQRWKDYHDQ\VHDPVRU
welds because the tows are continuous. In all the previous
application steps, the FRP system manufacturer’s recommendations should be followed.
6.6.4 Precured systems—Precured systems include shells,
strips, and open grid forms that are typically installed with
an adhesive. Adhesives should be uniformly applied to the
prepared surfaces where precured systems are to be placed,
H[FHSW LQ FHUWDLQ LQVWDQFHV RI FRQFUHWH FRQ¿QHPHQW ZKHUH
adhesion of the FRP system to the concrete substrate may
QRWEHUHTXLUHG
Precured laminate surfaces to be bonded should be clean
and prepared in accordance with the manufacturer’s recommendation. The precured sheets or curved shells should
be placed on or into the wet adhesive in a manner recommended by the FRP manufacturer. Entrapped air between
layers should be released or rolled out before the adhesive
sets. The adhesive should be applied at a rate recommended
by the FRP manufacturer.
6.6.5 Near-surface mounted (NSM) systems—NSM
systems consist of installing rectangular or circular FRP
bars in grooves cut onto the concrete surface and bonded in
place using an adhesive. Grooves should be dimensioned to
HQVXUH DGHTXDWH DGKHVLYH DURXQG WKH EDUV 7\SLFDO JURRYH
dimensions for NSM FRP rods and plates are found in
14.3. NSM systems can be used on the topside of structural
members and for overhead applications. Adhesive type and
LQVWDOODWLRQPHWKRGVKRXOGEHVSHFL¿HGE\WKH160V\VWHP
manufacturer.
6.6.6 Protective coatings—Coatings should be compatible
with the FRP strengthening system and applied in accordance with the manufacturer’s recommendations. Typically,
the use of solvents to clean the FRP surface before installing
coatings is not recommended due to the deleterious effects
that solvents can have on the polymer resins. The FRP system
manufacturer should approve any use of solvent wipe preparation of FRP surfaces before the application of protective
coatings. The coatings should be periodically inspected and
maintenance should be provided to ensure the effectiveness
of the coatings.
6.7—Alignment of FRP materials
7KH)53SO\RULHQWDWLRQDQGSO\VWDFNLQJVHTXHQFHVKRXOG
EHVSHFL¿HG6PDOOYDULDWLRQVLQDQJOHDVOLWWOHDVGHJUHHV
IURPWKHLQWHQGHGGLUHFWLRQRI¿EHUDOLJQPHQWFDQFDXVHD
substantial reduction in strength and modulus. Deviations
in ply orientation should only be made if approved by the
licensed design professional.
Sheet and fabric materials should be handled in a manner
WR PDLQWDLQ WKH ¿EHU VWUDLJKWQHVV DQG RULHQWDWLRQ )DEULF
kinks, folds, or other forms of waviness should be reported
to the licensed design professional.
6.8—Multiple plies and lap splices
Multiple plies can be used, provided that all plies are fully
impregnated with the resin system, the resin shear strength
LVVXI¿FLHQWWRWUDQVIHUWKHVKHDULQJORDGEHWZHHQSOLHVDQG
the bond strength between the concrete and FRP system is
VXI¿FLHQW)RUORQJVSDQVPXOWLSOHOHQJWKVRI¿EHUPDWHULDO
or precured stock can be used to continuously transfer the
ORDGE\SURYLGLQJDGHTXDWHODSVSOLFHV/DSVSOLFHVVKRXOG
be staggered unless noted otherwise by the licensed design
professional. Lap splice details, including lap length, should
be based on testing and installed in accordance with the
manufacturer’s recommendations. Due to the characteristics
of some FRP systems, multiple plies and lap splices are not
DOZD\VSRVVLEOH6SHFL¿FJXLGHOLQHVRQODSVSOLFHVDUHJLYHQ
in Chapter 14.
6.9—Curing of resins
Curing of resins is a time-temperature-dependent phenomenon. Ambient-cure resins can take several days to reach
IXOO FXUH 7HPSHUDWXUH H[WUHPHV RU ÀXFWXDWLRQV FDQ UHWDUG
or accelerate the resin curing time. The FRP system manuIDFWXUHU PD\ RIIHU VHYHUDO SUHTXDOL¿HG JUDGHV RI UHVLQ WR
accommodate these situations.
(OHYDWHG FXUH V\VWHPV UHTXLUH WKH UHVLQ WR EH KHDWHG WR
DVSHFL¿FWHPSHUDWXUHIRUDVSHFL¿HGWLPH9DULRXVFRPELQDWLRQVRIWLPHDQGWHPSHUDWXUHZLWKLQDGH¿QHGHQYHORSH
should provide full cure of the system.
All resins should be cured according to the manufacWXUHU¶VUHFRPPHQGDWLRQ)LHOGPRGL¿FDWLRQRIUHVLQFKHPistry should not be permitted. Cure of installed plies should
EH PRQLWRUHG EHIRUH SODFLQJ VXEVHTXHQW SOLHV ,QVWDOODWLRQ
of successive layers should be halted if there is a curing
anomaly.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
6.10—Temporary protection
$GYHUVHWHPSHUDWXUHVGLUHFWFRQWDFWE\UDLQGXVWRUGLUW
H[FHVVLYHVXQOLJKWKLJKKXPLGLW\RUYDQGDOLVPFDQGDPDJH
an FRP system during installation and cause improper cure
of the resins. Temporary protection, such as tents and plastic
VFUHHQV PD\ EH UHTXLUHG GXULQJ LQVWDOODWLRQ DQG XQWLO WKH
UHVLQVKDYHFXUHG,IWHPSRUDU\VKRULQJLVUHTXLUHGWKH)53
system should be fully cured before removing the shoring
and allowing the structural member to carry the design
loads. In the event of suspected damage to the FRP system
during installation, the licensed design professional should
EHQRWL¿HGDQGWKH)53V\VWHPPDQXIDFWXUHUFRQVXOWHG
CHAPTER 7—INSPECTION, EVALUATION, AND
ACCEPTANCE
4XDOLW\DVVXUDQFHDQGTXDOLW\FRQWURO 4$4& SURJUDPV
DQG FULWHULD DUH WR EH PDLQWDLQHG E\ WKH ¿EHUUHLQIRUFHG
SRO\PHU )53 V\VWHP PDQXIDFWXUHUV WKH LQVWDOODWLRQ
FRQWUDFWRUV DQG RWKHUV DVVRFLDWHG ZLWK WKH SURMHFW 4$
is typically an owner or a licensed professional activity
ZKHUHDV 4& LV D FRQWUDFWRU RU VXSSOLHU DFWLYLW\ 7KH 4&
program should be comprehensive and cover all aspects
of the strengthening project, and should be detailed in the
SURMHFWVSHFL¿FDWLRQVE\DOLFHQVHGSURIHVVLRQDO7KHGHJUHH
RI 4& DQG WKH VFRSH RI WHVWLQJ LQVSHFWLRQ DQG UHFRUG
keeping depends on the size and complexity of the project.
4XDOLW\DVVXUDQFHLVDFKLHYHGWKURXJKDVHWRILQVSHFWLRQV
and applicable tests to document the acceptability of the
LQVWDOODWLRQ3URMHFWVSHFL¿FDWLRQVVKRXOGLQFOXGHDUHTXLUHPHQWWRSURYLGHD4$SODQIRUWKHLQVWDOODWLRQDQGFXULQJRI
all FRP materials. The plan should include personnel safety
issues, application and inspection of the FRP system, location and placement of splices, curing provisions, means to
HQVXUHGU\VXUIDFHV4$VDPSOHVFOHDQXSDQGWKHVXJJHVWHG
submittals listed in 15.3.
7.1—Inspection
FRP systems and all associated work should be inspected
DVUHTXLUHGE\WKHDSSOLFDEOHFRGHV,QWKHDEVHQFHRIVXFK
UHTXLUHPHQWV WKH LQVSHFWLRQ VKRXOG EH FRQGXFWHG E\ RU
under the supervision of a licensed design professional or
D TXDOL¿HG LQVSHFWRU ,QVSHFWRUV VKRXOG EH NQRZOHGJHDEOH
of FRP systems and be trained in the installation of FRP
V\VWHPV7KHTXDOL¿HGLQVSHFWRUVKRXOGUHTXLUHFRPSOLDQFH
ZLWKWKHGHVLJQGUDZLQJVDQGSURMHFWVSHFL¿FDWLRQV'XULQJ
the installation of the FRP system, daily inspection should
be conducted and should include:
D 'DWHDQGWLPHRILQVWDOODWLRQ
E $PELHQW WHPSHUDWXUH UHODWLYH KXPLGLW\ DQG JHQHUDO
weather observations
F 6XUIDFHWHPSHUDWXUHRIFRQFUHWH
G 6XUIDFHPRLVWXUH
H 6XUIDFHSUHSDUDWLRQPHWKRGVDQGUHVXOWLQJSUR¿OHXVLQJ
WKH,&5,VXUIDFHSUR¿OHFKLSV
I 4XDOLWDWLYHGHVFULSWLRQRIVXUIDFHFOHDQOLQHVV
J 7\SHRIDX[LOLDU\KHDWVRXUFHLIDSSOLFDEOH
K :LGWKVRIFUDFNVQRWLQMHFWHGZLWKHSR[\
19
L )LEHURUSUHFXUHGODPLQDWHEDWFKQXPEHU V DQGDSSUR[imate location in structure
M %DWFKQXPEHUVPL[WXUHUDWLRVPL[LQJWLPHDQGTXDOLtative descriptions of the appearance of all mixed resins
including primers, putties, saturants, adhesives, and coatings
mixed for the day
N 2EVHUYDWLRQVRISURJUHVVRIFXUHRIUHVLQV
O &RQIRUPDQFHZLWKLQVWDOODWLRQSURFHGXUHV
P 3XOORIIWHVWUHVXOWVERQGVWUHQJWKIDLOXUHPRGHDQG
location
Q )53 SURSHUWLHV IURP WHVWV RI ¿HOG VDPSOH SDQHOV RU
ZLWQHVVSDQHOVLIUHTXLUHG
R /RFDWLRQDQGVL]HRIDQ\GHODPLQDWLRQVRUDLUYRLGV
S *HQHUDOSURJUHVVRIZRUN
The inspector should provide the licensed design professional or owner with the inspection records and witness
panels. Records and witness panels should be retained for
DPLQLPXPRI\HDUVRUDSHULRGVSHFL¿HGE\WKHOLFHQVHG
design professional. The installation contractor should retain
sample cups of mixed resin and maintain a record of the
placement of each batch.
7.2—Evaluation and acceptance
FRP systems should be evaluated and accepted or rejected
based on conformance or nonconformance with the design
GUDZLQJV DQG VSHFL¿FDWLRQV )53 V\VWHP PDWHULDO SURSHUWLHV LQVWDOODWLRQ ZLWKLQ VSHFL¿HG SODFHPHQW WROHUDQFHV
presence of delaminations, cure of resins, and adhesion to
substrate should be included in the evaluation. Placement
WROHUDQFHVLQFOXGLQJ¿EHURULHQWDWLRQFXUHGWKLFNQHVVSO\
orientation, width and spacing, corner radii, and lap splice
lengths, should be evaluated.
Witness panel and pull-off tests are used to evaluate the
installed FRP system. In-place load testing can also be used
WR FRQ¿UP WKH LQVWDOOHG EHKDYLRU RI WKH )53VWUHQJWKHQHG
PHPEHU 1DQQLDQG*ROG 7.2.1 Materials—Before starting the project, the FRP
V\VWHPPDQXIDFWXUHUVKRXOGVXEPLWFHUWL¿FDWLRQRIVSHFL¿HG
PDWHULDOSURSHUWLHVDQGLGHQWL¿FDWLRQRIDOOPDWHULDOVWREH
used. Additional material testing can be conducted if deemed
necessary based on the size and complexity of the project
or other factors. Evaluation of delivered FRP materials can
include tests for tensile strength, Tg, gel time, pot life, and
adhesive shear strength. These tests are usually performed
on material samples sent to a laboratory according to the
4&WHVWSODQ7HVWVIRUSRWOLIHRIUHVLQVDQGFXULQJKDUGQHVV
are usually conducted on site. Materials that do not meet the
PLQLPXPUHTXLUHPHQWVDVVSHFL¿HGE\WKHOLFHQVHGGHVLJQ
professional should be rejected.
Witness panels can be used to evaluate the tensile strength
and modulus, lap splice strength, hardness, and Tg of the FRP
system installed and cured on site using installation procedures similar to those used to install and cure the FRP system.
'XULQJLQVWDOODWLRQÀDWSDQHOVRISUHGHWHUPLQHGGLPHQVLRQV
and thickness can be fabricated on site according to a predetermined sampling plan. After curing on site, the panels can
then be sent to a laboratory for testing. Witness panels can be
retained or submitted to an approved laboratory in a timely
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20
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
manner for testing of strength and Tg. Strength and elastic
modulus of FRP materials can be determined in accordance
ZLWK WKH UHTXLUHPHQWV RI$670 ''0, D7205/
D7205M, or D7565/D7565M. The properties to be evaluDWHG E\ WHVWLQJ VKRXOG EH VSHFL¿HG 7KH OLFHQVHG GHVLJQ
SURIHVVLRQDOPD\ZDLYHRUDOWHUWKHIUHTXHQF\RIWHVWLQJ
Some FRP systems, including precured and machinewound systems, do not lend themselves to the fabrication
RIVPDOOÀDWZLWQHVVSDQHOV)RUWKHVHFDVHVWKHOLFHQVHG
GHVLJQSURIHVVLRQDOFDQPRGLI\WKHUHTXLUHPHQWVWRLQFOXGH
test panels or samples provided by the manufacturer. During
installation, sample cups of mixed resin should be prepared
according to a predetermined sampling plan and retained for
WHVWLQJWRGHWHUPLQHWKHGHJUHHRIFXUH 7.2.2 Fiber orientation—Fiber or precured-laminate
orientation should be evaluated by visual inspection. Fiber
ZDYLQHVV²D ORFDOL]HG DSSHDUDQFH RI ¿EHUV WKDW GHYLDWH
IURPWKHJHQHUDOVWUDLJKW¿EHUOLQHLQWKHIRUPRINLQNVRU
waves—should be evaluated for wet layup systems. Fiber
or precured laminate misalignment of more than 5 degrees
IURPWKDWVSHFL¿HGRQWKHGHVLJQGUDZLQJV DSSUR[LPDWHO\
LQIW>PPP@ VKRXOGEHUHSRUWHGWRWKHOLFHQVHGGHVLJQ
professional for evaluation and acceptance.
7.2.3 Delaminations—The cured FRP system should be
evaluated for delaminations or air voids between multiple
plies or between the FRP system and the concrete. Inspection methods should be capable of detecting delaminations
of 2 in.2 PP2 RU JUHDWHU 0HWKRGV VXFK DV DFRXVWLF
VRXQGLQJ KDPPHU VRXQGLQJ XOWUDVRQLFV DQG WKHUPRJraphy can be used to detect delaminations.
The effect of delaminations or other anomalies on the
structural integrity and durability of the FRP system should
EHHYDOXDWHG'HODPLQDWLRQVL]HORFDWLRQDQGTXDQWLW\UHODtive to the overall application area should be considered in
the evaluation.
General acceptance guidelines for wet layup systems are:
D 6PDOOGHODPLQDWLRQVOHVVWKDQLQ2 PP2 HDFK
are permissible as long as the delaminated area is less than 5
percent of the total laminate area and there are no more than
10 such delaminations per 10 ft2 P2 E /DUJHGHODPLQDWLRQVJUHDWHUWKDQLQ2 PP2 can affect the performance of the installed FRP and should
be repaired by selectively cutting away the affected sheet
DQGDSSO\LQJDQRYHUODSSLQJVKHHWSDWFKRIHTXLYDOHQWSOLHV
F 'HODPLQDWLRQVOHVVWKDQLQ2 PP2 PD\EH
repaired by resin injection or ply replacement, depending on
the size and number of delaminations and their locations.
For precured FRP systems, each delamination should
be evaluated and repaired in accordance with the licensed
design professional’s direction. Upon completion of the
repairs, the laminate should be reinspected to verify that the
repair was properly accomplished.
7.2.4 Cure of resins—The relative cure of FRP systems
can be evaluated by laboratory testing of witness panels or
resin cup samples using ASTM D3418. The relative cure of
the resin can also be evaluated on the project site by physical
observation of resin tackiness and hardness of work surfaces
or hardness of retained resin samples. The FRP system
PDQXIDFWXUHUVKRXOGEHFRQVXOWHGWRGHWHUPLQHWKHVSHFL¿F
UHVLQFXUHYHUL¿FDWLRQUHTXLUHPHQWV)RUSUHFXUHGV\VWHPV
adhesive hardness measurements should be made in accordance with the manufacturer’s recommendation.
7.2.5 Adhesion strength—For bond-critical applications, tension adhesion testing of cored samples should be
FRQGXFWHG LQ DFFRUGDQFH ZLWK WKH UHTXLUHPHQWV RIASTM
D7522/D7522. Such tests cannot be performed when
XVLQJQHDUVXUIDFHPRXQWHG 160 V\VWHPV7KHVDPSOLQJ
IUHTXHQF\ VKRXOG EH VSHFL¿HG 7HQVLRQ DGKHVLRQ VWUHQJWKV
VKRXOGH[FHHGSVL 03D DQGVKRXOGH[KLELWIDLOXUH
of the concrete substrate. Lower strengths or failure between
the FRP system and the concrete or between plies should be
reported to the licensed design professional for evaluation
and acceptance. For NSM strengthening, sample cores may
be extracted to visually verify the consolidation of the resin
adhesive around the FRP bar. The location of this core should
be chosen such that the continuity of the FRP reinforcement
LVPDLQWDLQHG WKDWLVDWWKHHQGVRIWKH160EDUV 7.2.6 Cured thickness—Small core samples, typically 0.5 in.
PP LQ GLDPHWHU PD\ EH WDNHQ WR YLVXDOO\ DVFHUWDLQ WKH
cured laminate thickness or number of plies. Cored samples
UHTXLUHG IRU DGKHVLRQ WHVWLQJ DOVR FDQ EH XVHG WR DVFHUWDLQ
the laminate thickness or number of plies. The sampling
IUHTXHQF\ VKRXOG EH VSHFL¿HG7DNLQJ VDPSOHV IURP KLJK
stress areas or splice areas should be avoided. For aesthetic
UHDVRQV WKH FRUHG KROH FDQ EH ¿OOHG DQG VPRRWKHG ZLWK D
UHSDLUPRUWDURUWKH)53V\VWHPSXWW\,IUHTXLUHGDWRLQ
WRPP RYHUODSSLQJ)53VKHHWSDWFKRIHTXLYDOHQW
SOLHVPD\EHDSSOLHGRYHUWKH¿OOHGDQGVPRRWKHGFRUHKROH
immediately after taking the core sample. The FRP sheet
patch should be installed in accordance with the manufacturer’s installation procedures.
CHAPTER 8—MAINTENANCE AND REPAIR
8.1—General
$V ZLWK DQ\ VWUHQJWKHQLQJ RU UHWUR¿W UHSDLU WKH RZQHU
should periodically inspect and assess the performance of
WKH¿EHUUHLQIRUFHGSRO\PHU )53 V\VWHPXVHGIRUVWUHQJWKHQLQJRUUHWUR¿WUHSDLURIFRQFUHWHPHPEHUV
8.2—Inspection and assessment
8.2.1 General inspection—A visual inspection looks for
changes in color, debonding, peeling, blistering, cracking,
FUD]LQJ GHÀHFWLRQV LQGLFDWLRQV RI UHLQIRUFLQJ EDU FRUURsion, and other anomalies. In addition, ultrasonic, acoustic
VRXQGLQJ KDPPHUWDS RUWKHUPRJUDSKLFWHVWVPD\LQGLFDWH
signs of progressive delamination.
8.2.2 Testing—Testing can include pull-off tension tests
7.2.5 RUFRQYHQWLRQDOVWUXFWXUDOORDGLQJWHVWV ACI 437R 8.2.3 Assessment—Test data and observations are used
to assess any damage and the structural integrity of the
strengthening system. The assessment can include a recomPHQGDWLRQ IRU UHSDLULQJ DQ\ GH¿FLHQFLHV DQG SUHYHQWLQJ
recurrence of degradation.
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MCPOL Licensed to: McMaster University Library
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
8.3—Repair of strengthening system
The method of repair for the strengthening system depends
on the causes of the damage, the type of material, the form of
GHJUDGDWLRQDQGWKHOHYHORIGDPDJH5HSDLUVWRWKH¿EHUUHLQIRUFHGSRO\PHU )53 V\VWHPVKRXOGQRWEHXQGHUWDNHQZLWKRXW
¿UVWLGHQWLI\LQJDQGDGGUHVVLQJWKHFDXVHVRIWKHGDPDJH
Minor damage should be repaired, including localized
FRP laminate cracking or abrasions that affect the structural
integrity of the laminate. Minor damage can be repaired
by bonding FRP patches over the damaged area. The FRP
patches should possess the same characteristics, such as
thickness or ply orientation, as the original laminate. The
FRP patches should be installed in accordance with the material manufacturer’s recommendation. Minor delaminations
can be repaired by resin injection. Major damage, including
SHHOLQJDQGGHERQGLQJRIODUJHDUHDVPD\UHTXLUHUHPRYDO
of the affected area, reconditioning of the cover concrete,
and replacement of the FRP laminate.
8.4—Repair of surface coating
In the event that the surface-protective coating should be
replaced, the FRP laminate should be inspected for structural
damage or deterioration. The surface coating may be replaced
using a process approved by the system manufacturer.
CHAPTER 9—GENERAL DESIGN
CONSIDERATIONS
General design recommendations are presented in this
chapter. The recommendations presented are based on the
traditional reinforced concrete design principles stated in
WKHUHTXLUHPHQWVRIACI 318DQGNQRZOHGJHRIWKHVSHFL¿F
PHFKDQLFDO EHKDYLRU RI ¿EHUUHLQIRUFHG SRO\PHU )53 reinforcement.
FRP strengthening systems should be designed to resist
tensile forces while maintaining strain compatibility
between the FRP and the concrete substrate. FRP reinforcement should not be relied on to resist compressive forces.
It is acceptable, however, for FRP tension reinforcement to
experience compression due to moment reversals or changes
in load pattern. The compressive strength of the FRP reinforcement, however, should be neglected.
9.1—Design philosophy
These design recommendations are based on limit-statesdesign principles. This approach sets acceptable levels of
safety for the occurrence of both serviceability limit states
H[FHVVLYH GHÀHFWLRQV DQG FUDFNLQJ DQG XOWLPDWH OLPLW
VWDWHV IDLOXUHVWUHVVUXSWXUHDQGIDWLJXH ,QDVVHVVLQJWKH
nominal strength of a member, the possible failure modes
DQGVXEVHTXHQWVWUDLQVDQGVWUHVVHVLQHDFKPDWHULDOVKRXOG
be assessed. For evaluating the serviceability of a member,
engineering principles, such as transformed section calculations using modular ratios, can be used.
FRP strengthening systems should be designed in accorGDQFHZLWK$&,VWUHQJWKDQGVHUYLFHDELOLW\UHTXLUHPHQWV
using the strength and load factors stated in ACI 318. Additional reduction factors applied to the contribution of the
)53UHLQIRUFHPHQWDUHUHFRPPHQGHGE\WKLVJXLGHWRUHÀHFW
21
uncertainties inherent in FRP systems different from steelreinforced and prestressed concrete. These reduction factors
were determined based on statistical evaluation of variability
in mechanical properties, predicted versus full-scale test
UHVXOWVDQG¿HOGDSSOLFDWLRQV)53UHODWHGUHGXFWLRQIDFWRUV
were calibrated to produce reliability indexes typically above
3.5. Reliability indexes between 3.0 and 3.5 can be encountered in cases where relatively low ratios of steel reinforcement combined with high ratios of FRP reinforcement are
used. Such cases are less likely to be encountered in design
because they violate the recommended strengthening limits
RI5HOLDELOLW\LQGH[HVIRU)53VWUHQJWKHQHGPHPEHUVDUH
determined based on the approach used for reinforced concrete
EXLOGLQJV Nowak and Szerszen 2003Szerszen and Nowak
2003 ,Q JHQHUDO ORZHU UHOLDELOLW\ LV H[SHFWHG LQ UHWUR¿WWHG
and repaired structures than in new structures.
9.2—Strengthening limits
Careful consideration should be given to determine reasonable strengthening limits. These limits are imposed to guard
against collapse of the structure should bond or other failure
of the FRP system occur due to damage, vandalism, or other
causes. The unstrengthened structural member, without FRP
UHLQIRUFHPHQWVKRXOGKDYHVXI¿FLHQWVWUHQJWKWRUHVLVWDFHUWDLQ
level of load. The existing strength of the structure should be
VXI¿FLHQWWRUHVLVWDOHYHORIORDGDVGHVFULEHGE\(T ࢥRn
existing•
SDL + 0.75SLL
new
A dead load factor of 1.1 is used because a relatively
accurate assessment of the dead loads of the structure can
be determined. A live load factor of 0.75 is used to exceed
the statistical mean of the yearly maximum live load factor
of 0.5, as given in ASCE 7. The strengthening limit resulting
IURPFRPSOLDQFHZLWK(T ZLOODOORZWKHVWUHQJWKHQHG
PHPEHU WR PDLQWDLQ VXI¿FLHQW VWUXFWXUDO FDSDFLW\ XQWLO WKH
damaged FRP is repaired.
In cases where the design live load acting on the member
to be strengthened has a high likelihood of being present for
a sustained period of time, a live load factor of 1.0 should
EHXVHGLQVWHDGRILQ(T ([DPSOHVLQFOXGHOLEUDU\
stack areas, heavy storage areas, warehouses, and other occupancies with a live load exceeding 150 lb/ft2 NJP2 0RUHVSHFL¿FOLPLWVIRUVWUXFWXUHVUHTXLULQJD¿UHUHVLVWDQFH
UDWLQJDUHJLYHQLQ
9.2.1 6WUXFWXUDO¿UHUHVLVWDQFH—The level of strengthening
that can be achieved through the use of externally bonded
)53UHLQIRUFHPHQWFDQEHOLPLWHGE\WKHFRGHUHTXLUHG¿UH
resistance rating of a structure. The polymer resins typically
used in wet layup and prepreg FRP systems and the polymer
adhesives used in precured FRP systems suffer deterioration
of mechanical and bond properties at temperatures close to
or exceeding the Tg of the polymer, as described in 1.2.1.3.
$OWKRXJKWKH)53V\VWHPLWVHOILVVLJQL¿FDQWO\DIIHFWHGE\
exposure to elevated temperature, a combination of the FRP
system with an existing concrete structure may still have an
DGHTXDWH¿UHUHVLVWDQFH:KHQFRQVLGHULQJWKH¿UHUHVLVWDQFH
of an FRP-strengthened concrete element, it is important to
@Seismicisolation
@Seismicisolation
American Concrete Institute – Copyrighted © Material – www.concrete.org
MCPOL Licensed to: McMaster University Library
22
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
recognize that the strength of a reinforced concrete element
LV UHGXFHG GXULQJ ¿UH H[SRVXUH GXH WR KHDWLQJ RI ERWK WKH
UHLQIRUFLQJ VWHHO DQG WKH FRQFUHWH 3HUIRUPDQFH LQ ¿UH RI
the existing concrete member can be enhanced by installing
an insulation system, which will provide thermal protection to existing concrete and internal reinforcing steel, thus
LPSURYLQJWKHRYHUDOO¿UHUDWLQJDOWKRXJKWKH)53V\VWHP
FRQWULEXWLRQPD\EHUHGXFHG Bisby et al. 2005aWilliams et
al. 2006Palmieri et al. 2011Firmo et al. 2012 By extending the methods in ACI 216.1 to FRP-strengthened reinforced concrete, limits on strengthening can be
used to ensure a strengthened structure will not collapse
LQD¿UHHYHQW$PHPEHU¶VUHVLVWDQFHWRORDGHIIHFWVZLWK
reduced steel and concrete strengths and without the contribution of the FRP reinforcement, can be compared with the
ORDGGHPDQGRQWKHPHPEHUGXULQJWKH¿UHHYHQWWRHQVXUH
the strengthened member can support these loads for the
UHTXLUHG¿UHGXUDWLRQ RU¿UHUDWLQJWLPH ZLWKRXWIDLOXUH
Rnș•SDL + 1.0SLL
D
Alternately, ACI 562VSHFL¿HVWKHIROORZLQJ
Rnș•SDL + 0.5SLL + 0.2SSL+ 1.0Ak
E
where Rnș is the nominal resistance of the member at an
elevated temperature, and SDL, SLL, and SSLDUHWKHVSHFL¿HG
dead, live, and snow loads, respectively, calculated for the
strengthened structure. For cases where the design live load
has a high likelihood of being present for a sustained period
of time, a live load factor of 1.0 should be used in place of
LQ(T E 'XHWRWKHODFNRIJXLGDQFHIRUWKHFDOFXlation of Ak WKH ORDG RU ORDG HIIHFW UHVXOWLQJ IURP WKH ¿UH
HYHQWXVHRI(T D LVUHFRPPHQGHG
If the FRP system is meant to allow greater load-carrying
capacity, such as an increase in live load, the load effects
should be computed using these greater loads. If the FRP
system is meant to address a loss in strength, such as deteULRUDWLRQWKHUHVLVWDQFHVKRXOGUHÀHFWWKLVORVV
The nominal resistance of the member at an elevated
temperature Rnș may be determined using the procedure
outlined in ACI 216.1 or through testing. The nominal resistance Rnș should be calculated based on the reduced material properties of the existing member. The resistance should
EH FRPSXWHG IRU WKH WLPH UHTXLUHG E\ WKH PHPEHU¶V ¿UH
UHVLVWDQFH UDWLQJ²IRU H[DPSOH D KRXU ¿UH UDWLQJ²DQG
should not account for the contribution of the FRP system
unless the continued effectiveness of the FRP can be proven
through testing. More research is needed to accurately identify temperatures at which effectiveness is lost for different
types of FRP. Until better information on the properties of
FRP at high temperature is available, the critical temperature can be taken as the lowest Tg of the components of the
system comprising the load path.
9.2.2 Overall structural strength—While FRP systems are
HIIHFWLYHLQVWUHQJWKHQLQJPHPEHUVIRUÀH[XUHDQGVKHDUDQG
SURYLGLQJ DGGLWLRQDO FRQ¿QHPHQW RWKHU PRGHV RI IDLOXUH
such as punching shear and bearing capacity of footings,
PD\ EH RQO\ PDUJLQDOO\ DIIHFWHG E\ )53 V\VWHPV Sharaf
et al. 2006 $OOPHPEHUVRIDVWUXFWXUHVKRXOGEHFDSDEOH
of withstanding the anticipated increase in loads associated
with the strengthened members.
Additionally, analysis should be performed on the member
strengthened by the FRP system to check that, under overORDGFRQGLWLRQVWKHVWUHQJWKHQHGPHPEHUZLOOIDLOLQDÀH[ural mode rather than in a shear mode.
9.2.3 Seismic applications—5HTXLUHPHQWV IRU VHLVPLF
strengthening using FRP are addressed in Chapter 13.
9.3—Selection of FRP systems
9.3.1 Environmental considerations—Environmental
FRQGLWLRQVXQLTXHO\DIIHFWUHVLQVDQG¿EHUVRIYDULRXV)53
V\VWHPV 7KH PHFKDQLFDO SURSHUWLHV IRU H[DPSOH WHQVLOH
VWUHQJWK XOWLPDWH WHQVLOH VWUDLQ DQG HODVWLF PRGXOXV RI
some FRP systems degrade under exposure to certain environments such as alkalinity, salt water, chemicals, ultraviolet light, high temperatures, high humidity, and freezingand-thawing cycles. The material properties used in design
VKRXOGDFFRXQWIRUWKLVGHJUDGDWLRQLQDFFRUGDQFHZLWK
The licensed design professional should select an FRP
system based on the known behavior of that system in the
anticipated service conditions. Some important environPHQWDO FRQVLGHUDWLRQV WKDW UHODWH WR WKH QDWXUH RI VSHFL¿F
V\VWHPV DUH JLYHQ DV IROORZV 6SHFL¿F LQIRUPDWLRQ FDQ EH
obtained from the FRP system manufacturer.
D Alkalinity/acidity—The performance of an FRP system
over time in an alkaline or acidic environment depends on
WKH PDWUL[ PDWHULDO DQG WKH UHLQIRUFLQJ ¿EHU 'U\ XQVDWXUDWHG EDUH RU XQSURWHFWHG FDUERQ ¿EHU LV UHVLVWDQW WR ERWK
DONDOLQH DQG DFLGLF HQYLURQPHQWV ZKHUHDV EDUH JODVV ¿EHU
can degrade over time in these environments. A properly
selected and applied resin matrix, however, should isolate
DQG SURWHFW WKH ¿EHU IURP WKH DONDOLQHDFLGLF HQYLURQPHQW
and resist deterioration. Sites with high alkalinity and high
moisture or relative humidity favor the selection of carbon¿EHUV\VWHPVRYHUJODVV¿EHUV\VWHPV
E Thermal expansion—FRP systems may have thermal
expansion properties that are different from those of concrete.
,QDGGLWLRQWKHWKHUPDOH[SDQVLRQSURSHUWLHVRIWKH¿EHUDQG
SRO\PHUFRQVWLWXHQWVRIDQ)53V\VWHPFDQYDU\&DUERQ¿EHUV
KDYH D FRHI¿FLHQW RI WKHUPDO H[SDQVLRQ QHDU ]HUR ZKHUHDV
JODVV ¿EHUV KDYH D FRHI¿FLHQW RI WKHUPDO H[SDQVLRQ VLPLODU
to concrete. The polymers used in FRP strengthening systems
W\SLFDOO\KDYHFRHI¿FLHQWVRIWKHUPDOH[SDQVLRQURXJKO\¿YH
times that of concrete. Calculation of thermally-induced strain
GLIIHUHQWLDOVDUHFRPSOLFDWHGE\YDULDWLRQVLQ¿EHURULHQWDWLRQ
¿EHUYROXPHIUDFWLRQDQGWKLFNQHVVRIDGKHVLYHOD\HUV([SHrience indicates, however, that thermal expansion differences
do not affect bond for small ranges of temperature change,
VXFK DV “ƒ) “ƒ& 0RWDYDOOL HW DO Soudki and
*UHHQ*UHHQHWDO F Electrical conductivity²*ODVV )53 *)53 DQG
DUDPLG )53 $)53 DUH HIIHFWLYH HOHFWULFDO LQVXODWRUV
ZKHUHDVFDUERQ)53 &)53 LVFRQGXFWLYH7RDYRLGSRWHQtial galvanic corrosion of steel elements, carbon-based FRP
materials should not come in direct contact with steel.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
9.3.2 Loading considerations—Loading conditions
XQLTXHO\DIIHFWGLIIHUHQW¿EHUVRI)53V\VWHPV7KHOLFHQVHG
design professional should select an FRP system based on
the known behavior of that system in the anticipated service
conditions. Some important loading considerations that
UHODWHWRWKHQDWXUHRIWKHVSHFL¿FV\VWHPVDUHJLYHQLQWKH
IROORZLQJ 6SHFL¿F LQIRUPDWLRQ VKRXOG EH REWDLQHG IURP
material manufacturers.
D Impact tolerance—AFRP and GFRP systems demonstrate better tolerance to impact than CFRP systems.
E Creep rupture and fatigue—CFRP systems are highly
resistive to creep rupture under sustained loading and fatigue
failure under cyclic loading. GFRP systems are more sensitive to both loading conditions.
9.3.3 Durability considerations—Durability of FRP
systems is the subject of considerable ongoing research
Dolan et al. 2008 Karbhari 2007 7KH OLFHQVHG GHVLJQ
professional should select an FRP system that has undergone
durability testing consistent with the application environment. Durability testing may include hot-wet cycling, alkaline immersion, freezing-and-thawing cycling, ultraviolet
H[SRVXUHGU\KHDWDQGVDOWZDWHU Cromwell et al. 2011 Any FRP system that completely encases or covers a
concrete section should be investigated for the effects of
a variety of environmental conditions including those of
freezing and thawing, steel corrosion, alkali and silica aggregate reactions, water entrapment, vapor pressures, and moisWXUHYDSRUWUDQVPLVVLRQ Masoud and Soudki 2006Soudki
DQG*UHHQ3RUWHUHWDO&KULVWHQVHQHWDO
7RXWDQML 0DQ\)53V\VWHPVFUHDWHDPRLVWXUHLPSHUmeable layer on the surface of the concrete. In areas where
PRLVWXUH YDSRU WUDQVPLVVLRQ LV H[SHFWHG DGHTXDWH PHDQV
should be provided to allow moisture to escape from the
concrete structure.
9.3.4 Protective-coating selection considerations—A
coating or insulation system can be applied to the installed
FRP system to protect it from exposure to certain environPHQWDOFRQGLWLRQV Bisby et al. 2005aWilliams et al. 2006 The thickness and type of coating should be selected based on
WKHUHTXLUHPHQWVRIWKHFRPSRVLWHUHSDLUUHVLVWDQFHWRHQYLronmental effects such as moisture, salt water, temperature
H[WUHPHV¿UHLPSDFWDQGXOWUDYLROHWH[SRVXUHUHVLVWDQFHWR
VLWHVSHFL¿FHIIHFWVDQGUHVLVWDQFHWRYDQGDOLVP&RDWLQJVDUH
relied on to retard the degradation of the mechanical properties of the FRP systems. The coatings should be periodically
inspected and maintained to ensure continued effectiveness.
([WHUQDO FRDWLQJV RU WKLFNHQHG FRDWV RI UHVLQ RYHU ¿EHUV
can protect them from damage due to impact or abrasion.
,Q KLJKLPSDFW RU WUDI¿F DUHDV DGGLWLRQDO OHYHOV RI SURWHFtion may be necessary. Portland cement plaster and polymer
coatings are commonly used for protection where minor
impact or abrasion is anticipated.
9.4—Design material properties
Unless otherwise stated, the material properties reported
by manufacturers, such as the ultimate tensile strength, typically do not consider long-term exposure to environmental
conditions and should be considered as initial properties.
23
Because long-term exposure to various types of environments can reduce the tensile properties and creep-rupture
and fatigue endurance of FRP laminates, the material propHUWLHVXVHGLQGHVLJQHTXDWLRQVVKRXOGEHUHGXFHGEDVHGRQ
the environmental exposure condition.
(TXDWLRQV D WKURXJK F JLYHWKHWHQVLOHSURSHUWLHV
WKDWVKRXOGEHXVHGLQDOOGHVLJQHTXDWLRQV7KHGHVLJQXOWLmate tensile strength should be determined using the enviURQPHQWDOUHGXFWLRQIDFWRUJLYHQLQ7DEOHIRUWKHDSSURSULDWH¿EHUW\SHDQGH[SRVXUHFRQGLWLRQ
ffu = CEffu*
D
Similarly, the design rupture strain should also be reduced
for environmental exposure conditions
İfu = CEİfu*
E
Because FRP materials are linear elastic until failure,
the design modulus of elasticity for unidirectional FRP can
be determined from Hooke’s law. The expression for the
PRGXOXV RI HODVWLFLW\ JLYHQ LQ (T F UHFRJQL]HV WKDW
the modulus is typically unaffected by environmental condiWLRQV7KHPRGXOXVJLYHQLQWKLVHTXDWLRQZLOOEHWKHVDPHDV
the initial value reported by the manufacturer
Ef = ffuİfu
F
7KH FRQVWLWXHQW PDWHULDOV ¿EHUV DQG UHVLQV RI DQ )53
system affect its durability and resistance to environmental
exposure. The environmental reduction factors given in
7DEOH DUH FRQVHUYDWLYH HVWLPDWHV EDVHG RQ WKH UHODWLYH
GXUDELOLW\RIHDFK¿EHUW\SH
$V7DEOHLOOXVWUDWHVLIWKH)53V\VWHPLVORFDWHGLQD
relatively benign environment, such as indoors, the reduction factor is closer to unity. If the FRP system is located
in an aggressive environment where prolonged exposure to
high humidity, freezing-and-thawing cycles, salt water, or
alkalinity is expected, a lower reduction factor should be
XVHG7KHUHGXFWLRQIDFWRUFDQEHPRGL¿HGWRUHÀHFWWKHXVH
of a protective coating if the coating has been shown through
testing to lessen the effects of environmental exposure and
the coating is maintained for the life of the FRP system.
Table 9.4—Environmental reduction factor for
various FRP systems and exposure conditions
([SRVXUHFRQGLWLRQV
Interior exposure
([WHULRUH[SRVXUH EULGJHVSLHUV
DQGXQHQFORVHGSDUNLQJJDUDJHV
$JJUHVVLYHHQYLURQPHQW FKHPLFDO
plants and wastewater treatment
SODQWV
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Fiber
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Carbon
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0.75
Carbon
0.85
Glass
0.50
Aramid
0.70
American Concrete Institute – Copyrighted © Material – www.concrete.org
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24
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
CHAPTER 10—FLEXURAL STRENGTHENING
%RQGLQJ¿EHUUHLQIRUFHGSRO\PHU )53 UHLQIRUFHPHQWWR
WKH WHQVLRQ IDFH RI D FRQFUHWH ÀH[XUDO PHPEHU ZLWK ¿EHUV
oriented along the length of the member will provide an
LQFUHDVH LQ ÀH[XUDO VWUHQJWK ,QFUHDVHV LQ RYHUDOO ÀH[XUDO
strength from 10 to 160 percent have been documented
0HLHU DQG .DLVHU 5LWFKLH HW DO Sharif et al.
:KHQWDNLQJLQWRDFFRXQWWKHVWUHQJWKHQLQJOLPLWVRI
and ductility and serviceability limits, however, strength
increases of up to 40 percent are more reasonable.
This chapter does not apply to FRP systems used to
HQKDQFH WKH ÀH[XUDO VWUHQJWK RI PHPEHUV LQ WKH H[SHFWHG
plastic hinge regions of ductile moment frames resisting
VHLVPLFORDGVWKHVHDUHDGGUHVVHGLQChapter 13.
10.1—Nominal strength
7KH VWUHQJWK GHVLJQ DSSURDFK UHTXLUHV WKDW WKH GHVLJQ
ÀH[XUDO VWUHQJWK RI D PHPEHU H[FHHG LWV UHTXLUHG IDFWRUHG
PRPHQW DV LQGLFDWHG E\ (T 7KH GHVLJQ ÀH[XUDO
VWUHQJWKࢥMn refers to the nominal strength of the member
multiplied by a strength reduction factor, and the factored
moment Mu refers to the moment calculated from factored
ORDGV IRUH[DPSOHĮDLMDLĮLLMLL
ࢥMn•Mu
This guide recommends that the factored moment Mu of
D VHFWLRQ EH FDOFXODWHG E\ XVH RI ORDG IDFWRUV DV UHTXLUHG
by ACI 318. An additional strength reduction factor for
)53ȥfVKRXOGEHDSSOLHGWRWKHÀH[XUDOFRQWULEXWLRQRIWKH
FRP reinforcement alone, Mnf, as described in 10.2.10. The
DGGLWLRQDOVWUHQJWKUHGXFWLRQIDFWRUȥf, is used to improve
the reliability of strength prediction and accounts for the
different failure modes observed for FRP-strengthened
PHPEHUV GHODPLQDWLRQRI)53UHLQIRUFHPHQW 7KH QRPLQDO ÀH[XUDO VWUHQJWK RI )53VWUHQJWKHQHG
concrete members with mild steel reinforcement and with
bonded prestressing steel can be determined based on strain
FRPSDWLELOLW\LQWHUQDOIRUFHHTXLOLEULXPDQGWKHFRQWUROOLQJ
mode of failure. For members with unbonded prestressed
steel, strain compatibility does not apply and the stress in the
unbonded tendons at failure depends on the overall deformation of the member and is assumed to be approximately the
same at all sections.
Failure modes²7KHÀH[XUDOVWUHQJWKRIDVHFWLRQ
depends on the controlling failure mode. The following
ÀH[XUDO IDLOXUH PRGHV VKRXOG EH LQYHVWLJDWHG IRU DQ )53
VWUHQJWKHQHGVHFWLRQ *DQJD5DRDQG9LMD\ D &UXVKLQJRIWKHFRQFUHWHLQFRPSUHVVLRQEHIRUH\LHOGLQJ
of the reinforcing steel
E <LHOGLQJRIWKHVWHHOLQWHQVLRQIROORZHGE\UXSWXUHRI
the FRP laminate
F <LHOGLQJ RI WKH VWHHO LQ WHQVLRQ IROORZHG E\ FRQFUHWH
crushing
G 6KHDUWHQVLRQGHODPLQDWLRQRIWKHFRQFUHWHFRYHU FRYHU
GHODPLQDWLRQ
H 'HERQGLQJRIWKH)53IURPWKHFRQFUHWHVXEVWUDWH )53
GHERQGLQJ
Concrete crushing is assumed to occur if the compressive strain in the concrete reaches its maximum usable
VWUDLQ İc İcu 5XSWXUH RI WKH H[WHUQDOO\ ERQGHG
FRP is assumed to occur if the strain in the FRP reaches its
GHVLJQUXSWXUHVWUDLQ İf İfu EHIRUHWKHFRQFUHWHUHDFKHVLWV
maximum usable strain.
Cover delamination or FRP debonding can occur if the
IRUFHLQWKH)53FDQQRWEHVXVWDLQHGE\WKHVXEVWUDWH )LJ
D 6XFKEHKDYLRULVJHQHUDOO\UHIHUUHGWRDVGHERQGLQJ
regardless of where the failure plane propagates within the
FRP-adhesive-substrate region. Guidance to avoid the cover
delamination failure mode is given in Chapter 13.
Away from the section where externally bonded FRP
terminates, a failure controlled by FRP debonding may
JRYHUQ )LJ D E 7R SUHYHQW VXFK DQ LQWHUPHGLDWH
crack-induced debonding failure mode, the effective strain
in FRP reinforcement should be limited to the strain at which
GHERQGLQJPD\RFFXUİfdDVGH¿QHGLQ(T ε fd = 0.083
ε fd
f c′
≤ 0.9ε fu (in.-lb)
nE f t f
f c′
= 0.41
≤ 0.9ε fu (SI)
nE f t f
(TXDWLRQ WDNHVDPRGL¿HGIRUPRIWKHGHERQGLQJ
VWUDLQHTXDWLRQSURSRVHGE\7HQJHWDO that was
EDVHGRQFRPPLWWHHHYDOXDWLRQRIDVLJQL¿FDQWGDWDEDVHIRU
ÀH[XUDO EHDP WHVWV H[KLELWLQJ )53 GHERQGLQJ IDLOXUH 7KH
SURSRVHG HTXDWLRQ ZDV FDOLEUDWHG XVLQJ DYHUDJH PHDVXUHG
YDOXHVRI)53VWUDLQVDWGHERQGLQJIRUÀH[XUDOWHVWVH[SHULencing intermediate crack-induced debonding to determine
WKHEHVW¿WFRHI¿FLHQWRI LQ6, 5HOLDELOLW\RIWKH
)53FRQWULEXWLRQWRÀH[XUDOVWUHQJWKLVDGGUHVVHGE\LQFRUSRUDWLQJDQDGGLWLRQDOVWUHQJWKUHGXFWLRQIDFWRUIRU)53ȥf
LQDGGLWLRQWRWKHVWUHQJWKUHGXFWLRQIDFWRUࢥSHU$&,
for structural concrete. Anchorage systems such as U-wraps,
PHFKDQLFDOIDVWHQHUV¿EHUDQFKRUVDQG8DQFKRUV H[DPSOHV DUH VKRZQ VFKHPDWLFDOO\ LQ )LJ E KDYH EHHQ
proven successful at delaying, and sometimes preventing,
GHERQGLQJ IDLOXUH RI WKH ORQJLWXGLQDO )53 Kalfat et al.
2013 Grelle and Sneed 2013 ([SHULPHQWDO VWXGLHV KDYH
shown that these anchorage systems can increase the effecWLYHVWUDLQLQWKHÀH[XUDO)53WRYDOXHVXSWRWHQVLOHUXSWXUH
Lee et al. 2010Orton et al. 2008 )RU QHDUVXUIDFHPRXQWHG 160 )53 DSSOLFDWLRQV WKH
YDOXH RI İfd PD\ YDU\ IURP İfu WR İfu, depending on
many factors such as member dimensions, steel and FRP
reinforcement ratios, and surface roughness of the FRP bar.
%DVHGRQDQDO\VLVRIDGDWDEDVHRIH[LVWLQJVWXGLHV Bianco
et al. 2014 WKH FRPPLWWHH UHFRPPHQGV WKH XVH RI İfd =
İfu. To achieve the debonding design strain of NSM FRP
EDUVİfd, the bonded length should be greater than the development length given in Chapter 13.
10.2—Reinforced concrete members
This section presents guidance on the calculation of the
ÀH[XUDO VWUHQJWKHQLQJ HIIHFW RI DGGLQJ ORQJLWXGLQDO )53
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
25
Fig. 10.1.1a—Debonding and delamination of externally bonded FRP systems.
Fig. 10.1.1b—FRP anchorage systems.
reinforcement to the tension face of a reinforced concrete
PHPEHU $ VSHFL¿F LOOXVWUDWLRQ RI WKH FRQFHSWV LQ WKLV
section applied to strengthening of existing rectangular
sections reinforced in the tension zone with nonprestressed
steel is given. The general concepts outlined herein can,
KRZHYHUEHH[WHQGHGWRQRQUHFWDQJXODUVKDSHV 7VHFWLRQV
DQG ,VHFWLRQV DQG WR PHPEHUV ZLWK VWHHO FRPSUHVVLRQ
reinforcement.
Assumptions—The following assumptions are
PDGH LQ FDOFXODWLQJ WKH ÀH[XUDO UHVLVWDQFH RI D VHFWLRQ
strengthened with an externally applied FRP system:
D 'HVLJQ FDOFXODWLRQV DUH EDVHG RQ WKH GLPHQVLRQV
internal reinforcing steel arrangement, and material properties of the existing member being strengthened.
E 7KHVWUDLQVLQWKHVWHHOUHLQIRUFHPHQWDQGFRQFUHWHDUH
directly proportional to their distance from the neutral axis.
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26
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
That is, a plane section before loading remains plane after
loading.
F 7KHUH LV QR UHODWLYH VOLS EHWZHHQ H[WHUQDO )53 UHLQforcement and the concrete.
G 7KH VKHDU GHIRUPDWLRQ ZLWKLQ WKH DGKHVLYH OD\HU LV
neglected because the adhesive layer is very thin with only
slight variations in its thickness.
H 7KHPD[LPXPXVDEOHFRPSUHVVLYHVWUDLQLQWKHFRQFUHWH
is 0.003.
I 7KHWHQVLOHVWUHQJWKRIFRQFUHWHLVQHJOHFWHG
J 7KH)53UHLQIRUFHPHQWKDVDOLQHDUHODVWLFVWUHVVVWUDLQ
relationship to failure.
While some of these assumptions are necessary for the
sake of computational ease, the assumptions do not accuUDWHO\UHÀHFWWKHWUXHIXQGDPHQWDOEHKDYLRURI)53ÀH[XUDO
reinforcement. For example, there will be shear deformation in the adhesive layer, causing relative slip between the
FRP and the substrate. The inaccuracy of the assumptions
ZLOOQRWKRZHYHUVLJQL¿FDQWO\DIIHFWWKHFRPSXWHGÀH[XUDO
strength of an FRP-strengthened member. An additional
VWUHQJWKUHGXFWLRQIDFWRU SUHVHQWHGLQ ZLOOFRQVHUvatively compensate for any such discrepancies.
Shear strength—When FRP reinforcement is being
XVHGWRLQFUHDVHWKHÀH[XUDOVWUHQJWKRIDPHPEHUWKHPHPEHU
should be capable of resisting the shear forces associated
ZLWKWKHLQFUHDVHGÀH[XUDOVWUHQJWK7KHSRWHQWLDOIRUVKHDU
failure of the section should be considered by comparing
WKHGHVLJQVKHDUVWUHQJWKRIWKHVHFWLRQWRWKHUHTXLUHGVKHDU
VWUHQJWK,IDGGLWLRQDOVKHDUVWUHQJWKLVUHTXLUHG)53ODPLnates oriented transverse to the beam longitudinal axis can
be used to resist shear forces, as described in Chapter 11.
Existing substrate strain—Unless all loads on a
member, including self-weight and any prestressing forces,
are removed before installation of FRP reinforcement, the
substrate to which the FRP is applied will be strained. These
strains should be considered initial strains and should be
H[FOXGHG IURP WKH VWUDLQ LQ WKH )53 Arduini and Nanni
1DQQLDQG*ROG 7KHLQLWLDOVWUDLQRQWKHERQGHG
VXEVWUDWHİbi, can be determined from an elastic analysis of
the existing member, considering all loads that will be on
the member during the installation of the FRP system. The
elastic analysis of the existing member should be based on
cracked section properties.
)OH[XUDO VWUHQJWKHQLQJ RI FRQFDYH VRI¿WV—The
SUHVHQFH RI FXUYDWXUH LQ WKH VRI¿W RI D FRQFUHWH PHPEHU
may lead to the development of tensile stresses normal to
the adhesive and surface to which the FRP is bonded. Such
tensile stresses result when the FRP tends to straighten under
load, and can promote the initiation of FRP debonding or
interlaminar failures that reduce the effectiveness of the
)53ÀH[XUDOVWUHQJWKHQLQJ Aiello et al. 2001Eshwar et al.
2003 ,IWKHH[WHQWRIWKHFXUYHGSRUWLRQRIWKHVRI¿WH[FHHGV
DOHQJWKRILQ P ZLWKDULVHRILQ PP WKH
VXUIDFHVKRXOGEHPDGHÀDWEHIRUHVWUHQJWKHQLQJ$OWHUQDWHO\
anchorage systems such as U-wraps, mechanical fasteners,
¿EHUDQFKRUVRU160DQFKRUVVKRXOGEHLQVWDOOHGWRPLWLJDWHGHODPLQDWLRQ Eshwar et al. 2005 Fig. 10.2.5—Effective depth of FRP systems.
Strain in FRP reinforcement—It is important to
determine the strain in the FRP reinforcement at the ultimate
limit state. Because FRP materials are linear elastic until
failure, the strain in the FRP will dictate the stress developed
in the FRP. The maximum strain that can be achieved in
the FRP reinforcement will be governed by either the strain
developed in the FRP at the point at which concrete crushes,
the point at which the FRP ruptures, or the point at which the
FRP debonds from the substrate. The effective strain in the
FRP reinforcement at the ultimate limit state can be found
IURP(T ⎛ d f − c⎞
ε fe = ε cu ⎜
− ε bi ≤ ε fd ⎝ c ⎟⎠
ZKHUHİbi is the initial substrate strain as described in 10.2.3,
and df is the effective depth of FRP reinforcement, as indicated in Fig. 10.2.5.
Stress in the FRP reinforcement—The effective stress
in the FRP reinforcement is the maximum level of stress that
FDQ EH GHYHORSHG LQ WKH )53 UHLQIRUFHPHQW EHIRUH ÀH[XUDO
failure of the section. This effective stress can be found from
the strain in the FRP, assuming perfectly elastic behavior
Effective Strain in FRP Reinforcement
attained at failure
Effective Stress in the FRP. Stress
attained at Section Failure
ffe = Efİfe
Tensile Modulus of Elasticity of FRP
Strength reduction factor—The use of externally
ERQGHG )53 UHLQIRUFHPHQW IRU ÀH[XUDO VWUHQJWKHQLQJ ZLOO
reduce the ductility of the original member. In some cases,
the loss of ductility is negligible. Sections that experience a
VLJQL¿FDQWORVVLQGXFWLOLW\KRZHYHUVKRXOGEHDGGUHVVHG7R
PDLQWDLQDVXI¿FLHQWGHJUHHRIGXFWLOLW\WKHVWUDLQLQWKHVWHHO
at the ultimate limit state should be checked. For reinforced
concrete members with nonprestressed steel reinforcement,
DGHTXDWHGXFWLOLW\LVDFKLHYHGLIWKHVWUDLQLQWKHVWHHODWWKH
point of concrete crushing or failure of the FRP, including
delamination or debonding, is at least 0.005, according to the
GH¿QLWLRQRIDWHQVLRQFRQWUROOHGVHFWLRQDVJLYHQLQACI 318.
The approach taken by this guide follows the philosophy
RI$&,$VWUHQJWKUHGXFWLRQIDFWRUJLYHQE\(T VKRXOGEHXVHGZKHUHİt is the net tensile strain in extreme
WHQVLRQVWHHODWQRPLQDOVWUHQJWKDVGH¿QHGLQ$&,
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
⎧0.90 for ε t ≥ 0.005
⎪
0.25(ε t − ε sy )
⎪
φ = ⎨0.65 +
for ε sy < ε t < 0.005
0.005 − ε sy
⎪
⎪0.65 for ε ≤ ε
t
sy
⎩
27
7KLVHTXDWLRQVHWVWKHUHGXFWLRQIDFWRUDWIRUGXFWLOH
sections and 0.65 for brittle sections where the steel does
not yield, and provides a linear transition for the reduction
IDFWRUEHWZHHQWKHVHWZRH[WUHPHV7KHXVHRI(T is limited to steel having a yield strength fy less than 80 ksi
03D ACI 318 Serviceability—The serviceability of a member
GHÀHFWLRQV DQG FUDFN ZLGWKV XQGHU VHUYLFH ORDGV VKRXOG
satisfy applicable provisions of ACI 318. The effect of the
FRP external reinforcement on the serviceability can be
assessed using the transformed-section analysis.
To avoid inelastic deformations of reinforced concrete
members with nonprestressed steel reinforcement strengthened with external FRP reinforcement, the existing internal
steel reinforcement should be prevented from yielding under
service load levels, especially for members subjected to
F\FOLF ORDGV El-Tawil et al. 2001 7KH VWUHVV LQ WKH VWHHO
reinforcement under service load should be limited to 80
SHUFHQWRIWKH\LHOGVWUHQJWKDVVKRZQLQ(T D ,Q
addition, the compressive stress in concrete under service
load should be limited to 60 percent of the compressive
VWUHQJWKDVVKRZQLQ(T E
fs,s”fy
D
fc,s”fcƍ
E
Creep rupture and fatigue stress limits—To avoid
creep rupture of the FRP reinforcement under sustained
stresses or failure due to cyclic stresses and fatigue of the
FRP reinforcement, the stress in the FRP reinforcement
under these stress conditions should be checked. Because
this stress will be within the elastic response range of the
member, the stresses can be computed by elastic analysis
using cracked section properties as appropriate.
In 4.4, the creep rupture phenomenon and fatigue characteristics of FRP material were described and the resistance to
LWVHIIHFWVE\YDULRXVW\SHVRI¿EHUVZDVH[DPLQHG$VVWDWHG
in 4.4.1, research has indicated that glass, aramid, and carbon
¿EHUV FDQ VXVWDLQ DSSUR[LPDWHO\ DQG WLPHV
their ultimate strengths, respectively, before encountering
D FUHHS UXSWXUH SUREOHP <DPDJXFKL HW DO Malvar
7RDYRLGIDLOXUHRIDQ)53UHLQIRUFHGPHPEHUGXHWR
creep rupture and fatigue of the FRP, stress limits for these
conditions should be imposed on the FRP reinforcement.
The stress in the FRP reinforcement can be computed using
elastic analysis and an applied moment due to all sustained
ORDGV GHDGORDGVDQGWKHVXVWDLQHGSRUWLRQRIWKHOLYHORDG plus the maximum moment induced in a fatigue loading
F\FOH )LJ 7KHVXVWDLQHGVWUHVVVKRXOGEHOLPLWHGDV
H[SUHVVHGE\(T WRPDLQWDLQVDIHW\9DOXHVIRUVDIH
Fig. 10.2.9—Illustration of the level of applied moment to
be used to check the stress limits in the FRP reinforcement.
VXVWDLQHGSOXVF\FOLFVWUHVVDUHJLYHQLQ7DEOH7KHVH
values are based approximately on the stress limits previously stated in 4.4.1 with an imposed safety factor of 1/0.6
ff,s”VXVWDLQHGSOXVF\FOLFVWUHVVOLPLW
Table 10.2.9—Sustained plus cyclic service load
stress limits in FRP reinforcement
)LEHUW\SH
6WUHVVW\SH
GFRP
AFRP
CFRP
Sustained plus cyclic
stress limit
0.20ffu
0.30ffu
0.55ffu
Ultimate strength of singly reinforced rectangular
section—To illustrate the concepts presented in this chapter,
this section describes the application of these concepts to a
nonprestressed singly-reinforced rectangular section. Figure
10.2.10 illustrates the internal strain and stress distribution
IRUDUHFWDQJXODUVHFWLRQXQGHUÀH[XUHDWWKHXOWLPDWHOLPLW
state.
The calculation procedure used to arrive at the ultimate
VWUHQJWKVKRXOGVDWLVI\VWUDLQFRPSDWLELOLW\DQGIRUFHHTXLlibrium, and should consider the governing mode of failure.
Several calculation procedures can be derived to satisfy
these conditions. The calculation procedure described herein
illustrates an iterative method that involves selecting an
assumed depth to the neutral axis, c, calculating the strain
LQ HDFK PDWHULDO XVLQJ VWUDLQ FRPSDWLELOLW\ FDOFXODWLQJ WKH
DVVRFLDWHG VWUHVV LQ HDFK PDWHULDO DQG FKHFNLQJ LQWHUQDO
IRUFH HTXLOLEULXP ,I WKH LQWHUQDO IRUFH UHVXOWDQWV GR QRW
HTXLOLEUDWHWKHGHSWKWRWKHQHXWUDOD[LVVKRXOGEHUHYLVHG
and the procedure repeated.
For any assumed depth to the neutral axis, c, the strain in
WKH )53 UHLQIRUFHPHQW FDQ EH FRPSXWHG IURP (T 7KLVHTXDWLRQFRQVLGHUVWKHJRYHUQLQJPRGHRIIDLOXUHIRUWKH
DVVXPHGQHXWUDOD[LVGHSWK,IWKHOHIWWHUPRIWKHLQHTXDOLW\
FRQWUROV FRQFUHWH FUXVKLQJ FRQWUROV ÀH[XUDO IDLOXUH RI WKH
VHFWLRQ,IWKHULJKWWHUPRIWKHLQHTXDOLW\FRQWUROV)53IDLOXUH
UXSWXUHRUGHERQGLQJ FRQWUROVÀH[XUDOIDLOXUHRIWKHVHFWLRQ
The effective stress in the FRP reinforcement can be
found from the strain in the FRP, assuming perfectly elastic
EHKDYLRUXVLQJ(T %DVHGRQWKHVWUDLQLQWKH)53
reinforcement, the strain in the nonprestressed steel rein-
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28
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Strain in concrete
Strain in concrete substrate at time of
FRP installation (Tension is positive)
Effective Strain in FRP Reinforcement
attained at failure
)LJ²,QWHUQDOVWUDLQDQGVWUHVVGLVWULEXWLRQIRUDUHFWDQJXODUVHFWLRQXQGHUÀH[XUH
at ultimate limit state.
IRUFHPHQW FDQ EH IRXQG IURP (T D XVLQJ VWUDLQ
compatibility
Effective Strain in FRP Reinforcement
attained at failure
Strain in concrete substrate at time of
FRP installation (Tension is positive)
⎛ d −c ⎞
ε s = (ε fe + ε bi ) ⎜
⎟
⎝ d f − c⎠
D
The stress in the steel is determined from the strain in the
steel using its assumed elastic-perfectly plastic stress-strain
curve
fs = Esİs”fy
E
With the stress in the FRP and steel reinforcement determined for the assumed neutral axis depth, internal force
HTXLOLEULXPPD\EHFKHFNHGXVLQJ(T F
Į1 fcƍȕ1bc = Asfs + Af ffe
F
7KH WHUPV Į1 DQG ȕ1 LQ (T F DUH SDUDPHWHUV
GH¿QLQJDUHFWDQJXODUVWUHVVEORFNLQWKHFRQFUHWHHTXLYDOHQW
to the nonlinear distribution of stress. If concrete crushing is
WKHFRQWUROOLQJPRGHRIIDLOXUH EHIRUHRUDIWHUVWHHO\LHOGLQJ Į1 DQG ȕ1 can be taken as the values associated with the
:KLWQH\VWUHVVEORFN ACI 318 WKDWLVĮ1 DQGȕ1 =
0.85 for fcƍEHWZHHQDQGSVL DQG03D DQG
ȕ1LVUHGXFHGOLQHDUO\DWDUDWHRIIRUHDFKSVL 03D RIFRQFUHWHVWUHQJWKH[FHHGLQJSVL 03D 1RWH
WKDWȕ1 shall not be taken less than 0.65. If FRP rupture, cover
delamination, or FRP debonding occur, the Whitney stress
block will give reasonably accurate results. A nonlinear stress
distribution in the concrete or a more accurate stress block
appropriate for the strain level reached in the concrete at the
ultimate-limit state may be used.
The depth to the neutral axis, c, is found by simultaneously
VDWLVI\LQJ(T D E DQG
F WKXVHVWDEOLVKLQJLQWHUQDOIRUFHHTXLOLEULXPDQG
strain compatibility. To solve for the depth of the neutral
axis, c, an iterative solution procedure can be used. An
initial value for cLV¿UVWDVVXPHGDQGWKHVWUDLQVDQGVWUHVVHV
DUH FDOFXODWHG XVLQJ (T D DQG
E $ UHYLVHG YDOXH IRU WKH GHSWK RI QHXWUDO D[LV
c LV WKHQ FDOFXODWHG IURP (T F 7KH FDOFXODWHG
and assumed values for c are then compared. If they agree,
then the proper value of c is reached. If the calculated and
assumed values do not agree, another value for c is selected,
and the process is repeated until convergence is attained.
7KH QRPLQDO ÀH[XUDO VWUHQJWK RI WKH VHFWLRQ ZLWK )53
H[WHUQDO UHLQIRUFHPHQW LV FRPSXWHG IURP (T G $QDGGLWLRQDOUHGXFWLRQIDFWRUIRU)53ȥf, is applied to the
ÀH[XUDOVWUHQJWKFRQWULEXWLRQRIWKH)53UHLQIRUFHPHQW7KH
UHFRPPHQGHGYDOXHRIȥf is 0.85. This reduction factor for
the strength contribution of FRP reinforcement is based on
the reliability analysis discussed in , which was based
on the experimentally calibrated statistical properties of the
Effective depth of FRP Flexural Reinforcement
ÀH[XUDOVWUHQJWK Okeil et al. 2007
Ratio of Depth of Equivalent Rectangular
Stress Block to Depth of the Neutral Axis
Effective stress in the FRP. Stress attained at failure
β c⎞
β c⎞
⎛
⎛
M n = As f s ⎜ d − 1 ⎟ + ψ f Af f fe ⎜ d f − 1 ⎟
⎝
⎝
⎠
2
2 ⎠
Distance from Extreme Compression
Fiber to the neutral axis
G
Reduction Factor for FRP
Area of External FRP Reinforcement
Stress in steel under service loads—The stress
in the steel reinforcement can be calculated based on a
cracked-section analysis of the FRP-strengthened reinforced
FRQFUHWHVHFWLRQDVLQGLFDWHGE\(T fs,s
⎡
kd ⎞ ⎤
⎛
⎢ M s + ε bi Af E f ⎜⎝ d f − 3 ⎟⎠ ⎥ (d − kd ) Es
⎦
=⎣
kd ⎞
⎤
⎡
⎛
⎢ As Es ⎜⎝ d − 3 ⎟⎠ (d − kd )
⎥
⎢
⎥
⎢
⎥
kd ⎞
⎛
+
−
(
)
−
A
E
d
d
kd
⎟⎠ f
⎢ f f ⎜⎝ f
⎥
3
⎣
⎦
The distribution of strain and stress in the reinforced
concrete section is shown in Fig. 10.2.10.1. Similar to
conventional reinforced concrete, the depth to the neutral
axis at service, kd FDQ EH FRPSXWHG E\ WDNLQJ WKH ¿UVW
moment of the areas of the transformed section. The transformed area of the FRP may be obtained by multiplying
the area of FRP by the modular ratio of FRP to concrete.
Although this method ignores the difference in the initial
VWUDLQRIWKH)53WKHLQLWLDOVWUDLQGRHVQRWJUHDWO\LQÀXHQFH
the depth to the neutral axis in the elastic response range of
the member.
The stress in the steel under service loads computed
IURP(T VKRXOGEHFRPSDUHGDJDLQVWWKHOLPLWV
described in 10.2.8. The value of MsIURP(T LV
HTXDOWRWKHPRPHQWGXHWRDOOVXVWDLQHGORDGV GHDGORDGV
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
29
Fig. 10.2.10.1—Elastic strain and stress distribution.
DQGWKHVXVWDLQHGSRUWLRQRIWKHOLYHORDG SOXVWKHPD[LPXP
moment induced in a fatigue loading cycle, as shown in Fig.
Stress in FRP under service loads—The stress in
WKH)53UHLQIRUFHPHQWFDQEHFRPSXWHGXVLQJ(T with fs,sIURP(T (TXDWLRQ JLYHVWKH
stress in the FRP reinforcement under an applied moment
within the elastic response range of the member
⎛ E f ⎞ d f − kd
f f ,s = fs,s ⎜ ⎟
− ε bi E f ⎝ Es ⎠ d − kd
EHEDVHGRQWKHDFWXDOFRQGLWLRQRIWKHPHPEHU FUDFNHGRU
XQFUDFNHGVHFWLRQ WRGHWHUPLQHWKHVXEVWUDWHLQLWLDOVWUDLQ
Strain in FRP reinforcement—The maximum
strain that can be achieved in the FRP reinforcement will
be governed by strain limitations due to either concrete
crushing, FRP rupture, FRP debonding, or prestressing steel
rupture. The effective design strain for FRP reinforcement
at the ultimate-limit state for failure controlled by concrete
FUXVKLQJFDQEHFDOFXODWHGE\WKHXVHRI(T For failure controlled by prestressing steel rupture,
(T D FDQEHXVHG)RU*UDGHDQGNVL
DQG03D VWUDQGWKHYDOXHRIİpu to be used in
(T D LV
The stress in the FRP under service loads computed
IURP(T VKRXOGEHFRPSDUHGDJDLQVWWKHOLPLWV
GHVFULEHGLQ
10.3—Prestressed concrete members
This section presents guidance on the effect of adding
longitudinal FRP reinforcement to the tension face of a rectangular prestressed concrete member. The general concepts
outlined herein can be extended to nonrectangular shapes
7VHFWLRQV DQG ,VHFWLRQV DQG WR PHPEHUV ZLWK WHQVLRQ
compression, or both, nonprestressed steel reinforcement.
Members with bonded prestressing steel
Assumptions—In addition to the basic assumptions for concrete and FRP behavior for a reinforced concrete
section listed in 10.2.1, the following assumptions are made
LQFDOFXODWLQJWKHÀH[XUDOUHVLVWDQFHRIDSUHVWUHVVHGVHFWLRQ
strengthened with an externally applied FRP system:
D 6WUDLQ FRPSDWLELOLW\ FDQ EH XVHG WR GHWHUPLQH VWUDLQ
in the externally bonded FRP, strain in the nonprestressed
steel reinforcement, and the strain or strain change in the
prestressing steel.
E $GGLWLRQDO ÀH[XUDO IDLOXUH PRGH FRQWUROOHG E\
prestressing steel rupture should be investigated.
F )RU FDVHV ZKHUH WKH SUHVWUHVVLQJ VWHHO LV GUDSHG RU
harped, several sections along the span of the member
VKRXOGEHHYDOXDWHGWRYHULI\VWUHQJWKUHTXLUHPHQWV
G 7KHLQLWLDOVWUDLQRIWKHFRQFUHWHVXEVWUDWHİbi, should be
calculated and excluded from the effective strain in the FRP.
The initial strain can be determined from an elastic analysis of
the existing member, considering all loads that will be applied
to the member at the time of FRP installation. Analysis should
⎛ d f − c⎞
ε fe = (ε pu − ε pi ) ⎜
⎟ − ε bi ≤ ε fd D
⎝ dp − c⎠
in which
ε pi =
Pe
P
+ e
Ap E p Ac Ec
⎛ e2 ⎞
⎜⎝1 + r 2 ⎟⎠ E
Strength reduction factor²7R PDLQWDLQ D VXI¿cient degree of ductility, the strain in the prestressing steel at
WKHQRPLQDOVWUHQJWKVKRXOGEHFKHFNHG$GHTXDWHGXFWLOLW\LV
achieved if the strain in the prestressing steel at the nominal
strength is at least 0.013. Where this strain cannot be achieved,
the strength reduction factor is decreased to account for a less
ductile failure. The strength reduction factor for a member
SUHVWUHVVHG ZLWK VWDQGDUG DQG NVL DQG 03D SUHVWUHVVLQJVWHHOLVJLYHQE\(T ZKHUHİps is
the prestressing steel strain at the nominal strength
for ε ps ≥ 0.013
⎧0.90
⎪
0.25(ε ps − 0.010)
⎪
φ = ⎨0.65 +
for 0.010 < ε ps < 0.013
0.013 − 0.010
⎪
for ε ps ≤ 0.010
⎪0.65
⎩
Serviceability—To avoid inelastic deformations
of the strengthened member, the prestressing steel should
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30
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
be prevented from yielding under service load levels. The
stress in the steel under service load should be limited per
(T D DQG E ,QDGGLWLRQWKHFRPSUHVVLYH
stress in the concrete under service load should be limited to
45 percent of the compressive strength
fps,s”fpy
D
fps,s”fpu
E
When fatigue is a concern, the stress in the prestressing
steel due to transient live loads should be limited to 18 ksi
03D ZKHQ WKH UDGLL RI SUHVWUHVVLQJ VWHHO FXUYDWXUH
H[FHHGVIW P RUWRNVL 03D ZKHQWKHUDGLLRI
SUHVWUHVVLQJVWHHO FXUYDWXUH GRHV QRW H[FHHG IW P A linear interpolation should be used for radii between 12
DQGIW DQGP AASHTO 2004 7KHVHOLPLWVKDYH
EHHQYHUL¿HGH[SHULPHQWDOO\IRUSUHVWUHVVHGPHPEHUVZLWK
harped and straight strands strengthened with externally
ERQGHG)53 Rosenboom and Rizkalla 2006 Creep rupture and fatigue stress limits—To avoid
creep rupture of the FRP reinforcement under sustained
stresses or failure due to cyclic stresses and fatigue of the
FRP reinforcement, the stress in the FRP reinforcement
under these stress conditions should not exceed the limits
SURYLGHGLQ
Nominal strength—The calculation procedure to
compute nominal strength should satisfy strain compatibility
DQG IRUFH HTXLOLEULXP DQG VKRXOG FRQVLGHU WKH JRYHUQLQJ
mode of failure. The calculation procedure described herein
uses an iterative method similar to that discussed in 10.2.
For any assumed depth to the neutral axis, c, the effective
strain and stress in the FRP reinforcement can be computed from
(T DQG UHVSHFWLYHO\7KLVHTXDWLRQFRQVLGHUV
the governing mode of failure for the assumed neutral axis
GHSWK,IWKHOHIWWHUPRIWKHLQHTXDOLW\LQ(T FRQWUROV
FRQFUHWHFUXVKLQJFRQWUROVÀH[XUDOIDLOXUHRIWKHVHFWLRQ,IWKH
ULJKW WHUP RI WKH LQHTXDOLW\ FRQWUROV )53 IDLOXUH UXSWXUH RU
GHERQGLQJ FRQWUROVÀH[XUDOIDLOXUHRIWKHVHFWLRQ
The strain in the prestressed steel can be found from
(T D EDVHGRQVWUDLQFRPSDWLELOLW\
ε ps = ε pe +
Pe
Ac Ec
⎛ e2 ⎞
⎜⎝1 + r 2 ⎟⎠ + ε pnet ≤ 0.035
D
LQ ZKLFK İpe is the effective strain in the prestressing steel
DIWHUORVVHVDQGİpnet is the net tensile strain in the prestressing
steel beyond decompression, at the nominal strength. The
YDOXHRIİpnet will depend on the mode of failure, and can be
FDOFXODWHGXVLQJ(T E DQGF
⎛ dp − c⎞
ε pnet = 0.003 ⎜
for concrete crushing failure
⎝ c ⎟⎠
E
⎛ dp − c⎞
ε pnet = (ε fe + ε bi ) ⎜
⎟ for FRP rupture or debonding failure modes
⎝ d f − c⎠
F
The stress in the prestressing steel is calculated using the
material properties of the steel. For a typical seven-wire lowrelaxation prestressing strand, the stress-strain curve may
EH DSSUR[LPDWHG E\ WKH IROORZLQJ HTXDWLRQV Prestressed/
Precast Concrete Institute 2004
)RU*UDGHNVL 03D VWHHO
f ps
f ps
⎧
⎪28, 500ε
for ε ps ≤ 0.0076
ps
⎪⎪
=⎨
(in.-lb)
⎪
0.04
⎪250 −
for ε ps > 0.0076
ε ps − 0.0064
⎪⎩
G
⎧
⎪196, 500ε
for ε ps ≤ 0.0076
ps
⎪⎪
(SI)
=⎨
⎪
0.276
⎪1720 −
for ε ps > 0.0076
ε ps − 0.0064
⎪⎩
)RU*UDGHNVL 03D VWHHO
f ps
⎧
⎪28, 500ε
for ε ps ≤ 0.0086
ps
⎪⎪
=⎨
(in.-lb)
⎪
0.04
⎪270 −
for ε ps > 0.0086
ε ps − 0.007
⎪⎩
f ps
⎧
⎪196, 500ε
for ε ps ≤ 0.0086
ps
⎪⎪
(SI)
=⎨
⎪
0.276
⎪1860 −
for ε ps > 0.0086
ε ps − 0.007
⎪⎩
H
With the strain and stress in the FRP and prestressing steel
determined for the assumed neutral axis depth, internal force
HTXLOLEULXPPD\EHFKHFNHGXVLQJ(T I
Į1fcƍȕ1bc = Apfp + Af ffe
I
)RUWKHFRQFUHWHFUXVKLQJPRGHRIIDLOXUHWKHHTXLYDOHQW
FRPSUHVVLYHVWUHVVEORFNIDFWRUĮ1 can be taken as 0.85, and
ȕ1 can be estimated as described in 10.2.10. If FRP rupture,
cover delamination, or FRP debonding failure occurs, the
XVHRIHTXLYDOHQWUHFWDQJXODUFRQFUHWHVWUHVVEORFNIDFWRUVLV
appropriate. Methods considering a nonlinear stress distribution in the concrete can also be used.
The depth to the neutral axis, c, is found by simultaneRXVO\ VDWLVI\LQJ (T DQG D WR
I WKXVHVWDEOLVKLQJLQWHUQDOIRUFHHTXLOLEULXPDQG
strain compatibility. To solve for the depth of the neutral
axis, c, an iterative solution procedure can be used. An initial
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
value for cLV¿UVWDVVXPHGDQGWKHVWUDLQVDQGVWUHVVHVDUH
FDOFXODWHG XVLQJ (T DQG D WR
H $ UHYLVHG YDOXH IRU WKH GHSWK RI QHXWUDO D[LV
c LV WKHQ FDOFXODWHG IURP (T I 7KH FDOFXODWHG
and assumed values for c are then compared. If they agree,
then the proper value of c is reached. If the calculated and
assumed values do not agree, another value for c is selected,
and the process is repeated until convergence is attained.
7KH QRPLQDO ÀH[XUDO VWUHQJWK RI WKH VHFWLRQ ZLWK )53
H[WHUQDOUHLQIRUFHPHQWFDQEHFRPSXWHGXVLQJ(T J 7KHDGGLWLRQDOUHGXFWLRQIDFWRUȥf LVDSSOLHGWRWKHÀH[ural-strength contribution of the FRP reinforcement
β c⎞
β c⎞
⎛
⎛
M n = Ap f ps ⎜ d p − 1 ⎟ + ψ f Af f fe ⎜ d f − 1 ⎟
⎝
⎝
2 ⎠
2 ⎠
J
Stress in prestressing steel under service loads—
The stress in the prestressing steel can be calculated based
RQ WKH DFWXDO FRQGLWLRQ FUDFNHG RU XQFUDFNHG VHFWLRQ RI
the strengthened reinforced concrete section. The strain in
SUHVWUHVVLQJVWHHODWVHUYLFHİps,s, can be calculated as
ε ps , s = ε pe +
Pe
Ac Ec
⎛ e2 ⎞
⎜⎝1 + r 2 ⎟⎠ + ε pnet , s
D
LQZKLFKİpeLVWKHHIIHFWLYHSUHVWUHVVLQJVWUDLQDQGİpnet,s is
the net tensile strain in the prestressing steel beyond decomSUHVVLRQDWVHUYLFH7KHYDOXHRIİpnet,s depends on the effective section properties at service, and can be calculated using
(T E DQG F
ε pnet , s =
M se
for uncracked section at service
Ec I g
E
ε pnet , s =
M snet e
for cracked section at service
Ec I cr
F
where Msnet is the net service moment beyond decompression. The stress in the prestressing steel under service loads
FDQWKHQEHFRPSXWHGIURP(T G DQG H and compared against the limits described in 10.3.1.4.
Stress in FRP under service loads²(TXDWLRQ
JLYHV WKH VWUHVV LQ WKH )53 UHLQIRUFHPHQW XQGHU
an applied moment within the elastic response range of the
PHPEHU7KHFDOFXODWLRQSURFHGXUHIRUWKHLQLWLDOVWUDLQİbi at
the time of FRP installation will depend on the state of the
concrete section at the time of FRP installation and at service
condition. Prestressed sections can be uncracked at installation/uncracked at service, uncracked at installation/cracked at
service, or cracked at installation/cracked at service. The initial
VWUDLQRQWKHERQGHGVXEVWUDWHİbi, can be determined from an
elastic analysis of the existing member, considering all loads
that will be on the member during the installation of the FRP
system. The elastic analysis of the existing member should be
31
based on cracked or uncracked section properties, depending
on existing conditions. In most cases, the initial strain before
cracking is relatively small, and may conservatively be ignored
⎛ Ef ⎞ M y
f f , s = ⎜ ⎟ s b − ε bi E f
⎝ Ec ⎠ I
'HSHQGLQJRQWKHDFWXDOFRQGLWLRQDWVHUYLFH FUDFNHGRU
XQFUDFNHG WKH PRPHQW RI LQHUWLD I, can be taken as the
moment of inertia of the uncracked section transformed to
concrete, Itr, or the moment of inertia of the cracked section
transformed to concrete, Icr. The variable yb is the distance
from the centroidal axis of the gross section, neglecting reinIRUFHPHQWWRWKHH[WUHPHERWWRP¿EHU7KHFRPSXWHGVWUHVV
in the FRP under service loads should not exceed the limits
SURYLGHGLQ
10.4—Moment redistribution
Moment redistribution for continuous reinforced concrete
beams strengthened using externally bonded FRP can be used
to decrease factored moments calculated by elastic theory at
sections of maximum negative or maximum positive moment
IRUDQ\DVVXPHGORDGLQJDUUDQJHPHQWE\QRWPRUHWKDQİt
percent, to a maximum of 20 percent. Moment redistribution
is only permitted when the strain in the tension steel reinIRUFHPHQWİt, exceeds 0.0075 at the section at which moment
is reduced. Moment redistribution is not permitted where
approximate values of bending moments are used.
The reduced moment should be used for calculating redistributed moments at all other sections within the spans.
6WDWLFHTXLOLEULXPVKRXOGEHPDLQWDLQHGDIWHUUHGLVWULEXWLRQ
of moments for each loading arrangement. El-Refaie et al.
demonstrated that continuous reinforced concrete
beams strengthened with carbon FRP sheets can redistribute
moment in the order of 6 to 31 percent. They also concluded
that lower moment redistribution was achieved for beam
VHFWLRQVUHWUR¿WWHGZLWKKLJKHUDPRXQWVRIFDUERQ)53UHLQforcement. 6LOYDDQG,EHOO demonstrated that sections
that can develop a curvature ductility capacity greater than
2.0 can produce moment redistribution of at least 7.5 percent
of the design moment.
CHAPTER 11—SHEAR STRENGTHENING
)LEHUUHLQIRUFHGSRO\PHU )53 V\VWHPVKDYHEHHQVKRZQ
to increase the shear strength of existing concrete beams and
columns by wrapping or partially wrapping the members
0DOYDUHWDO&KDMHVHWDO1RUULVHWDO
Kachlakev and McCurry 2000 2ULHQWLQJ)53¿EHUVWUDQVverse to the axis of the member or perpendicular to potential shear cracks is effective in providing additional shear
VWUHQJWK 6DWRHWDO $QLQFUHDVHLQVKHDUVWUHQJWKPD\
EHUHTXLUHGZKHQÀH[XUDOVWUHQJWKHQLQJLVLPSOHPHQWHGWR
HQVXUHWKDWÀH[XUDOFDSDFLW\UHPDLQVFULWLFDO)OH[XUDOIDLOures are relatively more ductile in nature compared with
shear failures.
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32
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
11.1—General considerations
This chapter presents guidance on the calculation of added
shear strength resulting from the addition of FRP shear reinforcement to a reinforced concrete beam or column. The
additional shear strength that can be provided by the FRP
system is based on many factors, including geometry of the
beam or column, wrapping scheme, and existing concrete
strength, but should be limited in accordance with the
recommendations of &KDSWHU.
Shear strengthening using external FRP may be provided
at locations of expected plastic hinges or stress reversal
DQGIRUHQKDQFLQJSRVW\LHOGÀH[XUDOEHKDYLRURIPHPEHUV
in moment frames resisting seismic loads, as described in
Chapter 13.
11.2—Wrapping schemes
The three types of FRP wrapping schemes used to
increase the shear strength of prismatic, rectangular beams,
or columns are illustrated in Fig. 11.2. Completely wrapping the FRP system around the section on all four sides is
WKHPRVWHI¿FLHQWZUDSSLQJVFKHPHDQGLVPRVWFRPPRQO\
used in column applications where access to all four sides
of the column is available. In beam applications where an
integral slab makes it impractical to completely wrap the
member, the shear strength can be improved by wrapping
WKH)53V\VWHPDURXQGWKUHHVLGHVRIWKHPHPEHU 8ZUDS or bonding to two opposite sides of the member.
$OWKRXJKDOOWKUHHWHFKQLTXHVKDYHEHHQVKRZQWRLPSURYH
the shear strength of a rectangular member, completely
ZUDSSLQJWKHVHFWLRQLVWKHPRVWHI¿FLHQWIROORZHGE\WKH
three-sided U-wrap. Bonding to two sides of a beam is the
OHDVWHI¿FLHQWVFKHPH
For shear strengthening of circular members, only
complete circumferential wrapping of the section in which
the FRP is oriented perpendicular to the longitudinal axis of
WKHPHPEHU WKDWLVĮ GHJUHHV LVUHFRPPHQGHG
In all wrapping schemes, the FRP system can be installed
continuously along the span of a member or placed as
discrete strips. As discussed in , the potential effects
of entrapping moisture in the substrate when using continXRXVUHLQIRUFHPHQWVKRXOGEHFDUHIXOO\FRQVLGHUHG6SHFL¿F
means of allowing moisture vapor transmission out of the
substrate should be employed where appropriate.
11.3—Nominal shear strength
The design shear strength of a concrete member strengthHQHG ZLWK DQ )53 V\VWHP VKRXOG H[FHHG WKH UHTXLUHG VKHDU
VWUHQJWK (T D 7KHUHTXLUHGVKHDUVWUHQJWKRIDQ)53
strengthened concrete member should be computed with the
ORDGIDFWRUVUHTXLUHGE\ACI 318. The design shear strength
should be calculated by multiplying the nominal shear strength
E\WKHVWUHQJWKUHGXFWLRQIDFWRUࢥDVVSHFL¿HGE\$&,
ࢥVn•Vu
Fig. 11.2—Typical wrapping schemes for shear strengthening using FRP laminates.
WLRQVIURPWKHUHLQIRUFLQJVWHHO VWLUUXSVWLHVRUVSLUDOV DQG
WKHFRQFUHWH (T E $QDGGLWLRQDOUHGXFWLRQIDFWRUȥf
is applied to the contribution of the FRP system
ࢥVn ࢥ Vc + VsȥfVf E
where Vc and Vs are the concrete and internal reinforcing steel
contributions to shear capacity calculated using the provisions of ACI 318, respectively. For prestressed members, Vc
is the minimum of Vci and VcwGH¿QHGE\$&,
Based on a reliability analysis using data from BousVHOKDP DQG &KDDOODO , 'HQLDXG DQG &KHQJ , )XQDNDZD HW DO , 0DWWK\V DQG 7ULDQWD¿OORX
, and 3HOOHJULQR DQG 0RGHQD , the reducWLRQ IDFWRU ȥf of 0.85 is recommended for the three-sided
FRP U-wrap or two-opposite-sides strengthening schemes.
,QVXI¿FLHQWH[SHULPHQWDOGDWDH[LVWWRSHUIRUPDUHOLDELOLW\
DQDO\VLV IRU IXOO\ZUDSSHG VHFWLRQV KRZHYHU WKHUH VKRXOG
be less variability with this strengthening scheme, as it is
OHVVERQGGHSHQGHQWDQGWKHUHIRUHWKHUHGXFWLRQIDFWRUȥf
RILVUHFRPPHQGHG7KHȥf factor was calibrated based
on design material properties. These recommendations are
given in Table 11.3.
Table 11.3—Recommended additional reduction
factors for FRP shear reinforcement
ȥf Completely wrapped members
ȥf = 0.85
Three-side and two-opposite-sides schemes
11.4—FRP contribution to shear strength
Figure 11.4 illustrates the dimensional variables used in
shear-strengthening calculations for FRP laminates. The
contribution of the FRP system to shear strength of a member
LV EDVHG RQ WKH ¿EHU RULHQWDWLRQ DQG DQ DVVXPHG FUDFN
SDWWHUQ .KDOLIDHWDO 7KHVKHDUVWUHQJWKSURYLGHGE\
the FRP reinforcement can be determined by calculating the
force resulting from the tensile stress in the FRP across the
assumed crack. The shear contribution of the FRP shear reinIRUFHPHQWLVWKHQJLYHQE\(T D
Vf =
Afv f fe (sin α + cos α )d fv
sf
D
D
For rectangular sections
The nominal shear strength of an FRP-strengthened
concrete member can be determined by adding the contribution of the FRP external shear reinforcement to the contribu-
Afv = 2ntfwf
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
33
7KH ERQGUHGXFWLRQ FRHI¿FLHQW LV D IXQFWLRQ RI WKH
concrete strength, the type of wrapping scheme used, and
WKHVWLIIQHVVRIWKHODPLQDWH7KHERQGUHGXFWLRQFRHI¿FLHQW
FDQ EH FRPSXWHG IURP (T E WKURXJK H .KDOLIDHWDO
Fig. 11.4—Illustration of the dimensional variables used
LQ VKHDUVWUHQJWKHQLQJ FDOFXODWLRQV IRU UHSDLU UHWUR¿W RU
strengthening using FRP laminates.
For circular sections, dfv is taken as 0.8 times the diameter
of the section and
Afv ʌ ntfwf
F
The tensile stress in the FRP shear reinforcement at
nominal strength is directly proportional to the strain that
can be developed in the FRP shear reinforcement at nominal
strength
ffe = Efİfe
7KLVVWUDLQOLPLWDWLRQLVEDVHGRQWHVWLQJ Priestley et al.
DQGH[SHULHQFH+LJKHUVWUDLQVVKRXOGQRWEHXVHGIRU
FRP shear-strengthening applications.
11.4.1.2 Bonded U-wraps or bonded face plies—FRP
V\VWHPV WKDW GR QRW HQFORVH WKH HQWLUH VHFWLRQ WZR DQG
WKUHHVLGHGZUDSV KDYHEHHQREVHUYHGWRGHODPLQDWHIURP
the concrete before the loss of aggregate interlock of the
section. For this reason, bond stresses have been analyzed to
GHWHUPLQHWKHHI¿FLHQF\RIWKHVHV\VWHPVDQGWKHHIIHFWLYH
VWUDLQWKDWFDQEHDFKLHYHG 7ULDQWD¿OORX 7KHHIIHFWLYHVWUDLQLVFDOFXODWHGXVLQJDERQGUHGXFWLRQFRHI¿FLHQWțv
applicable to shear
İfe țvİfu”
k1k2 Le
≤ 0.75
468ε fu
(in.-lb)
kk L
κ v = 1 2 e ≤ 0.75
11, 900ε fu
E
(SI)
The active bond length Le is the length over which the
majority of the bond stress is maintained. This length is
JLYHQE\(T F
Le =
2500
(in.-lb)
(nt f E f )0.58
23, 300
Le =
(SI)
(nt f E f )0.58
F
G
11.4.1 Effective strain in FRP laminates—The effective
strain is the maximum strain that can be achieved in the FRP
system at the nominal strength and is governed by the failure
mode of the FRP system and of the strengthened reinforced
concrete member. The licensed design professional should
consider all possible failure modes and use an effective strain
representative of the critical failure mode. The following
subsections provide guidance on determining this effective
VWUDLQIRUGLIIHUHQWFRQ¿JXUDWLRQVRI)53ODPLQDWHVXVHGIRU
shear strengthening of reinforced concrete members.
11.4.1.1 Completely wrapped members—For reinforced
concrete column and beam members completely wrapped
by FRP, loss of aggregate interlock of the concrete has been
REVHUYHGWRRFFXUDW¿EHUVWUDLQVOHVVWKDQWKHXOWLPDWH¿EHU
strain. To preclude this mode of failure, the maximum strain
used for design should be limited to 0.4 percent for members
WKDWDUHFRPSOHWHO\ZUDSSHGZLWK)53 (T İfe ”İfu
κv =
D
7KH ERQGUHGXFWLRQ FRHI¿FLHQW DOVR UHOLHV RQ WZR PRGL¿FDWLRQ IDFWRUV k1 and k2, that account for the concrete
strength and the type of wrapping scheme used, respectively.
([SUHVVLRQVIRUWKHVHPRGL¿FDWLRQIDFWRUVDUHJLYHQLQ(T
G DQG H
⎛ f′ ⎞
k1 = ⎜ c ⎟
⎝ 4000 ⎠
⎛ f '⎞
k1 = ⎜ c ⎟
⎝ 27 ⎠
2/3
(in.-lb)
2/3
G
(SI)
⎧ d fv − Le
for U-wraps
⎪
⎪ d fv
k2 = ⎨
⎪ d fv − 2 Le for two sides bonded
⎪ d fv
⎩
H
7KH PHWKRGRORJ\ IRU GHWHUPLQLQJ țv has been validated
for members in regions of high shear and low moment, such
as monotonically loaded simply supported beams. Although
WKHPHWKRGRORJ\KDVQRWEHHQFRQ¿UPHGIRUVKHDUVWUHQJWKHQLQJLQDUHDVVXEMHFWHGWRFRPELQHGKLJKÀH[XUDODQGVKHDU
stresses or in regions where the web is primarily in compresVLRQ QHJDWLYH PRPHQW UHJLRQV LW LV VXJJHVWHG WKDW țv is
VXI¿FLHQWO\FRQVHUYDWLYHIRUVXFKFDVHV7KHGHVLJQSURFHdures outlined herein have been developed by a combination
RIDQDO\WLFDODQGHPSLULFDOUHVXOWV .KDOLIDHWDO Anchorage details have been used to develop higher
strains in bonded U-wraps used in shear strengthening applications. Anchorage systems include mechanical fasteners,
)53VWULSV¿EHUDQFKRUVDQGQHDUVXUIDFHPRXQWHG 160 DQFKRUVH[DPSOHVDUHVKRZQVFKHPDWLFDOO\LQ)LJE
.KDOLID HW DO Kalfat et al. 2013 Grelle and Sneed
2013 3URSHUO\ DQFKRUHG 8ZUDSV FDQ EH GHVLJQHG WR IDLO
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34
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
E\)53UXSWXUH Belarbi et al. 2011 ,QQRFDVHKRZHYHU
should the effective strain in the anchored FRP U-wrap
H[FHHGWKHOHVVHURIRUİfuDQGȥf = 0.85 remains
appropriate for anchored U-wraps.
11.4.2 Spacing—Spaced FRP strips used for shear
strengthening should be investigated to evaluate their
contribution to the shear strength. Spacing should adhere
to the limits prescribed by ACI 318 for internal steel shear
UHLQIRUFHPHQW7KHVSDFLQJRI)53VWULSVLVGH¿QHGDVWKH
distance between the centerline of the strips.
11.4.3 Reinforcement limits—The total shear strength
provided by reinforcement should be taken as the sum of
the contribution of the FRP shear reinforcement and the
steel shear reinforcement. The sum of the shear strengths
provided by the shear reinforcement should be limited based
on the criteria given for steel alone in ACI 318
Vs + V f ≤ 8 f c′bw d
(in.-lb)
Vs + V f ≤ 0.66 f c′bw d (SI)
For circular sections, bwdLQ(T LVWDNHQDVD2,
where D is the member diameter.
CHAPTER 12—STRENGTHENING OF MEMBERS
SUBJECTED TO AXIAL FORCE OR COMBINED
AXIAL AND BENDING FORCES
&RQ¿QHPHQW RI UHLQIRUFHG FRQFUHWH FROXPQV E\ PHDQV
RI ¿EHUUHLQIRUFHG SRO\PHU )53 MDFNHWV FDQ EH XVHG WR
enhance their strength and ductility. An increase in capacity
is an immediate outcome typically expressed in terms of
improved peak load resistance. Ductility enhancement, on
WKHRWKHUKDQGUHTXLUHVPRUHFRPSOH[FDOFXODWLRQVWRGHWHUmine the ability of a member to sustain rotation and drift
without a substantial loss in strength. This chapter applies
RQO\WRPHPEHUVFRQ¿QHGZLWK)53V\VWHPV
12.1—Pure axial compression
FRP systems can be used to increase the axial compression
VWUHQJWKRIDFRQFUHWHPHPEHUE\SURYLGLQJFRQ¿QHPHQWZLWK
DQ )53 MDFNHW 1DQQL DQG %UDGIRUG 7RXWDQML &RQ¿QLQJDFRQFUHWHPHPEHULVDFFRPSOLVKHGE\RULHQWLQJ
WKH¿EHUVWUDQVYHUVHWRWKHORQJLWXGLQDOD[LVRIWKHPHPEHU
,QWKLVRULHQWDWLRQWKHWUDQVYHUVHRUKRRS¿EHUVDUHVLPLODU
to conventional spiral or tie reinforcing steel. Any contribuWLRQRIORQJLWXGLQDOO\DOLJQHG¿EHUVWRWKHD[LDOFRPSUHVVLRQ
strength of a concrete member should be neglected.
)53MDFNHWVSURYLGHSDVVLYHFRQ¿QHPHQWWRWKHFRPSUHVsion member, remaining unstressed until dilation and
cracking of the wrapped compression member occur. For
this reason, intimate contact between the FRP jacket and the
concrete member is critical.
'HSHQGLQJ RQ WKH OHYHO RI FRQ¿QHPHQW WKH XQLD[LDO
stress-strain curve of a reinforced concrete column could be
depicted by one of the curves in Fig. 12.1a, where fcƍ DQG
fccƍUHSUHVHQWWKHSHDNFRQFUHWHVWUHQJWKVIRUXQFRQ¿QHGDQG
FRQ¿QHGFDVHVUHVSHFWLYHO\7KHVHVWUHQJWKVDUHFDOFXODWHG
as the peak load minus the contribution of the steel reinforce-
ment, all divided by the cross-sectional area of the concrete.
7KHXOWLPDWHVWUDLQRIWKHXQFRQ¿QHGPHPEHUFRUUHVSRQGLQJ
to 0.85fcƍ &XUYH D LV İcu7KH VWUDLQ İccu corresponds to:
D fccƍLQWKHFDVHRIWKHOLJKWO\FRQ¿QHGPHPEHU &XUYH
E DQGE WKHIDLOXUHVWUDLQLQERWKWKHKHDYLO\FRQ¿QHG
VRIWHQLQJFDVH WKHIDLOXUHVWUHVVLVODUJHUWKDQfccƍ &XUYH
F RULQWKHKHDYLO\FRQ¿QHGKDUGHQLQJFDVH &XUYH G 7KH GH¿QLWLRQ RI İccu at 0.85fccƍ RU OHVV LV DUELWUDU\
although consistent with modeling of conventional concrete
+RJQHVWDG DQGVXFKWKDWWKHGHVFHQGLQJEUDQFKRIWKH
VWUHVVVWUDLQ FXUYH DW WKDW OHYHO RI VWUHVV fccƍ RU KLJKHU is not as sensitive to the test procedure in terms of rate of
ORDGLQJDQGVWLIIQHVVRIWKHHTXLSPHQWXVHG
The axial compressive strength of a nonslender, normalZHLJKWFRQFUHWHPHPEHUFRQ¿QHGZLWKDQ)53MDFNHWPD\EH
FDOFXODWHGXVLQJWKHFRQ¿QHGFRQFUHWHVWUHQJWK (T D DQG E 7KHD[LDOIRUFHDFWLQJRQDQ)53VWUHQJWKHQHG
concrete member should be computed using the load factors
UHTXLUHGE\$&,DQGWKHYDOXHVRIWKHࢥIDFWRUVDVHVWDElished in ACI 318 for both types of transverse reinforcing
VWHHO VSLUDOVRUWLHV DSSO\
For nonprestressed members with existing steel spiral
reinforcement
ࢥPn ࢥ>fccƍ Ag – Ast fy Ast@
D
For nonprestressed members with existing steel-tie
reinforcement
ࢥPn ࢥ>fccƍ Ag – Ast fy Ast@
E
Several models that simulate the stress-strain behavior
RI )53FRQ¿QHG FRPSUHVVLRQ VHFWLRQV DUH DYDLODEOH LQ WKH
OLWHUDWXUH Teng et al. 2002De Lorenzis and Tepfers 2003
Lam and Teng 2003a 7KHVWUHVVVWUDLQPRGHOE\/DPDQG
7HQJ Db IRU )53FRQ¿QHG FRQFUHWH LV LOOXVWUDWHG LQ
Fig. 12.1b and computed using the following expressions
⎧
( Ec − E2 ) 2
E
ε
−
⎪ c c
4 f c′
fc = ⎨
⎪ f ′+ E ε
2 c
⎩ c
0 ≤ ε c ≤ ε t′
F
ε t′ ≤ ε c ≤ ε c,max
İc,max”İccu”
G
E2 =
f cc′ − f c′
ε ccu
H
ε t′ =
2 f c′
Ec − E2
I
7KH PD[LPXP FRQ¿QHG FRQFUHWH FRPSUHVVLYH VWUHQJWK
fccƍDQGWKHPD[LPXPFRQ¿QHPHQWSUHVVXUHfƐ are calculated
XVLQJ(T J DQG K UHVSHFWLYHO\ /DPDQG7HQJ
DE ZLWKWKHLQFOXVLRQRIDQDGGLWLRQDOUHGXFWLRQIDFWRU
ȥf @Seismicisolation
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American Concrete Institute – Copyrighted © Material – www.concrete.org
MCPOL Licensed to: McMaster University Library
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
fccƍ fcƍȥfțafƐ
f =
2 E f nt f ε fe
D
35
J
K
,Q(T J fcƍLVWKHXQFRQ¿QHGF\OLQGHUFRPSUHVVLYH
VWUHQJWK RI FRQFUHWH DQG WKH HI¿FLHQF\ IDFWRU ța accounts
for the geometry of the section, circular and noncircular, as
GH¿QHG LQ DQG ,Q (T K WKH HIIHFWLYH
VWUDLQLQWKH)53DWIDLOXUHİfe, is given by
İfe țİİfu
L
7KH)53VWUDLQHI¿FLHQF\IDFWRUțİ accounts for the premaWXUHIDLOXUHRIWKH)53V\VWHP Pessiki et al. 2001 UHODWHG
primarily to stress concentration regions caused by cracking
of the concrete as it dilates. Based on experimental calibraWLRQ XVLQJ PDLQO\ FDUERQ )53 &)53 FRQ¿QHG FRQFUHWH
specimens, an average value of 0.586 was computed for
țİ by /DPDQG7HQJ D . Similarly, a database of 251
WHVW UHVXOWV Harries and Carey 2003 FRPSXWHG D YDOXH
RI țİ = 0.58, whereas experimental tests on medium- and
ODUJHVFDOHFROXPQVUHVXOWHGLQYDOXHVRIțİ = 0.57 and 0.61,
UHVSHFWLYHO\ Carey and Harries 2005 %DVHG RQ WHVWV E\ /DP DQG 7HQJ Db WKH UDWLR fƐ/
fcƍ VKRXOG QRW EH OHVV WKDQ 7KLV LV WKH PLQLPXP OHYHO
RI FRQ¿QHPHQW UHTXLUHG WR DVVXUH D QRQGHVFHQGLQJ VHFRQG
branch in the stress-strain performance, as shown by Curve
G LQ )LJ D 7KLV OLPLWDWLRQ ZDV ODWHU FRQ¿UPHG IRU
circular cross sections by 6SRHOVWUDDQG0RQWL using
WKHLUDQDO\WLFDOPRGHO$VWUDLQHI¿FLHQF\IDFWRUțİ of 0.55 and
DPLQLPXPFRQ¿QHPHQWUDWLRfƐ/fcƍRIVKRXOGEHXVHG
7KH PD[LPXP FRPSUHVVLYH VWUDLQ LQ WKH )53FRQ¿QHG
FRQFUHWH İccu FDQ EH IRXQG XVLQJ (T M Concrete
Society 2004 7KHPD[LPXPFRQFUHWHVWUDLQİc,max, used in
(T F VKRXOG EH OLPLWHG WR WR SUHYHQW H[FHVVLYH
cracking and the resulting loss of concrete integrity.
0.45
⎛
f ⎛ ε fe ⎞ ⎞
ε ccu = ε c′ ⎜1.50 + 12κ b ⎜ ⎟ ⎟
f c′ ⎝ ε c′ ⎠ ⎠
⎝
M
,Q (T M WKH HI¿FLHQF\ IDFWRU țb accounts for the
geometry of the section in the calculation of the ultimate
D[LDOVWUDLQDVGH¿QHGLQDQG
Strength enhancement for compression members with fcƍ
RISVL 03D RUKLJKHUKDVQRWEHHQH[SHULPHQWDOO\ YHUL¿HG (QKDQFHPHQW RI FRQFUHWH KDYLQJ VWUHQJWK fcƍ
LQH[FHVVRISVL 03D VKRXOGEHEDVHGRQH[SHULmental testing.
12.1.1 Circular cross sections—FRP jackets are most
HIIHFWLYHDWFRQ¿QLQJPHPEHUVZLWKFLUFXODUFURVVVHFWLRQV
'HPHUV DQG 1HDOH Pessiki et al. 2001 +DUULHV DQG
&DUH\Youssef 2003Matthys et al. 2005Rocca et al.
2006 7KH)53V\VWHPSURYLGHVDFLUFXPIHUHQWLDOO\XQLIRUP
FRQ¿QLQJSUHVVXUHWRWKHUDGLDOH[SDQVLRQRIWKHFRPSUHVVLRQ PHPEHU ZKHQ WKH ¿EHUV DUH DOLJQHG WUDQVYHUVH WR WKH
)LJ D²6FKHPDWLF VWUHVVVWUDLQ EHKDYLRU RI XQFRQ¿QHG
DQGFRQ¿QHGUHLQIRUFHGFRQFUHWHFROXPQV 5RFFDHWDO )LJE²6WUHVVVWUDLQPRGHOIRU)53FRQ¿QHGFRQFUHWH
(Lam and Teng 2003a).
longitudinal axis of the member. For circular cross sections,
WKHVKDSHIDFWRUVțaDQGțbLQ(T J DQG M UHVSHFtively, can be taken as 1.0.
12.1.2 Noncircular cross sections—Testing has shown
WKDW FRQ¿QLQJ VTXDUH DQG UHFWDQJXODU PHPEHUV ZLWK )53
jackets can provide marginal increases in the maximum axial
compressive strength fccƍRIWKHPHPEHU Pessiki et al. 2001
Wang and Restrepo 2001+DUULHVDQG&DUH\<RXVVHI
5RFFDHWDO 7KHSURYLVLRQVLQWKLVJXLGHDUHQRW
recommended for members featuring side aspect ratios h/b
greater than 2.0, or face dimensions b or h exceeding 36 in.
PP XQOHVVWHVWLQJGHPRQVWUDWHVWKHLUHIIHFWLYHQHVV
For noncircular cross sections, fƐ LQ (T K FRUUHVSRQGVWRWKHPD[LPXPFRQ¿QLQJSUHVVXUHRIDQHTXLYDOHQW
circular cross section with diameter DHTXDOWRWKHGLDJRQDO
of the rectangular cross section
D = b2 + h2
D
7KHVKDSHIDFWRUVțaLQ(T J DQGțbLQ(T M depend on two parameters: the cross-sectional area of effecWLYHO\FRQ¿QHGFRQFUHWHAe, and the side-aspect ratio h/b, as
VKRZQLQ(T E DQG F UHVSHFWLYHO\
κa =
Ae
Ac
⎛ b⎞
⎜⎝ ⎟⎠
h
κb =
Ae
Ac
⎛ h⎞
⎜⎝ ⎟⎠
b
@Seismicisolation
@Seismicisolation
2
E
0.5
F
American Concrete Institute – Copyrighted © Material – www.concrete.org
MCPOL Licensed to: McMaster University Library
36
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
exceed the creep rupture stress limit. In addition, axial deformations under service loads should be investigated to evaluate their effect on the performance of the structure.
Fig. 12.1.2—Equivalent circular cross section (Lam and
Teng 2003b).
The generally accepted theoretical approach for the
GH¿QLWLRQ RI Ae consists of four parabolas within which
WKH FRQFUHWH LV IXOO\ FRQ¿QHG RXWVLGH RI ZKLFK QHJOLJLEOH
FRQ¿QHPHQWRFFXUV )LJ 7KHVKDSHRIWKHSDUDERODV
DQGWKHUHVXOWLQJHIIHFWLYHFRQ¿QHPHQWDUHDLVDIXQFWLRQRI
WKH GLPHQVLRQV RI WKH FROXPQ b and h WKH UDGLXV RI WKH
corners, rcDQGWKHORQJLWXGLQDOVWHHOUHLQIRUFHPHQWUDWLRȡg,
and can be expressed as
12.2—Combined axial compression and bending
Wrapping with an FRP jacket can also provide strength
enhancement for a member subjected to combined axial
FRPSUHVVLRQDQGÀH[XUH 1RVKRSaadatmanesh et al.
Chaallal and Shahawy 2000 Sheikh and Yau 2002
Iacobucci et al. 2003 Bousias et al. 2004 Elnabelsy and
Saatcioglu 2004Harajli and Rteil 2004Sause et al. 2004
Memon and Sheikh 2005 )RUSUHGLFWLQJWKHHIIHFWRI)53FRQ¿QHPHQWRQVWUHQJWK
HQKDQFHPHQW(T D DQG E DUHDSSOLFDEOHZKHQ
WKHHFFHQWULFLW\SUHVHQWLQWKHPHPEHULVOHVVWKDQRUHTXDO
to 0.1h. When the eccentricity is larger than 0.1h, the methRGRORJ\ DQG HTXDWLRQV SUHVHQWHG LQ FDQ EH XVHG WR
determine the concrete material properties of the member
cross section under compressive stress. Based on that, the
D[LDOORDGPRPHQW P-M LQWHUDFWLRQGLDJUDPIRUWKH)53
FRQ¿QHGPHPEHUFDQEHFRQVWUXFWHGXVLQJZHOOHVWDEOLVKHG
SURFHGXUHV Bank 2006 The following limitations apply for members subjected to
combined axial compression and bending:
D 7KHHIIHFWLYHVWUDLQLQWKH)53MDFNHWVKRXOGEHOLPLWHG
WRWKHYDOXHJLYHQLQ(T WRHQVXUHWKHVKHDULQWHJULW\
RIWKHFRQ¿QHGFRQFUHWH
İfe ”țİİfu
Ae
=
Ac
1−
⎡⎛ b ⎞
2 ⎤
⎢⎜⎝ h ⎟⎠ (h − 2rc ) ⎥
⎥
⎢
⎢ ⎛ h⎞
2⎥
⎢ + ⎜⎝ b ⎟⎠ (b − 2rc ) ⎥
⎦
⎣
3 Ag
1 − ρg
− ρg
G
12.1.3 Serviceability considerations—As loads approach
factored load levels, damage to the concrete in the form of
VLJQL¿FDQWFUDFNLQJLQWKHUDGLDOGLUHFWLRQPLJKWRFFXU7KH
FRP jacket contains the damage and maintains the structural
integrity of the column. At service load levels, however,
this type of damage should be avoided. In this way, the FRP
jacket will only act during overloading conditions that are
temporary in nature.
To ensure that radial cracking will not occur under service
loads, the transverse strain in the concrete should remain
below its cracking strain at service load levels. This corresponds to limiting the compressive stress in the concrete to
0.65fcƍ,QDGGLWLRQWKHVHUYLFHVWUHVVLQWKHORQJLWXGLQDOVWHHO
should remain below 0.60fy to avoid plastic deformation
XQGHUVXVWDLQHGRUF\FOLFORDGV%\PDLQWDLQLQJWKHVSHFL¿HG
stress in the concrete at service, the stress in the FRP jacket
ZLOOEHUHODWLYHO\ORZ7KHMDFNHWLVRQO\VWUHVVHGWRVLJQL¿cant levels when the concrete is transversely strained above
the cracking strain and the transverse expansion becomes
large. Service load stresses in the FRP jacket should never
E 7KH VWUHQJWK HQKDQFHPHQW FDQ RQO\ EH FRQVLGHUHG
when the applied ultimate axial force and bending moment,
Pu and Mu, respectively, fall above the line connecting the
origin and the balanced point in the P-M diagram for the
XQFRQ¿QHGPHPEHU )LJ 7KLVOLPLWDWLRQVWHPVIURP
WKH IDFW WKDW VWUHQJWK HQKDQFHPHQW LV RQO\ VLJQL¿FDQW IRU
members in which compression failure is the controlling
PRGH %DQN P-M diagrams may be developed by satisfying strain
FRPSDWLELOLW\DQGIRUFHHTXLOLEULXPXVLQJWKHPRGHOIRUWKH
VWUHVVVWUDLQ EHKDYLRU IRU )53FRQ¿QHG FRQFUHWH SUHVHQWHG
LQ(T F WKURXJK I )RUVLPSOLFLW\WKHSRUWLRQRI
WKH XQFRQ¿QHG DQG FRQ¿QHG P-M diagrams corresponding
to compression-controlled failure can be reduced to two
ELOLQHDUFXUYHVSDVVLQJWKURXJKWKUHHSRLQWV )LJ )RU
values of eccentricity greater than 0.1h and up to the point
corresponding to the balanced condition, the methodology
provided in Appendix D may be used for the computation of
DVLPSOL¿HGLQWHUDFWLRQGLDJUDP7KHYDOXHVRIWKHࢥIDFWRUV
as established in ACI 318 for both types of transverse reinIRUFLQJVWHHO VSLUDOVRUWLHV DSSO\
12.3—Ductility enhancement
Increased ductility of a section results from the ability to
develop greater compressive strains in the concrete before
FRPSUHVVLYHIDLOXUH 6HLEOHHWDO 7KH)53MDFNHWFDQ
also serve to delay buckling of longitudinal steel reinforce-
@Seismicisolation
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American Concrete Institute – Copyrighted © Material – www.concrete.org
MCPOL Licensed to: McMaster University Library
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Fig. 12.2—Representative interaction diagram.
ment in compression and to clamp lap splices of longitudinal
steel reinforcement.
For seismic applications, FRP jackets should be designed
WRSURYLGHDFRQ¿QLQJVWUHVVVXI¿FLHQWWRGHYHORSFRQFUHWH
compression strains associated with the displacement
demands as described in Chapter 13. Shear forces should
also be evaluated in accordance with Chapter 11 to prevent
brittle shear failure in accordance with ACI 318.
12.3.1 Circular cross sections—The maximum compresVLYH VWUDLQ IRU )53FRQ¿QHG PHPEHUV ZLWK FLUFXODU FURVV
VHFWLRQV FDQ EH IRXQG IURP (T M ZLWK fccƍ IURP (T
J DQGXVLQJțb = 1.0.
12.3.2 Noncircular cross sections—The maximum
FRPSUHVVLYHVWUDLQIRU)53FRQ¿QHGPHPEHUVZLWKVTXDUH
RUUHFWDQJXODUVHFWLRQVFDQEHIRXQGIURP(T M ZLWK
fccƍIURP(T J DQGXVLQJțbDVJLYHQLQ(T F 7KH FRQ¿QLQJ HIIHFW RI )53 MDFNHWV VKRXOG EH DVVXPHG WR
be negligible for rectangular sections with aspect ratio h/b
exceeding 2.0, or face dimensions b or h exceeding 36 in.
PP XQOHVVWHVWLQJGHPRQVWUDWHVWKHLUHIIHFWLYHQHVV
12.4—Pure axial tension
FRP systems can be used to provide additional tensile
strength to a concrete member. Due to the linear-elastic
nature of FRP materials, the tensile contribution of the FRP
system is directly related to its strain and is calculated using
Hooke’s Law.
The tension capacity provided by the FRP is limited by the
design tensile strength of the FRP and the ability to transfer
VWUHVVHVLQWRWKHVXEVWUDWHWKURXJKERQG 1DQQLHWDO The effective strain in the FRP can be determined based on
WKH FULWHULD JLYHQ IRU VKHDU VWUHQJWKHQLQJ LQ (T WKURXJK G 7KHYDOXHRIk2LQ(T E FDQEH
taken as 1.0. A minimum bonded length of Ɛdf, as calculated
in 14.1.3, should be provided to develop this level of strain.
CHAPTER 13—SEISMIC STRENGTHENING
0DQ\VWUHQJWKHQLQJWHFKQLTXHVKDYHEHHQGHYHORSHGDQG
XVHG IRU UHSDLU DQG UHKDELOLWDWLRQ RI HDUWKTXDNH GDPDJHG
DQG VHLVPLFDOO\ GH¿FLHQW VWUXFWXUHV Federal Emergency
Management Agency 2006 ,GHQWL¿FDWLRQ RI DQ HIIHFWLYH
rehabilitation method is directly related to the outcome of a
seismic evaluation of the structure and is based on consideration of many factors, including type of structure, rehabilitation objective, strengthening scheme effectiveness,
constructability, and cost.
37
$ FODVVL¿FDWLRQ RI VHLVPLF UHKDELOLWDWLRQ PHWKRGV IRU
buildings in ASCE/SEI 41 and $&,5 gives the following
VWUDWHJLHV ORFDO PRGL¿FDWLRQ RI FRPSRQHQWV UHPRYDO RU
lessening of existing irregularities and discontinuities,
global structural stiffening, global structural strengthening,
mass reduction, seismic isolation, and supplemental energy
dissipation. Strengthening using FRP materials and systems
DOORZV IRU ORFDO PRGL¿FDWLRQ RI FRPSRQHQWV DQG FDQ EH
implemented in improving the overall seismic performance
of the structure. The main advantages of FRP strengthening
can be summarized as follows:
D $WWKHFRPSRQHQWOHYHO)53VWUHQJWKHQLQJFDQEHXVHG
WR HI¿FLHQWO\ PLWLJDWH EULWWOH PHFKDQLVPV RI IDLOXUH7KHVH
PD\ LQFOXGH VKHDU IDLOXUH RI XQFRQ¿QHG EHDPFROXPQ
MRLQWV VKHDU IDLOXUH RI EHDPV FROXPQV RU ERWK DQG ODS
splice failure. FRP strengthening can also be used to increase
WKH ÀH[XUDO FDSDFLW\ RI UHLQIRUFHG FRQFUHWH PHPEHUV WR
UHVLVWWKHEXFNOLQJRIÀH[XUDOVWHHOEDUVDQGWRLQFUHDVHWKH
inelastic rotational capacity of reinforced concrete members.
E ,PSOHPHQWLQJ )53 VWUHQJWKHQLQJ VFKHPHV WUDQVODWHV
into an increase in the global displacement and energy
dissipation capacities of the structure, thus improving the
overall behavior of reinforced concrete structures subjected
to seismic actions.
F )53VKHDUVWUHQJWKHQLQJDQGFRQ¿QHPHQWKDVDVPDOO
effect on the stiffness or mass of the structure. In such cases,
a reevaluation of the seismic demand after strengthening is
W\SLFDOO\ QRW UHTXLUHG :KHQ WKH VWUXFWXUDO VWLIIQHVV QHHGV
to be increased, FRP strengthening of local components can
EHFRXSOHGZLWKRWKHUWUDGLWLRQDOJOREDOXSJUDGHWHFKQLTXHV
0DQ\UHVHDUFKSURJUDPVKDYHHYDOXDWHGWKHDGHTXDF\RI
externally bonded FRP composites for seismic rehabilitaWLRQ RI FRQFUHWH VWUXFWXUHV Haroun et al. 2005 Pantelides
et al. 2000Ghobarah and Said 2002Gergely et al. 2000
$QWRQRSRXORV DQG7ULDQWD¿OORX Hamed and Rabinovitch 2005Pampanin et al. 2007Di Ludovico et al. 2008a 2WKHU UHVHDUFK SURJUDPV KDYH FRQ¿UPHG WKH SRWHQWLDO RI
)53 WHFKQLTXHV IRU XSJUDGLQJ WKH VHLVPLF SHUIRUPDQFH RI
ORFDOHOHPHQWVVXFKDVUHLQIRUFHGFRQFUHWHFROXPQV Bousias
et al. 2004 DQGFRQQHFWLRQV $QWRQRSRXORVDQG7ULDQWD¿OORX
Prota et al. 2004 5HVHDUFKUHVXOWVIRU)53DSSOLHGDW
the local element or partial structural frame level were subseTXHQWO\ YDOLGDWHG RQ IXOOVFDOH VWUXFWXUHV 3DQWHOLGHV HW DO
2004Balsamo et al. 2005Engindeniz et al. 2008a,b In addition, several structures that include FRP-strengthened
members have experienced seismic events. Failure of these
members has not been reported.
This chapter presents design guidelines for the seismic
strengthening of reinforced concrete elements using externally bonded FRP composites. The design guidelines
described herein are intended to be used in conjunction
with the fundamental concepts, analysis procedures, design
philosophy, seismic rehabilitation objectives, and acceptance criteria set forth in documents such as ASCE/SEI
DQG $&, 5 6WUHQJWKHQLQJ RI 5& EXLOGLQJ FRPSRnents or structures with FRP shall follow capacity protecWLRQSULQFLSOHV,QFDSDFLW\GHVLJQ +ROOLQJVPark and
3DXOD\ DGHVLUDEOHPHFKDQLVPRILQHODVWLFUHVSRQVH
@Seismicisolation
@Seismicisolation
American Concrete Institute – Copyrighted © Material – www.concrete.org
MCPOL Licensed to: McMaster University Library
38
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
under seismic action is ensured by providing a strength
KLHUDUFK\ VWURQJFROXPQZHDNEHDPVKHDUVWUHQJWK!ÀH[XUDO VWUHQJWK $SSOLFDWLRQ RI WKHVH GHVLJQ JXLGHOLQHV IRU
the seismic rehabilitation of nonbuilding structures such as
bridges, wharves, silos, and nuclear facilities warrant additional consideration.
7KHVHJXLGHOLQHVGRQRWSURYLGHLQIRUPDWLRQUHTXLUHGWR
complete a seismic evaluation of an existing structure, deterPLQHLIUHWUR¿WLVUHTXLUHGRULGHQWLI\WKHVHLVPLFGH¿FLHQcies that need to be corrected to achieve the desired performance objective. These guidelines are also not meant to
address post-seismic conditions or residual strength of the
VWUXFWXUHDQGWKH)53UHWUR¿WV\VWHP$IWHUDVHLVPLFHYHQW
D VWUXFWXUH WKDW KDV EHHQ UHWUR¿WWHG ZLWK )53 FRPSRVLWHV
could develop large displacements and excessive cracking,
resulting in residual stresses or damage to the FRP system.
In such cases, an investigation of the stability, ductility, and
residual strength of the structure should be performed after
WKH VHLVPLF HYHQW WR DVVHVV WKH DGHTXDF\ RI WKH H[LVWLQJ
)53UHWUR¿WV\VWHPDQGWRGHWHUPLQHLIDGGLWLRQDOUHPHGLDO
measures are needed.
13.1—Background
One of the most comprehensive documents developed
to assess the need for seismic rehabilitation of reinforced
concrete buildings is ASCE/SEI 41 )(0$ 3 Federal
(PHUJHQF\ 0DQDJHPHQW $JHQF\ SURYLGHV IXUWKHU
guidance in the selection of appropriate design criteria to
achieve the seismic performance objectives. $&,5 estimates the desired seismic performance of concrete components that are largely based on the format and content of
ASCE/SEI 41.
)(0$ Federal Emergency Management Agency 2006 provides a complete list of references on technical design
VWDQGDUGV DQG DQDO\VLV WHFKQLTXHV WKDW DUH DYDLODEOH WR
design professionals. Other resources dealing with seismic
upgrade of existing reinforced concrete structures can be
obtained from Japan Building Disaster Prevention AssociaWLRQ , (XURFRGH , International Federation for
6WUXFWXUDO&RQFUHWH , 2006 Italian National Research
&RXQFLO , and 6DEQLVHWDO .
Experience gained from examining the performance of
reinforced concrete structures after a seismic event indicates
WKDW PDQ\ VWUXFWXUDO GH¿FLHQFLHV UHVXOW IURP LQDGHTXDWH
FRQ¿QHPHQW RI FRQFUHWH LQVXI¿FLHQW WUDQVYHUVH DQG FRQWLnuity reinforcement in connections and structural members,
EXFNOLQJ RI ÀH[XUDO UHLQIRUFHPHQW ODS VSOLFH IDLOXUHV DQG
DQFKRUDJHIDLOXUHV 3ULHVWOH\HWDOHaroun et al. 2003
Sezen et al. 20033DQWHOLGHVHWDO, 2004 7KHVHGH¿ciencies have typically led to brittle failures, soft-story
IDLOXUHDQGODUJHUHVLGXDOGLVSODFHPHQWV Moehle et al. 2002
Di Ludovico et al. 2008b Prota et al. 2004 Pessiki et al.
([SHULPHQWDOZRUNKDVDOVRGHPRQVWUDWHGWKDWH[WHUnally bonded FRP systems can be effective in addressing
PDQ\RIWKHDIRUHPHQWLRQHGVWUXFWXUDOGH¿FLHQFLHV Engindeniz et al. 2005Pantelides et al. 2008Silva et al. 2007 13.2—FRP properties for seismic design
For seismic upgrades, the material environmental factors
JLYHQLQ7DEOHVKRXOGEHXVHGLQWKHGHVLJQRIWKH)53
VWUHQJWKHQLQJVROXWLRQ7KHFUHHSUXSWXUHOLPLWVLQ7DEOH
need not be considered for seismic strengthening applications unless initial strains are imposed on the FRP as part of
WKHUHWUR¿WVFKHPH7\SLFDOO\ZKHQXVHGIRUVHLVPLFUHWUR¿W
WKH)53PDWHULDOZLOOQRWEHH[SRVHGWRVLJQL¿FDQWVXVWDLQHG
service loads and creep rupture failure will not govern the
design. Creep rupture limits should be considered, however,
in cases where the application may impose initial or service
strains that can produce sustained stresses on the FRP. Some
examples include applications with expansive grouts, pretensioned FRP, or other methods that generate sustained stress
in the FRP material. When this chapter is used in conjunction with ASCE/SEI 41, FRP material properties should be
considered lower-bound material properties.
13.3—Confinement with FRP
Jacketing concrete structural members with FRP having
WKH SULPDU\ ¿EHUV RULHQWHG DURXQG WKH SHULPHWHU RI WKH
PHPEHU SURYLGHV FRQ¿QHPHQW WR SODVWLF KLQJHV PLWLJDWHV
the splitting failure mode of poorly detailed lap splices, and
prevents buckling of the main reinforcing bars.
13.3.1 General considerations—In seismic applications,
jacketing concrete structural members with FRP is not
recommended for rectangular sections with aspect ratios h/b
greater than 1.5, or face dimensions b or h exceeding 36 in.
PP 6HLEOHHWDO XQOHVVWHVWLQJGHPRQVWUDWHV
WKHHIIHFWLYHQHVVRI)53IRUFRQ¿QHPHQWRIWKHVHPHPEHUV
For rectangular sections with an aspect ratio greater than 1.5,
WKHVHFWLRQFDQEHPRGL¿HGWREHFLUFXODURURYDOWRHQKDQFH
WKHHIIHFWLYHQHVVRIWKH)53MDFNHW 6HLEOHHWDO )53
anchors have been shown to increase the effectiveness of the
FRP jacket in rectangular sections with aspect ratios greater
WKDQ Kim et al. 2011 13.3.2 3ODVWLF KLQJH UHJLRQ FRQ¿QHPHQW—FRP-jacketed
reinforced concrete members achieve higher inelastic rotaWLRQDOFDSDFLW\RIWKHSODVWLFKLQJH 6HLEOHHWDO )53
jacketing can be used to increase the concrete compressive strength when the concrete member complies with the
condition in 12.3. For concrete members that do not satisfy
this condition, only the ultimate concrete strains can be
LQFUHDVHGE\)53MDFNHWLQJ,QFUHDVHLQÀH[XUDOVWUHQJWKGXH
to higher concrete compressive strength should be considered to verify that hinges can form prior to reaching the
shear strength of members.
7KHGHVLJQFXUYDWXUHࢥDIRUDFRQ¿QHGUHLQIRUFHGFRQFUHWH
VHFWLRQDWWKHSODVWLFKLQJHFDQEHFDOFXODWHGXVLQJ(T D φD =
θp
Lp
+ φ y , frp ≤ φu , frp
D
ZKHUHșp is the plastic rotation demand, which can be determined following the analytical procedures outlined in ASCE/
6(,,Q(T D WKHFXUYDWXUHVRIWKH)53FRQ¿QHG
VHFWLRQDWVWHHO\LHOGLQJࢥy,frpDQGDWXOWLPDWHFDSDFLW\ࢥu,frp,
@Seismicisolation
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
39
DUHGHWHUPLQHGE\(T E DQG F DQGLp is the
SODVWLFKLQJHOHQJWKFRPSXWHGXVLQJ(T G φ y , frp =
εy
d − c y , frp
E
ZKHUHİy and cy,frp are the steel strain and depth of the neutral
axis at steel yielding, respectively, and d is the distance from
WKHH[WUHPHFRPSUHVVLRQ¿EHUVWRWKHH[WUHPHWHQVLRQVWHHO
φu , frp =
ε ccu
cu , frp
F
ZKHUHİccu and cu,frpDUHWKHH[WUHPHFRPSUHVVLRQ¿EHUVWUDLQ
and depth of the neutral axis at ultimate, respectively.
For beams, the plastic hinge length Lp can be approximated
DVWZLFHWKHEHDPKHLJKW h 7KHSODVWLFKLQJHOHQJWKFDQ
also be determined using detailed analysis but should not
be less than the beam height. In FRP-jacketed columns, the
plastic hinge length LpFDQEHFRPSXWHGXVLQJ(T G 3ULHVWOH\HWDO
Lp = g + 0.0003fydEƐ LQOE
G
Lp = g + 0.044fydEƐ 6,
where dEƐ and fyDUHWKHGLDPHWHUDQG\LHOGVWUHVVRIWKHÀH[ural steel, respectively, and g is the clear gap between the
FRP jacket and adjacent members, as shown in Fig. 13.3.2.
The gap gVKRXOGQRWEHJUHDWHUWKDQLQ PP ,QSODVWLFKLQJHUHJLRQVWKH)53FRQ¿QHPHQWVKRXOGEH
provided over a length not less than the larger of the plastic
hinge length and Ɛo, where Ɛo is the length, measured along
the member axis from the face of the joint, over which
special transverse reinforcement must be provided as
GH¿QHGLQ&KDSWHURIACI 318-14. It should be noted that
plastic hinges may occur at locations other than the ends of
the member. Complete wrapping around the perimeter of
WKH PHPEHU VKRXOG EH XVHG IRU SODVWLF KLQJH FRQ¿QHPHQW
&RQWLQXRXV IXOO FRYHUDJHRIWKHSODVWLFKLQJHOHQJWKZLWK
an FRP jacket is recommended. When a continuous jacket
is not possible, discrete transverse FRP strips around the
perimeter of the section can be used.
2QFH WKH GHVLJQ FXUYDWXUH ࢥD has been established, the
XOWLPDWHH[WUHPHFRPSUHVVLRQ¿EHUVWUDLQLQWKHFRQFUHWHDW
XOWLPDWHİccuFDQEHFDOFXODWHGXVLQJ(T H
İccu ࢥDcu”
H
where cu is the neutral axis depth at the ultimate design limit
VWDWH)RUPHPEHUVVXEMHFWHGWRFRPELQHGD[LDODQGÀH[XUDO
IRUFHVİccu should be limited to 0.01.
2QFHİccu is determined, the thickness of the FRP jacket
can be determined in accordance with 12.1 and 12.2. To
HQVXUHWKHVKHDULQWHJULW\RIWKHFRQ¿QHGFRQFUHWHVHFWLRQ
)LJ²&ROXPQSODVWLFKLQJHFRQ¿QHPHQW
WKHHIIHFWLYHGHVLJQVWUDLQLQWKH)53MDFNHWİfe, should be
OLPLWHGWRWKHYDOXHJLYHQE\(T 13.3.3 Lap splice clamping—The capacity of lap splices
KDYLQJ LQDGHTXDWH ODS OHQJWK HVSHFLDOO\ WKRVH ORFDWHG LQ
plastic hinge regions, can be improved by continuously
FRQ¿QLQJ WKH VHFWLRQ RYHU DW OHDVW WKH OHQJWK RI WKH VSOLFH
ZLWKH[WHUQDOO\ERQGHG)53 6HLEOHHWDOHaroun and
Elsanadedy 2005 7KHUHTXLUHGWKLFNQHVVRIWKH)53MDFNHW
can be calculated as follows
where D in inches and Ef in ksi,
circular sections: ntf D/Ef
rectangular sections: ntf D/Ef
D
where D in mm and Ef is in MPa
circular sections: ntf D/Ef
rectangular sections: ntf D/Ef
where nLVWKHQXPEHURI)53SOLHVtf is the thickness per
SO\ D is the diameter of a circular member or the greater
GLPHQVLRQRIUHFWDQJXODUVHFWLRQV SHU(T D DQGEf
is the tensile modulus of the FRP jacket.
:KLOHFRQ¿QLQJWKHVHFWLRQZLWK)53FDQPLWLJDWHWKHVSOLWting mode of failure, the pullout failure mode may control
WKHFDSDFLW\RIWKHFRQ¿QHGODSVSOLFH7KHUHIRUHUHJDUGOHVV
RI)53UHWUR¿WWKHVWUHVVLQWKHÀH[XUDOUHLQIRUFLQJEDUfs,
VKRXOGQRWH[FHHGWKHOLPLWJLYHQLQ(T E Harries
et al. 2006 fs ≤
fs ≤
33 prov
f c′
d b ψ t ψ e ψ s
2.75 prov
f c′
d b ψ t ψ e ψ s
(in.-lb)
E
(SI)
where ƐprovLVWKHOHQJWKRIVSOLFHSURYLGHGdEƐ is the diamHWHURIWKHÀH[XUDOUHLQIRUFHPHQWDQGWKHȥIDFWRUVDUHWKRVH
given in Section 25.4 of ACI 318-14.
13.3.4 3UHYHQWLQJ EXFNOLQJ RI ÀH[XUDO VWHHO EDUV—
&RQWLQXRXVRUGLVFUHWH)53VWULSVKDYLQJWKHSULPDU\¿EHUV
oriented around the perimeter of the member can be used to
SUHYHQW EXFNOLQJ RI WKH ÀH[XUDO VWHHO EDUV Priestley et al.
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MCPOL Licensed to: McMaster University Library
40
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
)RU FLUFXODU VHFWLRQV WKH YROXPHWULF UHLQIRUFHPHQW
UDWLRSURYLGHGE\WUDQVYHUVH)53ȡf, is
ρf =
4nt f w f
D sf
D
where nLVWKHQXPEHURI)53SOLHVtfLVWKHWKLFNQHVVSHUSO\
DLVWKHGLDPHWHURIWKHVHFWLRQwfLVWKH)53VWULSZLGWK
and sf is the center-to-center spacing of the FRP strips. For
FRQWLQXRXV FRQ¿QHPHQW wf/sf = 1. In rectangular sections,
WKHYROXPHWULFUHLQIRUFHPHQWUDWLRSURYLGHGE\WKH)53ȡf,
LV 3ULHVWOH\HWDO
⎛ b + h ⎞ wf
ρ f = 2nt f ⎜
⎝ bh ⎟⎠ s f
E
where b and h are the dimensions of the rectangular section.
The amount of volumetric transverse reinforcement ratio
should be at least
ρf ≥
0.0052ρ D f y
f fe
d b
F
ZKHUHȡƐLVWKHÀH[XUDOUHLQIRUFHPHQWUDWLRD is the diameter
of a circular section or the diagonal length of a rectangular
VHFWLRQ (T D dEƐ and fy are the diameter and the
\LHOGVWUHQJWKRIWKHÀH[XUDOUHLQIRUFHPHQWUHVSHFWLYHO\ȡf
is the volumetric transverse reinforcement ratio computed
E\(T D RU E DQGffe is the effective design
VWUHVVLQWKH)53MDFNHWFRPSXWHGE\(T G
ffe İfeEf
G
ZKHUHİfe is the effective design strain in the FRP jacket given
E\(T DQGEf is the tensile modulus of the FRP jacket.
When discrete FRP strips rather than a continuous jacket
are used, the clear spacing between FRP strips should not
H[FHHGWKHOLPLWVLQ(T H
⎡
⎛ f
⎞⎤
s f ≤ ⎢3 − 6 ⎜ u − 1⎟ ⎥ db ≤ 6db ⎝ f y ⎠ ⎦⎥
⎢⎣
H
where fu, fy, and dEƐ are the ultimate and yield strengths and
WKHVPDOOHVWGLDPHWHURIWKHLQWHUQDOÀH[XUDOUHLQIRUFHPHQW
UHVSHFWLYHO\7KHFOHDUVSDFLQJVKRXOGQRWH[FHHGLQ PP 7KHVHUHTXLUHPHQWVHQVXUHWKDWLIWKHFRYHUFRQFUHWH
spalls in the region between strips, the FRP can provide
VXI¿FLHQW UHVLVWDQFH DJDLQVW EDU EXFNOLQJ 7KLV DSSURDFK
neglects any contribution from the existing internal transverse reinforcement because the internal ties may not coincide within the open spaces between the FRP strips, and the
interaction of the internal ties and external FRP strips has
not been studied.
13.4—Flexural strengthening
7KH ÀH[XUDO FDSDFLW\ RI UHLQIRUFHG FRQFUHWH EHDPV DQG
columns in expected plastic hinge regions can be enhanced
using FRP only in cases where strengthening will eliminate inelastic deformations in the strengthened region and
transfer inelastic deformations to other locations in the
member or the structure that are able to handle the ensuing
GXFWLOLW\ GHPDQGV 7KH UHTXLUHG ÀH[XUDO VWUHQJWK VKRXOG
be calculated in accordance with the design standard being
used for rehabilitation, such as ASCE/SEI 41 and $&,5.
When this chapter is used in conjunction with ASCE/SEI
41, the strengthened reinforced concrete members with FRP
should be considered force-controlled unless a deformationFRQWUROOHG FODVVL¿FDWLRQ FDQ EH MXVWL¿HG EDVHG RQ H[SHULmental data.
7KH ÀH[XUDO FDSDFLW\ RI UHLQIRUFHG FRQFUHWH EHDPV DQG
columns can be enhanced using the design methodology
presented in Chapter 107KH ÀH[XUDO VWUHQJWK ࢥMn should
VDWLVI\WKHUHTXLUHPHQWRI(T ࢥMn•Mu
where Mu is the ultimate moment demand resulting from
FRPELQHGJUDYLW\DQGVHLVPLFGHPDQGV7KHÀH[XUDOFDSDFLW\
of reinforced concrete members should be evaluated based
on concrete and reinforcing steel strain limits set forth in the
design standard. ASCE/SEI 41 provides a comprehensive
list of concrete and reinforcing steel strain limits. In addition, the stress in the reinforcing steel should be limited to
the stress that can be achieved based on the existing development lengths and lap-splice details. The strength reduction
IDFWRUࢥVKRXOGEHSHUWKHGHVLJQVWDQGDUGEHLQJXVHGIRUWKH
rehabilitation. The additional strength reduction factor for
)53ȥfVKDOOEHDSSOLHGWRWKHÀH[XUDOFRQWULEXWLRQRIWKH
FRP reinforcement as described in 10.2.10.
13.4.2 'HYHORSPHQWDQGDQFKRUDJHRIÀH[XUDO)53UHLQforcement—This section provides conceptual methods for
DQFKRUDJH RI ÀH[XUDO )53 UHLQIRUFHPHQW XQGHU VHLVPLF
loads. Any anchorage method must be properly evaluated
EHIRUHLWLVVHOHFWHGIRU¿HOGLPSOHPHQWDWLRQ
In seismic applications and within plastic hinge regions,
WKH ÀH[XUDO )53 UHLQIRUFHPHQW VKRXOG EH FRQ¿QHG XVLQJ
FRP strips that completely wrap around the perimeter of the
VHFWLRQ$OWHUQDWLYHO\WKHÀH[XUDO)53UHLQIRUFHPHQWFRXOG
EH FRQ¿QHG RYHU LWV HQWLUH OHQJWK WR SURYLGH KLJKHU UHVLVWDQFHDJDLQVWGHERQGLQJRIWKHÀH[XUDO)53UHLQIRUFHPHQW
Because no anchorage design guidelines are currently available, the performance of any anchorage system should be
substantiated through representative physical testing.
Such detailing provides higher resistance against
GHERQGLQJRIWKHÀH[XUDO)53UHLQIRUFHPHQW,QDSSOLFDWLRQV
LQYROYLQJ ÀRRU V\VWHPV FRPSOHWH ZUDSSLQJ RI WKH EHDP
PD\UHTXLUHORFDOL]HGFXWWLQJRIWKHVODEWRFRQWLQXHWKH)53
around the section.
Away from the plastic hinge region, transverse FRP
U-wrap strips should be used to provide anchorage to the
)53ÀH[XUDOUHLQIRUFHPHQW2WKHUDQFKRUDJHV\VWHPVPD\
also be used alone or in conjunction with FRP U-wrap strips.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
41
$QFKRUDJH V\VWHPV PXVW EH YHUL¿HG H[SHULPHQWDOO\ WR
demonstrate their effectiveness in preventing the debonding
RIWKHÀH[XUDO)53UHLQIRUFHPHQW6HYHUDOGHWDLOVIRU)53
DQFKRUDJH DW HQGV RI UHWUR¿WWHG PHPEHUV DUH GLVFXVVHG LQ
2UWRQHWDO .
The area of the transverse FRP wrap reinforcement, Af,anchor,
VKRXOG EH GHWHUPLQHG LQ DFFRUGDQFH ZLWK (T ,Q
addition, the length over which the FRP anchorage wraps
are provided, Ɛd,E, should not be less than the value given by
(T D Ɛd,E•Ɛo + Ɛdf
D
where ƐoLVGH¿QHGSHU)LJDQGƐdfLVWKHUHTXLUHGGHYHORSPHQWOHQJWKRIWKH)53V\VWHPFRPSXWHGXVLQJ(T )RUDGHTXDWHO\DQFKRUHGÀH[XUDO)53UHLQIRUFHPHQWWKH
effective design strain for FRP should be limited to
İfd”PLQ İfu, CEİfu E
)LJXUH GHSLFWV D FRQFHSWXDO GHWDLO IRU ÀH[XUDO
strengthening of beams and columns at a joint and is intended
WRFRQYH\WKHFULWLFDOHOHPHQWVRIVXFKDÀH[XUDOVWUHQJWKHQLQJ 7KH GHVLJQ SURIHVVLRQDO VKRXOG GHWDLO WKH ÀH[XUDO
FRP reinforcement to achieve continuity of the FRP across
WKH MRLQW$SSURSULDWH GHYHORSPHQW RI WKH ÀH[XUDO )53 DW
ERWKHQGVDVZHOODVDGHTXDWHWUDQVYHUVHUHLQIRUFHPHQWIRU
FRQ¿QHPHQWRIWKHÀH[XUDO)53VKRXOGEHSURYLGHG
13.5—Shear strengthening
FRP shear strengthening can prevent brittle failures and
promote the development of plastic hinges, resulting in an
enhanced seismic behavior of concrete members. The design
VKHDUVWUHQJWKࢥVn of a concrete member strengthened with
)53VKRXOGVDWLVI\(T ࢥVn•Ve
ZKHUH ࢥ VKRXOG EH SHU WKH GHVLJQ VWDQGDUG EHLQJ XVHG IRU
the rehabilitation, and Ve is the design shear force. When this
chapter is used in conjunction with ASCE/SEI 41, the shear
in the strengthened member should be considered forceFRQWUROOHGXQOHVVDGHIRUPDWLRQFRQWUROOHGFODVVL¿FDWLRQFDQ
EHMXVWL¿HGEDVHGRQH[SHULPHQWDOGDWD
13.5.1 Design shear force Ve—The design shear force
should be calculated in accordance with the design standard
being used for the rehabilitation, such as ASCE/SEI 41 and
$&,57KHVKHDUFDSDFLW\VKRXOGEHHTXDOWRRUJUHDWHU
WKDQWKHVKHDUFRUUHVSRQGLQJWRWKHÀH[XUDOFDSDFLW\RIWKH
section. For example, when the rehabilitation is based on
ASCE/SEI 41, the design shear force is based on the seismic
category and targeted seismic performance of the structure.
:KHQUHTXLUHGE\$6&(6(,IRUWKHGHWHUPLQDWLRQRIWKH
GHVLJQVKHDUIRUFHWKHFDOFXODWLRQRIWKHSUREDEOHÀH[XUDO
strength should be based on FRP stress taken as the lesser
of 1.2ffd and ffu ࢥ VKRXOG EH WDNHQ DV XQLW\ DQG WKH )53
VWUHQJWKUHGXFWLRQIDFWRUȥf should be 1.0. Other limits for
Fig. 13.4.2—Conceptual FRP strengthening detail (cross
section elevation).
)53 VWUDLQ DQG VWUHQJWK VSHFL¿HG LQ WKLV GRFXPHQW VKRXOG
also be considered.
13.5.2 Nominal shear strength Vn—The shear strength
of the existing member Vn* should be determined following
the procedures described in the design standard being used
IRUUHKDELOLWDWLRQVXFKDV$6&(6(,DQG$&,57KH
shear strength of an FRP-strengthened concrete member is
FDOFXODWHGXVLQJ(T Vn = Vn*ȥfVf
ZKHUHȥf is the reduction factor applied to the contribution of
the FRP system in accordance with Chapter 11. The contributions of FRP to shear strength, Vf, should be determined in
accordance with Chapter 11. To account for effects of stress
reversal, FRP shear strengthening should be provided with
complete continuity around the perimeter of the section.
13.6—Beam-column joints
([SHULPHQWDOWHVWV %UDFFLHWDODProta et al. 2004
Pampanin et al. 2007 DQG REVHUYDWLRQV RI SRVWVHLVPLF
GDPDJH Moehle et al. 2002 LQVWUXFWXUHVGHVLJQHGWRZLWKVWDQGRQO\JUDYLW\ORDGVVKRZWKDWXQFRQ¿QHGEHDPFROXPQ
MRLQWVIUHTXHQWO\OHGWREULWWOHIDLOXUHVDQGSUHYHQWHGVWUXFWXUHV
from achieving higher global displacements before failure.
([SHULPHQWDO HYLGHQFH Pantelides et al. 2008 Silva et al.
20073DPSDQLQHWDO%UDFFLHWDOEF KDVVKRZQ
that FRP systems can be effective for increasing the shear and
HQHUJ\GLVVLSDWLRQFDSDFLW\RIXQFRQ¿QHGMRLQWV)53OD\RXW
and detailing will depend on the geometry of the existing joint
and the number of members framing into it. FRP reinforcePHQW LQ ERWK GLUHFWLRQV LV W\SLFDOO\ UHTXLUHG DW WKH MRLQW WR
UHVLVWWKHF\FOLFORDGLQJHIIHFWVRIDVHLVPLFHYHQW Engindeniz
et al. 2008a 7KH )53 XVHG WR FRQ¿QH WKH MRLQWV VKRXOG EH
DQFKRUHGWREHHIIHFWLYH3DQWHOLGHVHWDO 6LOYDHWDO
DQG (QJLQGHQL] HW DO E provide guidance on
determining if FRP is a viable option for enhancing the perforPDQFHRIXQFRQ¿QHGMRLQWV$GGLWLRQDOO\)53UHLQIRUFHPHQW
can be used to provide continuity across joints with disconWLQXRXVLQWHUQDOUHLQIRUFHPHQW 2UWRQHWDO 13.7—Strengthening reinforced concrete shear walls
13.7.1 General considerations—This section presents
design guidelines for the seismic strengthening of reinforced
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42
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
concrete walls. Applying horizontal FRP strips along the
height of the walls can increase the shear capacity of reinIRUFHGFRQFUHWHVKHDUZDOOV)RUVKRUWRUVTXDWZDOOVZLWK
height-to-length ratios less than 1.5, vertical FRP strips may
DOVREHUHTXLUHG ACI 318 /LNHZLVHWKHLQSODQHÀH[XUDO
capacity of reinforced concrete shear walls can be increased
by placing vertical FRP strips at the ends or boundaries of
ZDOOV Lombard et al. 2000Hiotakis et al. 2004 7KHVKHDUVWUHQJWKRIZDOOVUHLQIRUFHGZLWK)53IRUÀH[XUH
should be evaluated and compared to the shear strength
FRUUHVSRQGLQJWRWKHQRPLQDOÀH[XUDOVWUHQJWKRIWKHUHWUR¿WWHG VWUXFWXUH WR SURPRWH D ÀH[XUDO IDLOXUH UDWKHU WKDQ D
EULWWOHVKHDUIDLOXUH6LPLODUO\DVKHDUUHWUR¿WVKRXOGDFKLHYH
greater shear capacity than the shear corresponding to the
QRPLQDOÀH[XUDOFDSDFLW\RIWKHZDOO:KHQWKLVFKDSWHULV
used in conjunction with ASCE/SEI 41WKHÀH[XUHDQGVKHDU
in the strengthened portion of the wall should be considered
force-controlled action unless a deformation-controlled clasVL¿FDWLRQLVMXVWL¿HGEDVHGRQH[SHULPHQWDOGDWD
13.7.2 Flexural strengthening—FRP reinforcement for
ÀH[XUDOVWUHQJWKHQLQJRIZDOOVPD\EHSURYLGHGRQRQHRU
ERWKVLGHVRIWKHZDOO)LJXUHVKRZVDZDOOUHWUR¿WWHG
with FRP reinforcement placed at the extreme ends of the
ZDOO7KLV¿JXUHDOVRSURYLGHVDGHVFULSWLRQRIWKHPDLQYDULDEOHVUHTXLUHGIRUGHVLJQ
13.7.2.1 Concrete strain limits—The concrete compresVLYHVWUDLQVİcVKRXOGEHOLPLWHGE\(T D
⎛ 1 ⎞
≤ ε cu
ε c = ε fc ⎜
⎝ Lw /c − 1⎟⎠
D
ZKHUH İfd corresponds to the strain at which debonding of
WKH)53PD\RFFXUSHU(T ,QFRQFUHWHVKHDUZDOOV
WKHFRQFUHWHFRPSUHVVLYHVWUDLQVDWXOWLPDWHİcu, should be
OLPLWHGWRWKHIROORZLQJYDOXHV :DOODFH
İcu”IRUFRQ¿QHGFRQFUHWHDWERXQGDULHV
E
İcu”IRUXQFRQ¿QHGFRQFUHWHDWERXQGDULHV
:KHQ FRQ¿QHG ERXQGDU\ HOHPHQWV DUH UHTXLUHG SHU (T
E PHDQVRWKHUWKDQ)53PD\EHUHTXLUHGWRPHHW
WKHFRQFUHWHVWUDLQUHTXLUHPHQWV
13.7.2.2 $QFKRUDJH RI ÀH[XUDOO\ VWUHQJWKHQHG ZDOOV²
)OH[XUDOO\ VWUHQJWKHQHG ZDOOV UHTXLUH DQFKRUDJH WR WKH
IRXQGDWLRQV IRU ORDG SDWK FRQWLQXLW\ 6LPLODUO\ ÀH[XUDO
FRP should be continuous through existing slabs to ensure
continuity of the load path. Two conceptual methods for
anchorage of a strengthened shear wall to the foundation are
provided in Fig. 13.7.2.2. Any anchorage method, including
the ones shown in Fig. 13.7.2.2, should be properly evaluDWHGSULRUWR¿HOGLPSOHPHQWDWLRQ,QVKHDUZDOOVWKHYHUWLFDO
ÀH[XUDO)53UHLQIRUFHPHQWGRHVQRWQHHGWREHFRQ¿QHGE\
transverse FRP strips or U-wraps that extend around the
perimeter of the section.
13.7.3 Shear strengthening of reinforced concrete shear
walls—Experimental investigations have demonstrated
)LJ²)53UHLQIRUFHPHQWIRUÀH[XUDOVWUHQJWKHQLQJ
the effectiveness of FRP for enhancing the shear performance of reinforced concrete walls subjected to seismic or
F\FOLFORDGLQJ Haroun and Mosallam 2002Khomwan and
Foster 2005 7KHGHVLJQVKHDUVWUHQJWKࢥVn of a reinforced
concrete shear wall strengthened with FRP should satisfy
(T D ࢥVn•Vu
D
7KHVWUHQJWKUHGXFWLRQIDFWRUࢥVKRXOGEHSHUWKHGHVLJQ
standard being used for the rehabilitation.
For shear walls with externally bonded FRP, the nominal
shear strength VnFDQEHFRPSXWHGXVLQJ(T E
Vn = Vn*ȥfVf
E
where Vn* is the nominal shear strength of the existing shear
ZDOOȥf is the reduction factor applied to the contribution of
the FRP in accordance with Chapter 11DQGVf is the shear
strength provided by the FRP. The shear strength enhancement for a wall section of length Lw in the direction of the
applied shear force, with a laminate thickness tf on two
VLGHV RU RQH VLGH RI WKH ZDOO FDQ EH FDOFXODWHG XVLQJ (T
F Haroun et al. 2005
IRUDWZRVLGHGUHWUR¿WVf = 2tfİfeEfdfv
F
IRUDRQHVLGHGUHWUR¿WVf = 0.75tfİfeEfdfv
where dfvLVWKHHIIHFWLYHGHSWKRIWKHVKHDUZDOODVGH¿QHG
by Chapter 18 of ACI 318-14, but not to exceed hwDQGİfe
is according to 11.4.1 of this guide. FRP should be provided
on two faces of the wall if the ratio of the existing transYHUVHVWHHOUHLQIRUFHPHQWWRJURVVFRQFUHWHDUHDȡt, is less
than 0.0015. The intent of this provision is to ensure proper
shear resistance of concrete in the event of severe cracking
during a seismic event. The maximum nominal shear
strength of a wall segment should not exceed the value
JLYHQLQ(T G
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
43
VWUXFWXUH WKH VRXQGQHVV DQG TXDOLW\ RI WKH VXEVWUDWH DQG
the levels of load that are to be sustained by the FRP sheets
or laminates. Many bond-related failures can be avoided by
following these general guidelines for detailing FRP sheets
or laminates:
D 'RQRWWXUQLQVLGHFRUQHUVVXFKDVDWWKHLQWHUVHFWLRQRI
beams and joists or the underside of slabs
E 3URYLGHDPLQLPXPLQ PP UDGLXVZKHQWKH
sheet is wrapped around outside corners
F 3URYLGHDGHTXDWHGHYHORSPHQWOHQJWK
G 3URYLGHVXI¿FLHQWRYHUODSZKHQVSOLFLQJ)53SOLHV
Fig. 13.7.2.2—Conceptual anchorage methods for strengthened shear wall.
Vn ≤ 10 f c′Acw G
where Acw is the area of the concrete section of an individual
vertical wall.
13.7.3.1 Detailing of FRP shear reinforcement—Anchorage
RIVKHDU)53LVFRQVLGHUHGJRRGSUDFWLFHEXWLWLVQRWUHTXLUHG
to attain the shear strengths computed using the provisions of
this chapter. Anchoring of the FRP shear reinforcement can
be achieved by wrapping the FRP layers around the ends of
the wall, by using mechanical anchorage devices such as steel
DQFKRUVDQGVWHHOSODWHV Paterson and Mitchell 2003 RUE\
XVLQJ)53DQFKRUV Binici and Ozcebe 2006 The maximum clear spacing between the FRP shear strips
VKRXOGEHOLPLWHGWRWKHPLQLPXPRIRQH¿IWKRIWKHRYHUDOO
length of the wall, three times the thickness of the wall, or
LQ PP CHAPTER 14—FIBER-REINFORCED POLYMER
REINFORCEMENT DETAILS
This chapter provides guidance for detailing externally
ERQGHG ¿EHUUHLQIRUFHG SRO\PHU )53 UHLQIRUFHPHQW
Detailing will typically depend on the geometry of the
14.1—Bond and delamination
The actual distribution of bond stress in an FRP laminate
is complicated by cracking of the substrate concrete. The
general elastic distribution of interfacial shear stress and
normal stress along an FRP laminate bonded to uncracked
concrete is shown in Fig. 14.1.
The weak link in the concrete/FRP interface is the concrete.
The soundness and tensile strength of the concrete substrate
will limit the overall effectiveness of the bonded FRP
V\VWHP 'HVLJQ UHTXLUHPHQWV WR PLWLJDWH )53 GHERQGLQJ
failure modes are discussed in 10.1.1.
14.1.1 FRP debonding—In reinforced concrete members
having relatively long shear spans or where the end peeling
UHIHUWR KDVEHHQHIIHFWLYHO\PLWLJDWHGGHERQGLQJ
PD\LQLWLDWHDWÀH[XUDOFUDFNVÀH[XUDOVKHDUFUDFNVRUERWK
near the region of maximum moment. Under loading, these
cracks open and induce high local interfacial shear stress
that initiates FRP debonding that propagates across the
shear span in the direction of decreasing moment. Typically,
this failure does not engage the aggregate in the concrete,
progressing through the thin mortar-rich layer comprising
the surface of the concrete substrate. This failure mode is
exacerbated in regions having a high shear-moment ratio.
Anchorage systems, such as U-wraps, mechanical
IDVWHQHUV ¿EHU DQFKRUV DQG QHDUVXUIDFHPRXQWHG 160 anchors, have been proven successful at delaying, and sometimes preventing, debonding failure of the longitudinal FRP
Kalfat et al. 2013Grelle and Sneed 2013 1XPHULFDODQG
experimental studies have shown that these systems can
LQFUHDVH WKH HIIHFWLYH VWUDLQ LQ WKH ÀH[XUDO )53 WR YDOXHV
XS WR WHQVLOH UXSWXUH Lee et al. 2010 Orton et al. 2008 A few studies have proposed analytical models to predict
WKH EHKDYLRU RI VSHFL¿F DQFKRU V\VWHPV Kim and Smith
2010 KRZHYHUQRSXEOLVKHGDQFKRUDJHGHVLJQJXLGHOLQHV
are currently available. Therefore, the performance of any
anchorage system should be substantiated through representative physical testing.
14.1.2 FRP end peeling²)53HQGSHHOLQJ DOVRUHIHUUHG
WRDVFRQFUHWHFRYHUGHODPLQDWLRQ FDQUHVXOWIURPWKHQRUPDO
stresses developed at the ends of externally bonded FRP
reinforcement. With this type of delamination, the existing
internal reinforcing steel provides a weak horizontal plane
along which the concrete cover pulls away from the rest of
the beam, as shown in Fig. 14.1.2a.
The tensile concrete cover splitting failure mode is
controlled, in part, by stress at the termination point of
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44
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Fig. 14.1.2a—Delamination caused by tension failure of the
concrete cover.
Fig. 14.1—Conceptual interfacial shear and normal stress
distributions along the length of a bonded FRP laminate
(Roberts and Haji-Kazemi 1989; Malek et al. 1998).
the FRP. In general, the FRP end peeling failure mode can
EH PLWLJDWHG E\ XVLQJ DQFKRUDJH 8ZUDSV PHFKDQLFDO
IDVWHQHUV ¿EHU DQFKRUV RU 160 DQFKRUV E\ PLQLPL]LQJ
the stress at the FRP curtailment by locating the curtailment
as close to the region of zero moment as possible, or by
both. When the factored shear force at the termination point
LVJUHDWHUWKDQWZRWKLUGVRIWKHFRQFUHWHVKHDUVWUHQJWK Vu
!Vc WKH)53ODPLQDWHVVKRXOGEHDQFKRUHGZLWKWUDQVverse reinforcement to prevent the concrete cover layer from
splitting. The area of the transverse clamping FRP U-wrap
reinforcement, Afanchor, can be determined in accordance
ZLWK(T Reed et al. 2005
Afanchor =
( Af f fe )longitudinal
( E f κ v ε fu ) anchor
LQ ZKLFK țv LV FDOFXODWHG XVLQJ (T E ,QVWHDG RI
detailed analysis, the following general guidelines for the
location of cutoff points for the FRP laminate can be used to
avoid end peeling failure mode:
D )RU VLPSO\ VXSSRUWHG EHDPV D VLQJOHSO\ )53 ODPLQDWHVKRXOGEHWHUPLQDWHGDWOHDVWDGLVWDQFHHTXDOWRƐdf past
the point along the span at which the resisted moment falls
below the cracking moment Mcr. For multiple-ply laminates,
the termination points of the plies should be tapered. The
outermost ply should be terminated not less than Ɛdf past
the point along the span at which the resisted moment falls
below the cracking moment. Each successive ply should be
WHUPLQDWHGQRWOHVVWKDQDQDGGLWLRQDOLQ PP EH\RQG
WKHSUHYLRXVSO\ )LJE E )RU FRQWLQXRXV EHDPV D VLQJOHSO\ )53 ODPLQDWH
should be terminated at least a distance dRULQ PP EH\RQGWKHLQÀHFWLRQSRLQW SRLQWRI]HURPRPHQWUHVXOWLQJ
IURPIDFWRUHGORDGV )RUPXOWLSOHSO\ODPLQDWHVWKHWHUPLnation points of the plies should be tapered. The outermost
SO\VKRXOGEHWHUPLQDWHGQROHVVWKDQLQ PP EH\RQG
WKH LQÀHFWLRQ SRLQW (DFK VXFFHVVLYH SO\ VKRXOG EH WHUPLQDWHGQROHVVWKDQDQDGGLWLRQDOLQ PP EH\RQGWKH
SUHYLRXVSO\)RUH[DPSOHLIDWKUHHSO\ODPLQDWHLVUHTXLUHG
the ply directly in contact with the concrete substrate should
EH WHUPLQDWHG DW OHDVW LQ PP SDVW WKH LQÀHFWLRQ
SRLQW )LJE 7KHVHJXLGHOLQHVDSSO\IRUSRVLWLYHDQG
negative moment regions.
14.1.3 Development length—The bond capacity of FRP is
developed over a critical length Ɛdf. To develop the effective
FRP stress at a section, the available anchorage length of
)53VKRXOGH[FHHGWKHYDOXHJLYHQE\(T Teng et
al. 2003 df = 0.057
df =
nE f t f
f c′
nE f t f
(in.-lb)
(SI)
f c′
14.2—Detailing of laps and splices
Splices of FRP laminates should be provided only as
SHUPLWWHG RQ GUDZLQJV VSHFL¿FDWLRQV RU DV DXWKRUL]HG E\
the licensed design professional as recommended by the
system manufacturer.
7KH ¿EHUV RI )53 V\VWHPV VKRXOG EH FRQWLQXRXV DQG
oriented in the direction of the largest tensile forces. Fiber
continuity can be maintained with a lap splice. For FRP
systems, a lap splice should be made by overlapping the
¿EHUVDORQJWKHLUOHQJWK7KHUHTXLUHGRYHUODSRUODSVSOLFH
length, depends on the tensile strength and thickness of the
FRP material system and on the bond strength between adjaFHQWOD\HUVRI)53ODPLQDWHV6XI¿FLHQWRYHUODSVKRXOGEH
provided to promote the failure of the FRP laminate before
GHERQGLQJ RI WKH RYHUODSSHG )53 ODPLQDWHV 7KH UHTXLUHG
overlap for an FRP system should be provided by the material manufacturer and substantiated through testing that is
independent of the manufacturer.
Jacket-type FRP systems used for column members should
provide appropriate development area at splices, joints, and
termination points to ensure failure through the FRP jacket
thickness rather than failure of the spliced sections.
)RUXQLGLUHFWLRQDO)53ODPLQDWHVODSVSOLFHVDUHUHTXLUHG
RQO\LQWKHGLUHFWLRQRIWKH¿EHUV/DSVSOLFHVDUHQRWUHTXLUHG
LQ WKH GLUHFWLRQ WUDQVYHUVH WR WKH ¿EHUV )53 ODPLQDWHV
consisting of multiple unidirectional sheets oriented in more
WKDQ RQH GLUHFWLRQ RU PXOWLGLUHFWLRQDO IDEULFV UHTXLUH ODS
splices in more than one direction to maintain the continuity
RIWKH¿EHUVDQGWKHRYHUDOOVWUHQJWKRIWKH)53ODPLQDWHV
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
45
Fig. 14.1.2b—Graphical representation of the guidelines for allowable termination points
of a three-ply FRP laminate.
Fig. 14.3a—Minimum dimensions of grooves.
14.3—Bond of near-surface-mounted systems
)RU QHDUVXUIDFHPRXQWHG 160 V\VWHPV WKH PLQLPXP
dimension of the grooves should be taken at least 1.5 times the
GLDPHWHURIWKH)53EDU De Lorenzis and Nanni 2001Hassan
and Rizkalla 2003 :KHQ D UHFWDQJXODU EDU ZLWK D ODUJH
DVSHFWUDWLRLVXVHGKRZHYHUWKHOLPLWPD\ORVHVLJQL¿FDQFH
due to constructibility. In such a case, a minimum groove size
of 3.0ab x 1.5bb, as depicted in Fig. 14.3a, is suggested, where
ab is the smallest bar dimension. The minimum clear groove
spacing for NSM FRP bars should be greater than twice the
depth of the NSM groove to avoid overlapping of the tensile
stresses around the NSM bars. Furthermore, a clear edge
distance of four times the depth of the NSM groove should
be provided to minimize edge effects that could accelerate
GHERQGLQJIDLOXUH +DVVDQDQG5L]NDOOD Bond properties of NSM FRP bars depend on many factors
such as cross-sectional shape and dimensions and surface
SURSHUWLHV RI WKH )53 EDU +DVVDQ DQG 5L]NDOOD De
Lorenzis et al. 2004 )LJXUH E VKRZV WKH HTXLOLEULXP
condition of an NSM FRP bar with an embedded length
HTXDOWRLWVGHYHORSPHQWOHQJWKƐdb having a bond strength
RI IJmax. Using a triangular stress distribution, the average
Fig. 14.3b—Transfer of force in NSM FRP bars.
ERQGVWUHQJWKFDQEHH[SUHVVHGDVIJb IJmax. Average bond
VWUHQJWKIJb for NSM FRP bars in the range of 500 to 3000 psi
WR03D KDVEHHQUHSRUWHG +DVVDQDQG5L]NDOOD
'H /RUHQ]LV HW DO WKHUHIRUH IJb = 1000 psi
03D LVUHFRPPHQGHGIRUFDOFXODWLQJWKHEDUGHYHORSPHQW OHQJWK 8VLQJ IRUFH HTXLOLEULXP WKH IROORZLQJ HTXDtions for development length can be derived
db =
db =
db
f fd for circular bars 4τ b
D
ab bb
f fd for rectangular bars E
2(ab + bb )(τ b )
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46
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
CHAPTER 15—DRAWINGS, SPECIFICATIONS,
AND SUBMITTALS
15.1—Engineering requirements
Although federal, state, and local codes for the design of
H[WHUQDOO\ERQGHG¿EHUUHLQIRUFHGSRO\PHU )53 V\VWHPVGR
QRWH[LVWRWKHUDSSOLFDEOHFRGHUHTXLUHPHQWVPD\LQÀXHQFH
the selection, design, and installation of the FRP system. For
H[DPSOHFRGHUHTXLUHPHQWVUHODWHGWR¿UHRUSRWDEOHZDWHU
PD\ LQÀXHQFH WKH VHOHFWLRQ RI WKH FRDWLQJV XVHG ZLWK WKH
FRP system. All design work should be performed under the
guidance of a licensed design professional familiar with the
properties and applications of FRP strengthening systems.
15.2—Drawings and specifications
The licensed design professional should document calculations summarizing the assumptions and parameters used
to design the FRP strengthening system and should prepare
GHVLJQ GUDZLQJV DQG SURMHFW VSHFL¿FDWLRQV 7KH GUDZLQJV
DQGVSHFL¿FDWLRQVVKRXOGVKRZDWDPLQLPXPWKHIROORZLQJ
LQIRUPDWLRQVSHFL¿FWRH[WHUQDOO\DSSOLHG)53V\VWHPV
D )53V\VWHPWREHXVHG
E /RFDWLRQRIWKH)53V\VWHPUHODWLYHWRWKHH[LVWLQJVWUXFWXUH
F 'LPHQVLRQV DQG RULHQWDWLRQ RI HDFK SO\ ODPLQDWH RU
QHDUVXUIDFHPRXQWHG 160 EDU
G 1XPEHURISOLHVDQGEDUVDQGWKHVHTXHQFHRILQVWDOODWLRQ
H /RFDWLRQRIVSOLFHVDQGODSOHQJWK
I *HQHUDOQRWHVOLVWLQJGHVLJQORDGVDQGDOORZDEOHVWUDLQV
in the FRP laminates
J 0DWHULDOSURSHUWLHVRIWKH)53ODPLQDWHVDQGFRQFUHWH
substrate
K &RQFUHWH VXUIDFH SUHSDUDWLRQ UHTXLUHPHQWV LQFOXGLQJ
corner preparation, groove dimensions for NSM bars, and
maximum irregularity limitations
L ,QVWDOODWLRQ SURFHGXUHV LQFOXGLQJ VXUIDFH WHPSHUDture and moisture limitations, and application time limits
between successive plies
M &XULQJSURFHGXUHVIRU)53V\VWHPV
N 3URWHFWLYHFRDWLQJVDQGVHDODQWVLIUHTXLUHG
O 6KLSSLQJVWRUDJHKDQGOLQJDQGVKHOIOLIHJXLGHOLQHV
P 4XDOLW\ FRQWURO DQG LQVSHFWLRQ SURFHGXUHV LQFOXGLQJ
acceptance criteria
Q ,QSODFHORDGWHVWLQJRILQVWDOOHG)53V\VWHPLIQHFHVVDU\
15.3—Submittals
6SHFL¿FDWLRQV VKRXOG UHTXLUH WKH )53 V\VWHP PDQXIDFWXUHU LQVWDOODWLRQ FRQWUDFWRU DQG LQVSHFWLRQ DJHQF\ LI
UHTXLUHG WR VXEPLW SURGXFW LQIRUPDWLRQ DQG HYLGHQFH RI
WKHLU TXDOL¿FDWLRQV DQG H[SHULHQFH WR WKH OLFHQVHG GHVLJQ
professional for review.
15.3.1 FRP system manufacturer²6XEPLWWDOVUHTXLUHGRI
the FRP system manufacturer should include:
D ,QGLFDWLRQ RI FRPSOLDQFH ZLWK H[LVWLQJ VSHFL¿FDWLRQV
VXFKDVACI 440.8 DVDSSOLFDEOH
E 3URGXFWGDWDVKHHWVLQGLFDWLQJWKHSK\VLFDOPHFKDQLFDO
and chemical characteristics of the FRP system and all its
constituent materials
F 7HQVLOH SURSHUWLHV RI WKH )53 V\VWHP LQFOXGLQJ WKH
PHWKRGRIUHSRUWLQJSURSHUWLHV QHW¿EHURUJURVVODPLQDWH test methods used, and the statistical basis used for deterPLQLQJWKHSURSHUWLHV 4.3
G ,QVWDOODWLRQLQVWUXFWLRQVPDLQWHQDQFHLQVWUXFWLRQVDQG
general recommendations regarding each material to be
XVHGLQVWDOODWLRQSURFHGXUHVVKRXOGLQFOXGHVXUIDFHSUHSDUDWLRQUHTXLUHPHQWV
H 0DQXIDFWXUHU¶V6DIHW\'DWD6KHHWV 6'6V IRUDOOPDWHrials to be used
I 4XDOLW\ FRQWURO SURFHGXUH IRU WUDFNLQJ )53 PDWHULDOV
DQGPDWHULDOFHUWL¿FDWLRQV
J 'XUDELOLW\WHVWGDWDIRUWKH)53V\VWHPLQWKHW\SHVRI
environments expected
K 6WUXFWXUDOWHVWUHSRUWVSHUWLQHQWWRWKHSURSRVHGDSSOLFDWLRQ
L 5HIHUHQFHSURMHFWV
15.3.2 FRP system installation contractor—Submittals
UHTXLUHG RI WKH )53 V\VWHP LQVWDOODWLRQ FRQWUDFWRU VKRXOG
include:
D 'RFXPHQWDWLRQIURPWKH)53V\VWHPPDQXIDFWXUHURI
having been trained to install the proposed FRP system
E 3URMHFWUHIHUHQFHVLQFOXGLQJLQVWDOODWLRQVVLPLODUWRWKH
SURSRVHGLQVWDOODWLRQ IRUH[DPSOHIRUDQRYHUKHDGDSSOLFDtion, the contractor should submit a list of previous installations involving the installation of the proposed FRP system
LQDQRYHUKHDGDSSOLFDWLRQ
F (YLGHQFHRIFRPSHWHQF\LQVXUIDFHSUHSDUDWLRQWHFKQLTXHV
G 4XDOLW\ FRQWURO WHVWLQJ SURFHGXUHV LQFOXGLQJ YRLGV
and delaminations, FRP bond to concrete, and FRP tensile
properties
H 'DLO\ORJRULQVSHFWLRQIRUPVXVHGE\WKHFRQWUDFWRU
15.3.3 FRP system inspection agency—If an independent
LQVSHFWLRQDJHQF\LVXVHGVXEPLWWDOVUHTXLUHGRIWKDWDJHQF\
should include:
D $OLVWRILQVSHFWRUVWREHXVHGRQWKHSURMHFWDQGWKHLU
TXDOL¿FDWLRQV
E 6DPSOHLQVSHFWLRQIRUPV
F $OLVWRISUHYLRXVSURMHFWVLQVSHFWHGE\WKHLQVSHFWRU
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
CHAPTER 16—DESIGN EXAMPLES
47
Table 16.1a—FRP system tension test results
16.1—Calculation of FRP system tensile
properties
This example calculation shown in Table 16.1b illustrates
WKH GHULYDWLRQ RI PDWHULDO SURSHUWLHV EDVHG RQ QHW¿EHU
area versus the properties based on gross-laminate area. As
described in 4.3.1, both methods of determining material
properties are valid. It is important, however, that any design
calculations consistently use material properties based on
RQO\ RQH RI WKH WZR PHWKRGV IRU H[DPSOH LI WKH JURVV
laminate thickness is used in any calculation, the strength
based on gross-laminate area should be used in the calculaWLRQVDVZHOO 5HSRUWHGGHVLJQSURSHUWLHVVKRXOGEHEDVHG
on a population of 20 or more coupons tested in accordance
with $670''0. Reported properties should be
statistically adjusted by subtracting three standard deviations
from the mean tensile stress and strain, as discussed in 4.3.1.
$WHVWSDQHOLVIDEULFDWHGIURPWZRSOLHVRIDFDUERQ¿EHU
UHVLQXQLGLUHFWLRQDO¿EHUUHLQIRUFHGSRO\PHU )53 V\VWHP
6SHFLPHQ
width
0HDVXUHGFRXSRQ
WKLFNQHVV
Measured
UXSWXUHORDG
&RXSRQ
ID
in.
mm.
in.
mm.
NLSV
N1
T-1
2
50.8
0.055
1.40
17.8
T-2
2
50.8
0.062
1.58
16.4
T-3
2
50.8
1.75
16.7
74.3
T-4
2
50.8
0.053
1.35
16.7
74.3
T-5
2
50.8
0.061
1.55
17.4
77.4
Average
2
50.8
0.060
1.52
17.0
75.6
XVLQJWKHZHWOD\XSWHFKQLTXH%DVHGRQWKHNQRZQ¿EHU
FRQWHQWRIWKLV)53V\VWHPWKHQHW¿EHUDUHDLVLQ2/
LQ PP2PP ZLGWK SHU SO\$IWHU WKH V\VWHP KDV
FXUHG¿YHLQ PP ZLGHWHVWFRXSRQVDUHFXWIURP
the panel. The test coupons are tested in tension to failure
LQ DFFRUGDQFH ZLWK$670 ''0 7DEXODWHG LQ
Table 16.1a are the results of the tension tests.
Table 16.1b—FRP system net fiber and gross laminate property calculations
1HW¿EHUDUHDSURSHUW\FDOFXODWLRQV
2
Af PP PP PP
= 16.8 mm2
Af = ntfwf
Calculate the average FRP system tensile
VWUHQJWKEDVHGRQQHW¿EHUDUHD
f fu =
average rupture load
Af
f fu =
Calculate the average FRP system tensile
VWUHQJWKSHUXQLWZLGWKEDVHGRQQHW¿EHU
area:
p fu =
f fu Af
wf
2
Af LQ LQ LQ LQ
Calculate AfXVLQJWKHNQRZQQHW¿EHU
area ply thickness:
f fu =
*URVVODPLQDWHDUHDSURSHUW\FDOFXODWLRQV
2
p fu =
17 kip
= 650 ksi
0.026 in.2
75.62 kN
= 4.5 kN/mm 2
16.8 mm 2
(650 ksi)(0.026 in.2 )
= 8.4 kip/in.
2 in.
(4.5 kN/mm 2 )(16.8 mm 2 )
50.8 mm
= 1.49 kN/mm
p fu =
Calculate Af using the average, measured
laminate thickness:
Af LQ LQ LQ2
Af = tfwf
Af PP PP PP2
Calculate the average FRP system tensile
strength based on gross-laminate area:
f fu =
average rupture load
Af
Calculate the average FRP system tensile
strength per unit width based on laminate
area:
p fu =
f fu Af
wf
@Seismicisolation
@Seismicisolation
f fu =
f fu =
p fu =
17 kip
= 140 ksi
0.120 in.2
75.62 kN
= 0.997 kN/mm 2
77.4 mm 2
(140 ksi)(0.120 in.2 )
= 8.4 kip/in.
2 in.
(0.98 kN/mm 2 )(77.4 mm 2 )
50.8 mm
= 1.49 kN/mm
p fu =
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48
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.2—Comparison of FRP systems’ tensile
properties
Two FRP systems are being considered for strengthening concrete members. The mechanical properties of two
FRP systems are available from respective manufacturers.
6\VWHP$FRQVLVWVRIGU\FDUERQ¿EHUXQLGLUHFWLRQDOVKHHWV
and is installed with an adhesive resin using the wet layup
WHFKQLTXH6\VWHP%FRQVLVWVRISUHFXUHGFDUERQ¿EHUUHVLQ
laminates that are bonded to the concrete surface with an
adhesive resin. Excerpts from the data sheets provided by the
FRP system manufacturers are given in Table 16.2a. After
reviewing the material data sheets sent by the FRP system
manufacturers, the licensed design professional compares
the tensile strengths of the two systems.
Because the data sheets for both systems are reporting
statistically based properties, it is possible to directly
compare the tensile strength and modulus of both systems,
as shown in Table 16.2b.
Table 16.2a—Material properties and description of two types of FRP systems
6\VWHP$ H[FHUSWVIURPGDWDVKHHW
6\VWHP% H[FHUSWVIURPGDWDVKHHW
System type: dry, unidirectional sheet
Fiber type: high-strength carbon
Polymer resin: epoxy
System type: precured, unidirectional laminate
Fiber type: high-strength carbon
Polymer resin: epoxy
System A is installed using a wet layup procedure where the dry carbon¿EHUVKHHWVDUHLPSUHJQDWHGDQGDGKHUHGZLWKDQHSR[\UHVLQRQVLWH
System B’s precured laminates are bonded to the concrete substrate using
System B’s epoxy paste adhesive.
Mechanical properties*†‡
Mechanical properties*†
tf LQ PP
tf LQ PP
ffu* NVL 1PP2
ffu NVL 1PP2
İfu* = 1.6%
İfu* = 1.5%
Ef NVL 1PP2
Ef NVL 1PP2
*
5HSRUWHGSURSHUWLHVDUHEDVHGRQDSRSXODWLRQRIRUPRUHFRXSRQVWHVWHGLQDFFRUGDQFHZLWK$670''0
Reported properties have been statistically adjusted by subtracting three standard deviations from the mean tensile stress and strain.
‡
7KLFNQHVVLVEDVHGRQWKHQHW¿EHUDUHDIRURQHSO\RIWKH)53V\VWHP5HVLQLVH[FOXGHG$FWXDOLQVWDOOHGWKLFNQHVVRIFXUHG)53LVWRLQ WRPP SHUSO\
†
Table 16.2b—Procedure comparing two types of FRP systems
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
Step 1A—Calculate the tensile
strength per unit width of System A
pfu* = ffu*tf
pfu* NVL LQ NLSLQ
pfu* N1PP2 PP N1PP
Step 1B—Calculate the tensile
strength per unit width of System B
pfu* = ffu*tf
pfu
NVL LQ NLSLQ
pfu
N1PP2 PP N1PP
Step 2A—Calculate the tensile
modulus per unit width of System
A
kf = Eftf
kf NVL LQ NLSLQ
kf N1PP2 PP N1PP
Step 2B—Calculate the tensile
modulus per unit width of System B
kf = Eftf
kf NVL LQ NLSLQ
kf N1PP2 PP N1PP
Step 3—Compare the two systems
Compare the tensile strengths:
pfu* 6\VWHP$
pfu* 6\VWHP%
Compare the stiffnesses:
kf 6\VWHP$
kf 6\VWHP%
p*fu (System B)
p*fu (System A)
=
19 kip/in.
= 2.66
7.15 kip/in.
‫׵‬WKUHHSOLHVRI6\VWHP$DUHUHTXLUHGIRUHDFKSO\RI
6\VWHP%IRUDQHTXLYDOHQWWHQVLOHVWUHQJWK
k f (System B)
k f (System A)
=
1100 kip/in.
= 2.56
429 kip/in.
‫׵‬WKUHHSOLHVRI6\VWHP$DUHUHTXLUHGIRUHDFKSO\RI
6\VWHP%IRUDQHTXLYDOHQWVWLIIQHVV
p*fu (System B)
p*fu (System A)
=
3.33 kN/mm
= 2.66
1.25 kN/mm
‫׵‬WKUHHSOLHVRI6\VWHP$DUHUHTXLUHGIRUHDFKSO\RI
6\VWHP%IRUDQHTXLYDOHQWWHQVLOHVWUHQJWK
k f (System A)
k f (System B)
=
192.7 kN/mm
= 2.56
75.1 kN/mm
‫׵‬WKUHHSOLHVRI6\VWHP$DUHUHTXLUHGIRUHDFKSO\RI
6\VWHP%IRUDQHTXLYDOHQWVWLIIQHVV
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Because all the design procedures outlined in this document limit the strain in the FRP material, the full nominal
strength of the material is not used and should not be the
basis of comparison between two material systems. When
considering various FRP material systems for a particular
application, the FRP systems should be compared based
RQ HTXLYDOHQW VWLIIQHVV RQO\ ,Q DGGLWLRQ HDFK )53 V\VWHP
under consideration should have the ability to develop the
VWUDLQ DVVRFLDWHG ZLWK WKH HIIHFWLYH VWUDLQ UHTXLUHG E\ WKH
DSSOLFDWLRQZLWKRXWUXSWXULQJİfu!İfe.
49
In many instances, it may be possible to vary the width of
WKH)53VWULSDVRSSRVHGWRWKHQXPEHURISOLHV XVHODUJHU
ZLGWKVIRUV\VWHPVZLWKORZHUWKLFNQHVVHVDQGYLFHYHUVD ,QVXFKLQVWDQFHVHTXLYDOHQWVWLIIQHVVFDOFXODWLRQVW\SLFDOO\
ZLOO QRW \LHOG HTXLYDOHQW FRQWULEXWLRQV WR WKH VWUHQJWK RI D
PHPEHU ,Q JHQHUDO WKLQQHU ORZHU ntf DQG ZLGHU KLJKHU
wf )53V\VWHPVZLOOSURYLGHDKLJKHUOHYHORIVWUHQJWKWRD
PHPEHUGXHWRORZHUERQGVWUHVVHV7KHH[DFWHTXLYDOHQF\
however, can only be found by performing complete calcuODWLRQV DFFRUGLQJ WR SURFHGXUHV GHVFULEHG LQ Chapters 10,
11, and 12RIWKLVJXLGH IRUHDFKV\VWHP
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50
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.3—Flexural strengthening of an interior
reinforced concrete beam with FRP laminates
A simply supported concrete beam reinforced with three No.
EDUV )LJ LVORFDWHGLQDQXQRFFXSLHGZDUHKRXVHDQG
is subjected to a 50 percent increase in its live-load-carrying
UHTXLUHPHQWV$QDQDO\VLVRIWKHH[LVWLQJEHDPLQGLFDWHVWKDW
WKHEHDPVWLOOKDVVXI¿FLHQWVKHDUVWUHQJWKWRUHVLVWWKHQHZ
UHTXLUHG VKHDU VWUHQJWK DQG PHHWV WKH GHÀHFWLRQ DQG FUDFN
FRQWURO VHUYLFHDELOLW\ UHTXLUHPHQWV ,WV ÀH[XUDO VWUHQJWK
KRZHYHULVLQDGHTXDWHWRFDUU\WKHLQFUHDVHGOLYHORDG
Summarized in Table 16.3a are the existing and new loadings and associated midspan moments for the beam. The
existing reinforced concrete beam should be strengthened
ZLWKWKH)53V\VWHPGHVFULEHGLQ7DEOHEVSHFL¿FDOO\
WZRLQ PP ZLGH[IW P ORQJSOLHVERQGHG
WRWKHVRI¿WRIWKHEHDPXVLQJWKHZHWOD\XSWHFKQLTXH
By inspection, the degree of strengthening is reasonable
LQWKDWLWGRHVPHHWWKHVWUHQJWKHQLQJOLPLWFULWHULDVSHFL¿HG
LQ(T 7KDWLVWKHH[LVWLQJPRPHQWVWUHQJWKZLWKRXW
)53 ࢥMn w/o NLSIW N1P LVJUHDWHUWKDQWKH
XQVWUHQJWKHQHGPRPHQWOLPLW MDL + 0.75MLL new = 177
NLSIW N1P 7KH GHVLJQ FDOFXODWLRQV XVHG WR YHULI\
WKLVFRQ¿JXUDWLRQIROORZLQ7DEOHF
)LJ²6FKHPDWLFRIWKHLGHDOL]HGVLPSO\VXSSRUWHGEHDPZLWK)53H[WHUQDOUHLQIRUFHPHQW
Table 16.3a—Loadings and corresponding moments
Loading/moment
([LVWLQJORDGV
$QWLFLSDWHGORDGV
Dead loads wDL
1.00 kip/ft
14.6 N/mm
1.00 kip/ft
14.6 N/mm
Live load wLL
1.20 kip/ft
17.5 N/mm
1.80 kip/ft
26.3 N/mm
8QIDFWRUHGORDGV wDL + wLL
2.20 kip/ft
32.1 N/mm
2.80 kip/ft
1PP
8QVWUHQJWKHQHGORDGOLPLW wDL + 0.75wLL
NA
NA
2.50 kip/ft
35.8 N/mm
)DFWRUHGORDGV wDL + 1.6wLL
3.12 kip/ft
45.5 N/mm
4.08 kip/ft
1PP
Dead-load moment MDL
72 kip-ft
N1P
72 kip-ft
N1P
Live-load moment MLL
86 kip-ft
117 kN-m
130 kip-ft
176 kN-m
Service-load moment Ms
158 kip-ft
214 kN-m
202 kip-ft
274 kN-m
8QVWUHQJWKHQHGPRPHQWOLPLW MDL + 0.75MLL
NA
NA
177 kip-ft
240 kN-m
Factored moment Mu
224 kip-ft
304 kN-m
NLSIW
N1P
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
51
Table 16.3b—Manufacturer’s reported FRP system properties
Thickness per ply tf
Ultimate tensile strength
ffu*
5XSWXUHVWUDLQİfu*
Modulus of elasticity of FRP laminates Ef
0.040 in.
1.02 mm
NVL
621 N/mm2
0.015 in./in.
0.015 mm/mm
5360 ksi
37,000 N/mm2
Table 16.3c—Procedure for flexural strengthening of an interior reinforced concrete beam with fiberreinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
ffu = CEffu*
ffu NVL NVL
ffu 1PP2 1PP2
İfu = CEİfu*
İfu LQLQ LQLQ
İfu PPPP PPPP
ȕ1 from ACI 318-14, Section 22.2.2.4.3
ȕ1 ± fcƍ ȕ1 ± fcƍ Ec = 57, 000 f c′
Ec = 57, 000 5000 psi = 4,030,000 psi
Ec = 4700 34.5 N/mm 2 = 27,600 N/mm 2
Properties of the existing reinforcing steel:
As LQ2 LQ2
As PP2 PP2
Af SOLHV LQSO\ LQ LQ2
Af SOLHV PPSO\ PP PP2
6WHS²&DOFXODWHWKH)53V\VWHP
GHVLJQPDWHULDOSURSHUWLHV
The beam is located in an interior space
DQGDFDUERQ)53 &)53 PDWHULDOZLOO
EHXVHG7KHUHIRUHSHU7DEOHDQ
HQYLURQPHQWDOUHGXFWLRQIDFWRURILV
suggested.
6WHS²3UHOLPLQDU\FDOFXODWLRQV
Properties of the concrete:
Properties of the externally bonded FRP
reinforcement:
Af = ntfwf
6WHS²'HWHUPLQHWKHH[LVWLQJVWDWHRI
VWUDLQRQWKHVRI¿W
The existing state of strain is calculated
assuming the beam is cracked and the only
loads acting on the beam at the time of the
FRP installation are dead loads. A cracked
section analysis of the existing beam gives k =
0.334 and Icr LQ4 = 2471 × 106 mm4
ε bi =
M DL d f − kd
NLSLQ >LQ − LQ @
LQ4 NVL
= 0.00061
ε bi =
I cr Ec
N1PP >PP − PP @
× 6 PP 4 N1PP 2
= 0.00061
ε bi =
6WHS²'HWHUPLQHWKHGHVLJQVWUDLQRI
the FRP system
The design strain of FRP accounting for
GHERQGLQJIDLOXUHPRGHİfd is calculated
XVLQJ(T ε fd = 0.083
5000 psi
SVL LQ
≤ = ε fd = 0.41
34.5 N/mm 2
1PP3 PP
= ≤ = Because the design strain is smaller than
the rupture strain, debonding controls the
design of the FRP system.
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52
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.3c (cont.)—Procedure for flexural strengthening of an interior reinforced concrete beam with
fiber-reinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
c LQ LQ
c PP PP
⎛ 24 in. − 4.3 in.⎞
ε fe = 0.003 ⎜
⎟⎠ − 0.00061 ≤ 0.009
⎝
4.3 in.
⎛ PP − PP ⎞
ε fe = ⎜
⎟⎠ − ≤ ⎝
PP
İfe !
İfe !
İfe İfd İfe İfd 4.3 in.
⎛
⎞
ε c = (0.09 + 0.00061) ⎜
= 0.0021
⎝ 24 in. − 4.3 in.⎟⎠
PP
⎛
⎞
ε c = + ⎜
= ⎝ PP − PP ⎟⎠
⎛ 21.5 in. − 4.3 in.⎞
ε s = (0.09 + 0.00061) ⎜
= 0.0084
⎝ 24 in. − 4.3 in. ⎟⎠
⎛ 546.1 mm − 109.2 mm ⎞
ε s = (0.09 + 0.00061) ⎜
= 0.0084
⎝ 609.6 mm − 109.2 mm ⎟⎠
fs = Esİs”fy
fs NVL ”NVL
fs NVL”NVL
Hence, fs = 60 ksi
fs N1PP2 ”N1PP2
fs = 1.68 kN/mm2”N1PP2
Hence, fs = 0.414 kN/mm2
ffe = Efİfe
ffe NVL NVL
ffe N1PP2 N1PP2
6WHS²(VWLPDWHcWKHGHSWKWRWKH
QHXWUDOD[LV
A reasonable initial estimate of c is
0.20d. The value of the c is adjusted after
FKHFNLQJHTXLOLEULXP
c = 0.20d
6WHS²'HWHUPLQHWKHHIIHFWLYHOHYHORI
VWUDLQLQWKH)53UHLQIRUFHPHQW
The effective strain level in the FRP may
EHIRXQGIURP(T ⎛ d f − c⎞
ε fe = 0.003 ⎜
= ε bi ≤ ε fd
⎝ c ⎟⎠
Note that for the neutral axis depth
selected, FRP debonding would be in
the failure mode because the second
H[SUHVVLRQLQWKLVHTXDWLRQFRQWUROV,IWKH
¿UVWH[SUHVVLRQJRYHUQHGWKHQFRQFUHWH
crushing would be in the failure mode.
Because FRP controls the failure of the
section, the concrete strain at failure
İc may be less than 0.003 and can be
calculated using similar triangles:
⎛ c ⎞
ε c = (ε fe + ε bi ) ⎜
⎟
⎝ d f − c⎠
6WHS²&DOFXODWHWKHVWUDLQLQWKH
H[LVWLQJUHLQIRUFLQJVWHHO
The strain in the reinforcing steel can
be calculated using similar triangles
DFFRUGLQJWR(T ⎛ c ⎞
ε s = ε fe + ε bi ⎜
⎟
⎝ d f − c⎠
6WHS²&DOFXODWHWKHVWUHVVOHYHOLQWKH
UHLQIRUFLQJVWHHODQG)53
7KHVWUHVVHVDUHFDOFXODWHGXVLQJ(T
E DQG+RRNH¶V/DZ
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
53
Table 16.3c (cont.)—Procedure for flexural strengthening of an interior reinforced concrete beam with
fiber-reinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
6WHS²&DOFXODWHWKHLQWHUQDOIRUFH
UHVXOWDQWVDQGFKHFNHTXLOLEULXP
Concrete stress block factors may be
calculated using ACI 318. Approximate
stress block factors may also be calculated
based on the parabolic stress-strain
relationship for concrete as follows:
β1 =
4ε ′c − ε c
6ε ′c − 2ε c
α1 =
3ε ′c ε c − ε c2
3β1ε′c 2
β1 =
α1 =
4(0.0021) − 0.0021
= 0.749
6(0.0021) − 2(0.0021)
β1 =
− 2
= 0.886
2
α1 =
4(0.0021) − 0.0021
= 0.749
6(0.0021) − 2(0.0021)
− 2
= 0.886
2
ZKHUHİcƍLVVWUDLQFRUUHVSRQGLQJWRfcƍ
calculated as
ε ′c =
1.7 f c′
Ec
ε ′c =
= 0.0021
4.03 × 106
ε ′c =
= 0.0021
27, 600
)RUFHHTXLOLEULXPLVYHUL¿HGE\FKHFNLQJ
the initial estimate of cZLWK(T J c=
As f s + Af f fe
c=
α1 f c′β1b
(3.00 in.2 )(60 ksi) + (0.96 in.2 )(48.2 ksi)
(0.886)(5 ksi)(0.749)(12 in.)
c LQLQQJ
‫׵‬revise estimate of cDQGUHSHDW6WHSVWKURXJK
XQWLOHTXLOLEULXPLVDFKLHYHG
(1935.48 mm 2 )(414 N/mm 2 ) + (619 mm 2 )(330 N/mm 2 )
(0.886)(34.5 N/mm 2 )(0.749)(304.8 mm)
c=
c PPPPQJ
‫ ׵‬revise estimate of cDQGUHSHDW6WHSVWKURXJK
XQWLOHTXLOLEULXPLVDFKLHYHG
6WHS²$GMXVWcXQWLOIRUFHHTXLOLEULXP
LVVDWLV¿HG
6WHSVWKURXJKZHUHUHSHDWHGVHYHUDO
times with different values of c until
HTXLOLEULXPZDVDFKLHYHG7KHUHVXOWVRI
WKH¿QDOLWHUDWLRQDUH
c LQİs fs = fy NVL
ȕ1 Į1 DQGffd = 48.2 ksi
c=
LQ2 NVL + LQ2 NVL
NVL LQ
c=
PP 2 1PP 2 + PP 2 1PP 2
1PP 2 PP
c = 5.17 in.
‫ ׵‬the value of cVHOHFWHGIRUWKH¿QDOLWHUDWLRQLV
correct.
c = 131 mm
‫ ׵‬the value of cVHOHFWHGIRUWKH¿QDOLWHUDWLRQLV
correct.
0.786(5.17 in.) ⎞
⎛
M ns = (3.00 in.2 )(60 ksi) ⎜ 21.5 in. −
⎟⎠
⎝
2
0.786(131 mm) ⎞
⎛
M ns = (1935.5 mm 2 )(414 N/mm 2 ) ⎜ 546.1 mm −
⎝
⎠⎟
2
Mns NLSLQ NLSIW
Mns î81PP N1P
0.786(5.17 in.) ⎞
⎛
M nf = (0.96 in.2 )(48.2 ksi) ⎜ 24 in. −
⎝
⎠⎟
2
0.786(131 mm) ⎞
⎛
M nf = (619 mm 2 )(330 N/mm 2 ) ⎜ 609.6 mm −
⎟⎠
⎝
2
Mnf = 1020 kip-in. = 85 kip-ft
Mnf = 1.140 × 108 N-mm = 114 kN-m
6WHS²&DOFXODWHÀH[XUDOVWUHQJWK
FRPSRQHQWV
7KHGHVLJQÀH[XUDOVWUHQJWKLVFDOFXODWHG
XVLQJ(T G $QDGGLWLRQDO
UHGXFWLRQIDFWRUȥf = 0.85, is applied to
the contribution of the FRP system.
Steel contribution to bending:
β c⎞
⎛
M ns = As f s ⎜ d − 1 ⎟
⎝
2 ⎠
FRP contribution to bending:
β c⎞
⎛
M nf = Af f fe ⎜ d f − 1 ⎟
⎝
2 ⎠
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.3c (cont.)—Procedure for flexural strengthening of an interior reinforced concrete beam with
fiber-reinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
ࢥMn >NLSIW NLSIW @
ࢥMn NLSIW•Mu NLSIW
ࢥMn >N1P N1P @
ࢥMn N1P•Mu N1P
‫׵‬the strengthened section is capable of sustaining the
QHZUHTXLUHGPRPHQWVWUHQJWK
‫׵‬the strengthened section is capable of sustaining
WKHQHZUHTXLUHGPRPHQWVWUHQJWK
*
k = 0.343
k = 0.343
kd LQ LQ
kd PP PP
†
§
fs,s NVL” NVL NVL
fs,s 1PP2” 1PP2 1PP2
‫׵‬the stress level in the reinforcing steel is within the
recommended limit.
‫׵‬the stress level in the reinforcing steel is within the
recommended limit.
6WHS²&DOFXODWHGHVLJQÀH[XUDO
VWUHQJWKRIWKHVHFWLRQ
7KHGHVLJQÀH[XUDOVWUHQJWKLVFDOFXODWHG
XVLQJ(T DQG G %HFDXVH
İs !DVWUHQJWKUHGXFWLRQ
IDFWRURIࢥ LVDSSURSULDWHSHU(T
ࢥMn ࢥ>MnsȥfMnf]
6WHS²&KHFNVHUYLFHVWUHVVHVLQWKH
UHLQIRUFLQJVWHHODQGWKH)53
Calculate the elastic depth to the cracked
QHXWUDOD[LV7KLVFDQEHVLPSOL¿HGIRUD
rectangular beam without compression
reinforcement as follows:
k=
Ef ⎞
⎛ Es
⎜⎝ ρs E + ρ f E ⎟⎠
c
c
2
Ef ⎛ d f ⎞⎞
⎛ E
+2 ⎜ ρs s + ρ f
E
Ec ⎝⎜ d ⎠⎟ ⎟⎠
⎝
c
‡
Ef ⎞
⎛ E
− ⎜ ρs s + ρ f
Ec ⎟⎠
⎝ Ec
Calculate the stress level in the reinforcing
VWHHOXVLQJ(T DQGYHULI\WKDW
it is less than the recommended limit per
(T D f s ,s =
⎡
kd ⎞ ⎤
⎛
⎢ M s + ε bi Af E f ⎝⎜ d f − 3 ⎠⎟ ⎥ (d − kd ) Es
⎣
⎦
kd ⎞
kd ⎞
⎛
⎛
As Es ⎜ d − ⎟ (d − kd ) + Af E f ⎜ d f − ⎟ (d f − kd )
⎝
⎝
3⎠
3⎠
fs,s”fy
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
55
Table 16.3c (cont.)—Procedure for flexural strengthening of an interior reinforced concrete beam with
fiber-reinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
⎛ 5360 ksi ⎞ ⎛ 24 in. − 7.37 in. ⎞
f f ,s = 40.4 ksi ⎜
⎝ NVL ⎟⎠ ⎝⎜ LQ − LQ⎠⎟
⎛ N1PP 2 ⎞ ⎛ PP − PP ⎞
f f ,s = 0.278 kN/mm 2 ⎜
⎜
⎟
⎝ 200 kN/mm 2 ⎟⎠ ⎝ 546 mm − 187 mm ⎠
− NVL
− 1PP 2
6WHS²&KHFNFUHHSUXSWXUHOLPLWDW
VHUYLFHRIWKH)53
Calculate the stress level in the FRP using
(T DQGYHULI\WKDWLWLVOHVV
than creep-rupture stress limit given in
7DEOH$VVXPHWKDWWKHIXOOVHUYLFH
load is sustained.
⎛ E f ⎞ ⎛ d f − kd ⎞
− ε bi E f
f f ,s = f s.s ⎜ ⎟ ⎜
⎝ Es ⎠ ⎝ d − kd ⎟⎠
For a carbon FRP system, the sustained
plus cyclic stress limit is obtained from
7DEOH
ff,s NVL” NVL NVL
ff,s = 38 N/mm2” 1PP2 1PP2
‫׵‬the stress level in the FRP is within the
recommended sustained plus cyclic stress limit.
‫׵‬the stress level in the FRP is within the
recommended sustained plus cyclic stress limit.
Sustained plus cyclic stress limit = 0.55ffu
*
2
⎡
⎡
⎛ ⎞
⎛ ⎞ ⎤
⎛ ⎞
⎛ ⎞ ⎛ LQ ⎞ ⎤ ⎡
⎛ ⎞
⎛ ⎞ ⎤
k = ⎢0.0116 ⎜
+ 0.00372 ⎜
+ 2 ⎢0.0116 ⎜
+ 0.00372 ⎜
− 0.0116 ⎜
+ 0.00372 ⎜
⎝ 4030 ⎟⎠
⎝ 4030 ⎟⎠ ⎥⎦
⎝ 4030 ⎟⎠
⎝ 4030 ⎟⎠ ⎜⎝ 21.5 in.⎟⎠ ⎥⎦ ⎢⎣
⎝ 4030 ⎟⎠
⎝ 4030 ⎟⎠ ⎥⎦
⎣
⎣
†
f s ,s
‡
⎛⎡
⎞
7.37 in.⎞ ⎤ ⎤
⎡
⎛
3
⎟ ⎥ × [ LQ − LQ NVL ]⎟
⎜ ⎢ NLSLQ + ⎢ LQ × NVL ⎝⎜ LQ −
3 ⎠ ⎥⎦ ⎦
⎝⎣
⎠
⎣
=
⎛⎡
7.37 in.⎞
7.37 in.⎞
⎤⎞
⎤ ⎡
⎛
⎛
2
2
⎟ LQ − LQ ⎥⎟
⎟ LQ − LQ ⎥ + ⎢ LQ NVL ⎝⎜ LQ −
⎢ LQ NVL × ⎜⎝ LQ −
3 ⎠
3 ⎠
⎝⎜ ⎣
⎦ ⎣
⎦⎠
2
⎡
⎡
⎛ ⎞
⎛ ⎞ ⎤
⎛ ⎞
⎛ ⎞ ⎛ PP ⎞ ⎤ ⎡
⎛ ⎞
⎛ ⎞ ⎤
k = ⎢0.0116 ⎜
+ 0.00372 ⎜
+ 2 ⎢0.0116 ⎜
+ 0.00372 ⎜
− 0.0116 ⎜
+ 0.00372 ⎜
⎝ 27.6 ⎟⎠
⎝ 27.6 ⎟⎠ ⎥⎦
⎝ 27.6 ⎟⎠
⎝ 27.6 ⎟⎠ ⎜⎝ 546 mm ⎟⎠ ⎥⎦ ⎢⎣
⎝ 27.6 ⎟⎠
⎝ 27.6 ⎟⎠ ⎥⎦
⎣
⎣
§
f s ,s
⎛⎡
⎞
187 mm ⎞ ⎤ ⎤
⎡
⎛
2
2
2
⎟ ⎥ × ⎡ PP − PP N1PP ⎤⎦⎟
⎜ ⎢ N1PP + ⎢ PP N1PP × ⎜⎝ PP −
3 ⎠ ⎥⎦ ⎦ ⎣
⎝⎣
⎠
⎣
=
⎛⎡
187 mm ⎞
187 mm ⎞
⎤⎞
⎤ ⎡
⎛
2
2
2
2 ⎛
PP
N1PP
PP
PP
PP
PP
N
1PP
PP
−
PP
−
PP ⎥⎟
×
−
−
+
⎜⎝
⎟
⎟
⎥ ⎢
⎜⎝ ⎢
⎝⎜
3 ⎠
3 ⎠
⎣
⎦ ⎣
⎦⎠
In detailing the FRP reinforcement, the FRP should be
terminated a minimum of ƐdfFDOFXODWHGSHU(T SDVW
the point on the moment diagram that represents cracking.
The factored shear force at the termination should also be
checked against the shear force that causes FRP end peeling,
estimated as two-thirds of the concrete shear strength. If the
shear force is greater than two-thirds of the concrete shear
strength, the FRP strips should be extended further toward
the supports. U-wraps may also be used to reinforce against
cover delamination.
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56
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.4—Flexural strengthening of an interior
reinforced concrete beam with near-surfacemounted FRP bars
$Q H[LVWLQJ UHLQIRUFHG FRQFUHWH EHDP )LJ LV WR
be strengthened using the loads given in Table 16.3a and
WKHQHDUVXUIDFHPRXQWHG 160 )53V\VWHPGHVFULEHGLQ
7DEOH D 6SHFL¿FDOO\ WKUHH 1R FDUERQ )53 &)53 EDUVDUHWREHXVHGDWDGLVWDQFHLQ PP IURPWKH
H[WUHPHWRS¿EHURIWKHEHDP
By inspection, the degree of strengthening is reasonable
in that it does meet the strengthening limit criteria put forth
LQ(T 7KDWLVWKHH[LVWLQJÀH[XUDOVWUHQJWKZLWKRXW
)53 ࢥMn w/o NLSIW N1P LVJUHDWHUWKDQWKH
XQVWUHQJWKHQHGPRPHQWOLPLW MDL + 0.75MLL new = 177
NLSIW N1P 7KH GHVLJQ FDOFXODWLRQV XVHG WR YHULI\
WKLVFRQ¿JXUDWLRQIROORZLQ7DEOHE
)LJ ²6FKHPDWLF RI WKH LGHDOL]HG VLPSO\ VXSSRUWHG EHDP ZLWK )53 H[WHUQDO
reinforcement.
Table 16.4a—Manufacturer’s reported NSM FRP system properties
Area per No. 3 bar
0.10 in.2
64.5 mm2
Ultimate tensile strength ffu*
250 ksi
1725 N/mm2
5XSWXUHVWUDLQİfu*
Modulus of elasticity of FRP laminates Ef
0.013 in./in.
0.013 mm/mm
NVL
132,700 N/mm2
Length of the beam Ɛ
IW
8.84 m
Bay width l2
30 ft
P
Width of beam w
24 in.
610 mm
dp
22.5 in.
571 mm
h
25 in.
635 mm
(IIHFWLYHÀDQJHZLGWKbf
87 in.
2210 mm
Flange thickness hf
4 in.
102 mm
4000 psi
27.6 N/mm2
Strands diameter
1/2 in.
12.7 mm
fpe
165 ksi
1138 N/mm2
fpy
230 ksi
1586 N/mm2
fpu
270 ksi
1860 N/mm2
Ep
28,500 ksi
î5 N/mm2
ࢥMn without FRP
336 kip-ft
455 kN-m
fcƍ
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
57
Table 16.4b—Procedure for flexural strengthening of an interior reinforced concrete beam with NSM FRP bars
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
ffu = CEffu*
ffu NVL NVL
ffu 1PP2 1PP2
İfu = CEİfu*
İfu LQLQ LQLQ
İfu PPPP PPPP
6WHS²&DOFXODWHWKH)53V\VWHP
GHVLJQPDWHULDOSURSHUWLHV
The beam is located in an interior space
and a CFRP material will be used.
7KHUHIRUHSHU7DEOHDQHQYLURQPHQWDO
UHGXFWLRQIDFWRURILVVXJJHVWHG
6WHS²3UHOLPLQDU\FDOFXODWLRQV
Properties of the concrete:
ȕ1 from ACI 318-14, Section 22.2.2.4.3
β1 = 1.05 − 0.05
Ec = 57, 000 f c′
f c′
= 0.85
1000
β1 = 1.05 − 0.05
f c′
= 0.85
Ec = 57,000 5000 psi = 4,030,00 psi
Ec = 4700 34.5 N/mm 2 = 27,600 N/mm 2
As LQ2 LQ2
As PP2 PP2
Af EDUV LQ2EDU LQ2
Af EDUV PP2EDU PP2
6WHS²'HWHUPLQHWKHH[LVWLQJVWDWHRI
VWUDLQRQWKHVRI¿W
The existing state of strain is calculated
assuming the beam is cracked and the only
loads acting on the beam at the time of the
FRP installation are dead loads. A cracked
section analysis of the existing beam gives k =
0.334 and Icr LQ4 = 2471 × 106 mm4
ε bi =
M DL d f − kd
ε bi =
I cr Ec
(864 kip-in.) [23.7 in. − (0.334)(21.5 in.)]
(97.6 kN-mm) [602 mm − (0.334)(546 mm)]
= 0.00061 ε bi =
= 0.00061
(5937 in.4 )(4030 ksi)
(2471 × 106 mm 4 )(27.6 kN/mm 2 )
6WHS²'HWHUPLQHWKHERQGGHSHQGHQW
FRHI¿FLHQWRIWKH)53V\VWHP
Based on the manufacturer’s
recommendation, the dimensionless bondGHSHQGHQWFRHI¿FLHQWIRUÀH[XUHțm is 0.7.
țm = 0.7
țm = 0.7
c LQ LQ
c PP PP
6WHS²(VWLPDWHcWKHGHSWKWRWKH
QHXWUDOD[LV
A reasonable initial estimate of c is
0.20d. The value of the c is adjusted after
FKHFNLQJHTXLOLEULXP
c = 0.20d
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.4b (cont.)—Procedure for flexural strengthening of an interior reinforced concrete beam with
NSM FRP bars
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
⎛ 23.7 in. − 4.3 in.⎞
ε fe = 0.003 ⎜
⎟⎠ − 0.00061 = 0.0129
⎝
4.3 in.
⎛ 602 mm − 109 mm ⎞
ε fe = 0.003 ⎜
⎟⎠ − 0.00061 = 0.0129
⎝
109 mm
țmİfd țmİfd +HQFHİfe = 0.00865
0RGHRIIDLOXUHLV)53GHERQGLQJ
+HQFHİfe = 0.00865
0RGHRIIDLOXUHLV)53GHERQGLQJ
4.3 ⎞
⎛
ε c = + ⎜
= ⎝ 23.7 − 4.3 ⎟⎠
⎛ ⎞
ε c = + ⎜
= ⎝ − ⎟⎠
⎛ 21.5 − 4.3 ⎞
ε s = (0.00865 + 0.00061) ⎜
= 0.0082
⎝ 23.7 − 4.3 ⎟⎠
⎛ 546 − 109 ⎞
ε s = (0.00865 + 0.00061) ⎜
= 0.0082
⎝ 602 − 109 ⎟⎠
fs = Esİs”fy
fs NVL ”NVL
fs NVL!NVL
therefore, fs = 60 ksi
fs N1PP2 ”N1PP2
fs = 1.64 kN/mm2”N1PP2
therefore, fs = 0.414 kN/mm2
ffe = Efİfe
ffe NVL NVL
ffe 1PP2 1PP2
6WHS²'HWHUPLQHWKHHIIHFWLYHOHYHORI
VWUDLQLQWKH)53UHLQIRUFHPHQW
The effective strain level in the FRP may
EHIRXQGIURP(T ⎛ d f − c⎞
− ε bi ≤ κ m ε fd
ε fe = ⎜
⎝ c ⎟⎠
Note that for the neutral axis depth
selected, FRP debonding would be
the failure mode because the second
H[SUHVVLRQLQWKLVHTXDWLRQFRQWUROV,IWKH
¿UVWH[SUHVVLRQJRYHUQHGWKHQFRQFUHWH
crushing would be the failure mode.
Because FRP controls the failure of the
section, the concrete strain at failure,
İc, may be less than 0.003 and can be
calculated using similar triangles:
⎛ c ⎞
ε c = ε fd + ε bi ⎜
⎟
⎝ d f − c⎠
6WHS²&DOFXODWHWKHVWUDLQLQWKH
H[LVWLQJUHLQIRUFLQJVWHHO
The strain in the reinforcing steel can
be calculated using similar triangles
DFFRUGLQJWR(T D ⎛ d −c ⎞
ε s = (ε fe + ε bi ) ⎜
⎟
⎝ d f − c⎠
6WHS²&DOFXODWHWKHVWUHVVOHYHOLQWKH
UHLQIRUFLQJVWHHODQG)53
7KHVWUHVVHVDUHFDOFXODWHGXVLQJ(T
E DQG+RRNH¶V/DZ
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
59
Table 16.4b (cont.)—Procedure for flexural strengthening of an interior reinforced concrete beam with
NSM FRP bars
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
6WHS²&DOFXODWHWKHLQWHUQDOIRUFH
UHVXOWDQWVDQGFKHFNHTXLOLEULXP
Concrete stress block factors may be
calculated using ACI 318. Approximate
stress block factors may also be calculated
based on the parabolic stress-strain
relationship for concrete as follows:
β1 =
4ε ′c − ε c
6ε ′c − 2ε c
α1 =
3ε ′c ε c − ε c2
3β1ε′c 2
β1 =
α1 =
− = 0.743
− − 2
β1 =
2
= 0.870
α1 =
− = 0.743
− − 2
2
= 0.870
ZKHUHİcƍLVVWUDLQFRUUHVSRQGLQJWRfcƍ
calculated as
ε ′c =
1.7 f c′
Ec
ε ′c =
= 0.0021
4030 × 106
ε ′c =
= 0.0021
27, 606
)RUFHHTXLOLEULXPLVYHUL¿HGE\FKHFNLQJ
the initial estimate of cZLWK(T J c=
As f s + Af f fe
c=
α1 f c ' β1b
LQ2 NVL LQ2 NVL
NVL LQ
c=
PP 2 1PP 2 + PP 2 1PP 2
1PP 2 PP
c LQLQQJ
c PPLQQJ
‫׵‬revise estimate of cDQGUHSHDW6WHSVWKURXJK
XQWLOHTXLOLEULXPLVDFKLHYHG
‫׵‬revise estimate of cDQGUHSHDW6WHSVWKURXJK
XQWLOHTXLOLEULXPLVDFKLHYHG
6WHS²$GMXVWcXQWLOIRUFH
HTXLOLEULXPLVVDWLV¿HG
6WHSVWKURXJKZHUHUHSHDWHGVHYHUDO
times with different values of c until
HTXLOLEULXPZDVDFKLHYHG7KHUHVXOWVRI
WKH¿QDOLWHUDWLRQDUH
c LQİs fs = fy NVLİfe
İc ȕ1 Į1 DQGffe = 166 ksi
c=
LQ2 NVL + LQ2 NVL
NVL LQ
c=
PP 2 1PP 2 + PP 2 1PP 2
1PP 2 PP
c LQ§LQ
c PP§PP
‫ ׵‬the value of cVHOHFWHGIRUWKH¿QDOLWHUDWLRQLVFRUUHFW
‫׵‬the value of cVHOHFWHGIRUWKH¿QDOLWHUDWLRQLVFRUUHFW
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60
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.4b (cont.)—Procedure for flexural strengthening of an interior reinforced concrete beam with
NSM FRP bars
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
6WHS²&DOFXODWHÀH[XUDOVWUHQJWK
FRPSRQHQWV
7KHGHVLJQÀH[XUDOVWUHQJWKLVFDOFXODWHG
XVLQJ(T G $QDGGLWLRQDO
UHGXFWLRQIDFWRUȥf = 0.85, is applied to
the contribution of the FRP system.
Steel contribution to bending:
β c⎞
⎛
M ns = As f s ⎜ d − 1 ⎟
⎝
2 ⎠
0.786(5.25 in.) ⎞
⎛
M ns = (3.0 in.2 )(60 ksi) ⎜ 21.5 in. −
⎟⎠
⎝
2
M ns = (1935 mm 2 )(414 N/mm 2 ) ⎛⎜ 546 mm −
⎝
Mns NLSLQ NLSIW
0.786(133 mm)⎞
⎠⎟
2
Mns N1P
FRP contribution to bending:
β c⎞
⎛
M nf = As f fe ⎜ d f − 1 ⎟
⎝
2 ⎠
0.786(5.25 in.) ⎞
⎛
M nf = (0.3 in.2 )(166 ksi) ⎜ 23.7 in. −
⎟⎠
⎝
2
⎛
⎝
M nf = (194 mm )(1147 N/mm ) ⎜ 602.1 mm −
2
2
0.786(133 mm ) ⎞
2
Mnf NLSLQ NLSIW
Mnf = 122 kN-m
ࢥMn >NLSIW NLSIW @
ࢥMn NLSIW•Mu NLSIW
ࢥMn >N1P N1P @
ࢥMn N1P•Mu N1P
⎟⎠
6WHS²&DOFXODWHGHVLJQÀH[XUDO
VWUHQJWKRIWKHVHFWLRQ
7KHGHVLJQÀH[XUDOVWUHQJWKLVFDOFXODWHG
XVLQJ(T DQG G %HFDXVH
İs !DVWUHQJWKUHGXFWLRQ
IDFWRURIࢥ LVDSSURSULDWHSHU(T
ࢥMn ࢥ>MnsȥfMnf]
‫׵‬the strengthened section is capable of sustaining the ‫׵‬the strengthened section is capable of sustaining the
QHZUHTXLUHGÀH[XUDOVWUHQJWK
QHZUHTXLUHGÀH[XUDOVWUHQJWK
6WHS²&KHFNVHUYLFHVWUHVVHVLQWKH
UHLQIRUFLQJVWHHODQGWKH)53
Calculate the elastic depth to the cracked
QHXWUDOD[LV7KLVFDQEHVLPSOL¿HGIRUD
rectangular beam without compression
reinforcement as follows:
k=
Ef ⎞
⎛ Es
⎜⎝ ρs E + ρ f E ⎟⎠
c
c
⎛
+2 ⎜ ρs
⎝
‡
*
k = 0.345
kd LQ LQ
2
E ⎛ d ⎞⎞
Es
+ ρ f f ⎜ f ⎟⎟
Ec
Ec ⎝ d ⎠ ⎠
k = 0.345
kd PP PP
Ef ⎞
⎛ E
− ⎜ ρs s + ρ f
Ec ⎟⎠
⎝ Ec
Calculate the stress level in the reinforcing
VWHHOXVLQJ(T DQGYHULI\WKDW
it is less than the recommended limit per
(T D f s ,s =
⎡
kd ⎞ ⎤
⎛
⎢ M s + ε bi Af E f ⎝⎜ d f − 3 ⎠⎟ ⎥ (d − kd ) Es
⎦
⎣
kd ⎞
kd ⎞
⎛
⎛
As Es ⎜ d − ⎟ (d − kd ) + Af E f ⎜ d f − ⎟ (d f − kd )
⎝
⎝
3⎠
3⎠
fs,s”fy
†
fs,s NVL” NVL NVL
‫׵‬the stress level in the reinforcing steel is within the
recommended limit.
§
fs,s = 278 N/mm2” 1PP2 1PP2
‫׵‬the stress level in the reinforcing steel is within the
recommended limit.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
61
Table 16.4b (cont.)—Procedure for flexural strengthening of an interior reinforced concrete beam with
NSM FRP bars
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
⎛ NVL ⎞ ⎛ LQ − LQ⎞
f f ,s = 40.3 ksi ⎜
⎝ NVL ⎟⎠ ⎜⎝ LQ − LQ ⎟⎠
⎛ 133 kN/mm 2 ⎞ ⎛ 602 mm − 188 mm ⎞
f f .s = 0.278 kN/mm 2 ⎜
⎜
⎟
⎝ 200 kN/mm 2 ⎟⎠ ⎝ 546 mm − 188 mm ⎠
− NVL
− 1PP 2
6WHS²&KHFNFUHHSUXSWXUHOLPLWDW
VHUYLFHRIWKH)53
Calculate the stress level in the FRP using
(T DQGYHULI\WKDWLWLVOHVV
than creep-rupture stress limit given in
7DEOH$VVXPHWKDWWKHIXOOVHUYLFH
load is sustained.
⎛ E f ⎞ ⎛ d f − kd ⎞
f f ,s = f s ,s ⎜ ⎟ ⎜
− ε bi E f
⎝ Es ⎠ ⎝ d − kd ⎠⎟
For a carbon FRP system, the sustained
plus cyclic stress limit is obtained from
7DEOH
Sustained plus cyclic stress limit = 0.55ffu
*
ff,s = 134 N/mm2” 1PP2 1PP2
‫׵‬the stress level in the FRP is within the
recommended sustained plus cyclic stress limit.
‫׵‬the stress level in the FRP is within the
recommended sustained plus cyclic stress limit.
2
⎡
⎡
⎛ ⎞
⎛ ⎞ ⎤
⎛ ⎞
⎛ ⎞ ⎛ LQ⎞ ⎤ ⎡
⎛ ⎞
⎛ ,230 ⎞ ⎤
k = ⎢0.0116 ⎜
+ 0.0012 ⎜
+ 2 ⎢0.0116 ⎜
+ 0.0012 ⎜
− 0.0116 ⎜
+ 0.0012 ⎜
⎝ 4030 ⎟⎠
⎝ 4030 ⎟⎠ ⎥⎦
⎝ 4030 ⎟⎠
⎝ 4030 ⎟⎠ ⎜⎝ 21.5 in. ⎟⎠ ⎥⎦ ⎢⎣
⎝ 4030 ⎟⎠
⎝ 4030 ⎟⎠ ⎥⎦
⎣
⎣
†
f s ,s =
‡
ff,s NVL” NVL NVL
⎛⎡
⎞
⎡
7.4 in.⎞ ⎤ ⎤
⎛
2
⎜ ⎢ NLSLQ + ⎢ LQ × NVL ⎝⎜ LQ − 3 ⎠⎟ ⎥ ⎥ × [ LQ − LQ NVL ]⎟
⎝⎣
⎠
⎣
⎦⎦
⎛⎡
⎤⎞
7.4 in.⎞
7.4 in.⎞
⎤ ⎡
⎛
⎛
2
LQ2 NVL ⎜ LQ −
⎟ × LQ − LQ ⎥⎟
⎟ × LQ − LQ ⎥ + ⎢ LQ NVL ⎝⎜ LQ −
⎝
3 ⎠
3 ⎠
⎝⎜ ⎢⎣
⎦⎠
⎦ ⎣
2
⎡
⎡
⎛ 200 ⎞
⎛ 133 ⎞ ⎤
⎛ 200 ⎞
⎛ 133 ⎞ ⎛ 602 mm ⎞ ⎤ ⎡
⎛ 200 ⎞
⎛ 133 ⎞ ⎤
k = ⎢0.0116 ⎜
+ 0.0012 ⎜
+ 2 ⎢0.0116 ⎜
+ 0.0012 ⎜
− 0.0116 ⎜
+ 0.0012 ⎜
⎝ 27.6 ⎠⎟
⎝ 27.6 ⎠⎟ ⎥⎦
⎝ 27.6 ⎠⎟
⎝ 27.6 ⎠⎟ ⎝⎜ 546 mm ⎠⎟ ⎥⎦ ⎢⎣
⎝ 27.6 ⎠⎟
⎝ 27.6 ⎠⎟ ⎥⎦
⎣
⎣
§
f s ,s =
⎛⎡
⎞
188 mm ⎞ ⎤ ⎤
⎡
⎛
2
2
2
⎟ ⎥ × ⎡ PP − PP N1PP ⎦⎤⎟
⎜ ⎢ N1PP + ⎢ PP × N1PP × ⎝⎜ PP −
3 ⎠ ⎦⎥ ⎦ ⎣
⎝⎣
⎠
⎣
⎛⎡
188 mm ⎞
188 mm ⎞
⎤⎞
⎤ ⎡
⎛
⎛
2
2
2
2
⎟ PP − PP ⎥⎟
⎟ PP − PP ⎥ + ⎢ PP N1PP × ⎜⎝ PP −
⎜⎝ ⎢ PP N1PP × ⎜⎝ PP −
3 ⎠
3 ⎠
⎣
⎦ ⎣
⎦⎠
In detailing the FRP reinforcement, FRP bars should
EH WHUPLQDWHG DW D GLVWDQFH HTXDO WR WKH EDU GHYHORSPHQW
length past the point on the moment diagram that represents
cracking.
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62
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.5—Flexural strengthening of an interior
prestressed concrete beam with FRP laminates
A number of continuous prestressed concrete beams with
¿YHLQ PP GLDPHWHUERQGHGVWUDQGV )LJ are located in a parking garage that is being converted to
DQ RI¿FH VSDFH $OO SUHVWUHVVLQJ VWUDQGV DUH *UDGH NVL 1PP2 ORZUHOD[DWLRQ VHYHQZLUH VWUDQGV
7KH EHDPV UHTXLUH DQ LQFUHDVH LQ WKHLU OLYHORDGFDUU\LQJ
capacity from 50 to 75 lb/ft2 WRNJP2 7KHEHDPV
DUHDOVRUHTXLUHGWRVXSSRUWDQDGGLWLRQDOGHDGORDGRIOE
ft2 NJP2 $QDO\VLV LQGLFDWHV WKDW HDFK H[LVWLQJ EHDP
KDVDGHTXDWHÀH[XUDOFDSDFLW\WRFDUU\WKHQHZORDGVLQWKH
QHJDWLYH PRPHQW UHJLRQ DW WKH VXSSRUWV EXW LV GH¿FLHQW LQ
ÀH[XUHDWPLGVSDQDQGLQVKHDUDWWKHVXSSRUWV7KHEHDP
PHHWVWKHGHÀHFWLRQDQGFUDFNFRQWUROVHUYLFHDELOLW\UHTXLUH-
PHQWV 7KH FDVWLQSODFH EHDPV VXSSRUW D LQ PP slab. For bending at midspan, beams should be treated as
T-sections. Summarized in Table 16.5a are the existing and
new loads and associated midspan moments for the beam.
FRP system properties are shown in Table 16.3b.
By inspection, the degree of strengthening is reasonable
in that it does meet the strengthening limit criteria put forth
LQ(T 7KDWLVWKHH[LVWLQJÀH[XUDOVWUHQJWKZLWKRXW
)53 ࢥMn w/o NLSIW N1P LVJUHDWHUWKDQWKH
XQVWUHQJWKHQHGPRPHQWOLPLW MDL + 0.75MLL new = 273
NLSIW N1P 7KH GHVLJQ FDOFXODWLRQV XVHG WR YHULI\
WKLV FRQ¿JXUDWLRQ IROORZ 7KH EHDP LV WR EH VWUHQJWKHQHG
using the FRP system described in Table 16.3b. A one-ply,
LQ PP ZLGH VWULS RI )53 LV FRQVLGHUHG IRU WKLV
evaluation.
)LJ ²6FKHPDWLF RI WKH LGHDOL]HG FRQWLQXRXV SUHVWUHVVHG EHDP ZLWK )53 H[WHUQDO
reinforcement.
Table 16.5a—Loadings and corresponding moments
Loading/moment
([LVWLQJORDGV
$QWLFLSDWHGORDGV
Dead loads wDL
2.77 kip/ft
40.4 N/mm
NLSIW
45.1 N/mm
Live load wLL
1.60 kip/ft
23.3 N/mm
2.4 kip/ft
35 N/mm
8QIDFWRUHGORDGV wDL + wLL
4.37 kip/ft
63.8 N/mm
NLSIW
80.2 N/mm
8QVWUHQJWKHQHGORDGOLPLW wDL + 0.75wLL
NA
NA
5.2 kip/ft
1PP
)DFWRUHGORDGV wDL + 1.6wLL
5.88 kip/ft
1PP
7.55 kip/ft
110.2 N/mm
Dead-load moment MDL
147 kip-ft
N1P
162 kip-ft
220.2 kN-m
Live-load moment MLL
85 kip-ft
115 kN-m
126 kip-ft
171.1 kN-m
232 kip-ft
314 kN-m
288 kip-ft
N1P
NA
NA
273 kip-ft
371 kN-m
312 kip-ft
423 kN-m
NLSIW
538 kN-m
Service-load moment Ms
8QVWUHQJWKHQHGPRPHQWOLPLW MDL + 0.75MLL
Factored moment Mu
new
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
63
Table 16.5b—Procedure for flexural strengthening of an interior prestressed concrete beam with FRP
laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
ffu = CEffu*
ffu NVL NVL
ffu 1PP2 1PP2
İfu = CEİfu*
İfu LQLQ LQLQ
İfu PPPP PPPP
6WHS²&DOFXODWHWKH)53V\VWHP
GHVLJQPDWHULDOSURSHUWLHV
The beam is located in an interior space
and a CFRP material will be used.
7KHUHIRUHSHU7DEOHDQHQYLURQPHQWDO
UHGXFWLRQIDFWRURILVVXJJHVWHG
6WHS²3UHOLPLQDU\FDOFXODWLRQV
Properties of the concrete:
ȕ1 from ACI 318-14, Section 22.2.2.4.3
β1 = 1.05 − 0.05
f c′
= 0.85
1000
β1 = 1.05 − 0.05
f c′
= 0.85
Ec = 57, 000 f c′
Ec = 57, 000 4000 psi = 3,605,00 psi
Ec = 4700 27.6 N/mm 2 = 24,700 N/mm 2
Properties of the existing prestressing steel:
Aps LQ2 LQ2
Aps PP2 PP2
Af SO\ LQSO\ LQ LQ2
Af SO\ PPSO\ PP PP2
Acg LQ LQ LQ LQ±LQ LQ2
Acg PP PP PP PP±
PP î5 mm2
Area of FRP reinforcement:
Af = ntfwf
Cross-sectional area:
Acg = bfhf + bw h – hf
'LVWDQFHIURPWKHWRS¿EHUWRWKHVHFWLRQ
centroid:
bf
h 2f
yt =
2
h − hf ⎞
⎛
+ b h − hf ⎜ hf +
w
2 ⎠⎟
⎝
Acg
yt =
87 in. ×
4 in.2
+ 24 in. × 21 × 14.5
2
= LQ
852
yt =
2210 mm ×
102 mm 2
+ 610 mm × 533 × 368
2
= 238 mm
5.5 × 105
Gross moment of inertia:
Ig =
2
b f h3f
hf ⎞
bw h − h f
⎛
+ b f h f ⎜ yt − ⎟ +
12
2
12
⎝
⎠
h − hf ⎞
⎛
+ bw h − h f ⎜ yt −
2 ⎟⎠
⎝
2
3
87 in. × 4 in.3
+ LQ × LQ LQ − 12
3
24 in. × 21
+
+ LQ × − 2
12
= 38, 610 in.4
Ig =
2
2210 mm × 102 mm3
+ 2210 mm
12
610mm × 5333
× PP − 2 +
12
+ PP × − 2 = × 10 PP 4
Ig =
Radius of gyration:
r=
Ig
Acg
1.61 × 1010
= 171 mm
5.5 × 105
r=
38, 610
= 6.73 in.
852
r=
ε pe =
165
= 0.00578
28, 500
ε pe =
Effective prestressing strain:
ε pe =
f pe
Ep
1138
= 0.00579
1.96 × 105
Effective prestressing force:
Pe = Apsfpe
Pe = 0.765 × 165 = 126.2 kip
Pe î 1
e ± LQ
e = 571 – 238 = 333 mm
Eccentricity of prestressing force:
e = dp – yt
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.5b (cont.)—Procedure for flexural strengthening of an interior prestressed concrete beam with
fiber-reinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
yb ± LQ
yb ± PP
6WHS²'HWHUPLQHWKHH[LVWLQJVWDWHRI
VWUDLQRQWKHVRI¿W
The existing state of strain is calculated
assuming the beam is uncracked and the
only loads acting on the beam at the time
of the FRP installation are dead loads.
'LVWDQFHIURPH[WUHPHERWWRP¿EHUWRWKH
section centroid:
yb = h – yt
,QLWLDOVWUDLQLQWKHEHDPVRI¿W
ε bi =
−ρe
Ec Acg
⎛ eyb ⎞ M DL yb
⎜⎝1 + 2 ⎟⎠ +
r
Ec I g
ε bi =
−126.2 ⎛ 13.1 × 15.6 ⎞ 147 × 12 × 15.6
⎜1 +
⎟+
3605 × 852 ⎝
6.732 ⎠ 3605 × 38, 610
ε bi =
199 × 106 × 397
−563, 310
⎛ 333 × 397 ⎞
⎜1 +
⎟+
24, 700 × 5.5 × 105 ⎝
1712 ⎠ 24, 700 × 1.61 × 1010
İbi = –2.88 × 10–5
İbi = –2.88 × 10–5
6WHS²'HWHUPLQHWKHGHVLJQVWUDLQRI
the FRP system
The design strain of FRP accounting for
GHERQGLQJIDLOXUHPRGHİfd is calculated
XVLQJ(T Because the design strain is smaller than
the rupture strain, debonding controls the
design of the FRP system.
ε fd = 0.083
4000 psi
SVL LQ
≤ = ε fd = 0.042
27.6 N/mm 2
1PP 2 PP
≤ 6WHS²(VWLPDWHcWKHGHSWKWRWKH
QHXWUDOD[LV
A reasonable initial estimate of c is
0.1h. The value of the c is adjusted after
FKHFNLQJHTXLOLEULXP
c = 0.1h
c LQ LQ
c PP PP
⎛ 25 − 2.5 ⎞
ε fe = 0.003 ⎜
− 0.00003 = 0.027
⎝ 2.5 ⎟⎠
⎛ 635 − 63.5 ⎞
ε fe = 0.003 ⎜
− 0.00003 = 0.027
⎝ 63.5 ⎠⎟
!İfd = 0.0113
!İfd = 0.0113
Failure is governed by FRP debonding
Failure is governed by FRP debonding
İfe İfd = 0.0113
İfe İfd = 0.0113
6WHS²'HWHUPLQHWKHHIIHFWLYHOHYHORI
VWUDLQLQWKH)53UHLQIRUFHPHQW
The effective strain level in the FRP may
EHIRXQGIURP(T F ⎛ d f − c⎞
ε fe = 0.003 ⎜
− ε bi ≤ ε fd
⎝ c ⎠⎟
Note that for the neutral axis depth
selected, FRP debonding would be
the failure mode because the second
H[SUHVVLRQLQWKLVHTXDWLRQFRQWUROV,IWKH
¿UVW OLPLWLQJ H[SUHVVLRQJRYHUQHGWKHQ
FRP rupture would be the failure mode.
@Seismicisolation
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
65
Table 16.5b (cont.)—Procedure for flexural strengthening of an interior prestressed concrete beam with
fiber-reinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
⎛ 22.5 − 2.5 ⎞
ε pnet = (0.0113 + 0.00003) ⎜
⎝ 25 − 2.5 ⎟⎠
⎛ 571 − 63.5 ⎞
ε pnet = (0.0113 + 0.00003) ⎜
⎝ 635 − 63.5 ⎟⎠
İpnet = 0.01
İpnet = 0.01
6WHS²&DOFXODWHWKHVWUDLQLQWKH
H[LVWLQJSUHVWUHVVLQJVWHHO
The strain in the prestressing steel can
EHFDOFXODWHGXVLQJ(T F DQG
D ⎛ dp − c⎞
ε pnet = ε fe + ε bi ⎜
⎟
⎝ d f − c⎠
ε ps = ε pe +
Pe ⎛ e 2 ⎞
+ ε pnet ≤ 0.035
1+
Acg Ec ⎜⎝ r 2 ⎟⎠
ε ps = 0.00589 +
126.2 ⎛ 13.12 ⎞
+ 0.01
1+
852 × 3605 ⎜⎝ 6.732 ⎟⎠
ε ps = 0.00589 +
İps ”
⎛ 3332 ⎞
563, 310
+ 0.01
1+
5.5 × 105 × 24, 700 ⎜⎝ 1712 ⎟⎠
İps ”
6WHS²&DOFXODWHWKHVWUHVVOHYHOLQWKH
SUHVWUHVVLQJVWHHODQG)53
7KHVWUHVVHVDUHFDOFXODWHGXVLQJ(T
H DQG+RRNH¶V/DZ
⎧28,500ε ps for ε ps ≤ 0.0086
⎪
f ps = ⎨
0.04
⎪270 − ε − 0.007 for ε ps > 0.0086
ps
⎩
f ps = 270 −
0.04
= 265.6 ksi
0.016 − 0.007
f ps = 1860 −
0.276
= 1831 N/mm 2
0.016 − 0.007
ffe NVL NVL
ffe 1PP2 1PP2
⎛ 2.5 ⎞
ε c = + ⎜
= ⎝ 25 − 2.5 ⎟⎠
⎛ 63.5 ⎞
ε c = + ⎜
= ⎝ 635 − 63.5 ⎟⎠
ffe = Efİfe
6WHS²&DOFXODWHWKHHTXLYDOHQW
FRQFUHWHFRPSUHVVLYHVWUHVVEORFN
SDUDPHWHUVĮ1DQGȕ1.
The strain in concrete at failure can be
calculated from strain compatibility as
follows:
⎛ c ⎞
ε c = ε fe + ε bi ⎜
⎟
⎝ d f − c⎠
7KHVWUDLQİcƍFRUUHVSRQGLQJWRfcƍLV
calculated as
ε c′ =
1.7 f c′
Ec
ε c′ =
= 3605 × 106
ε c′ =
= 24, 700
Concrete stress block factors can be
estimated using ACI 318. Approximate
stress block factors may be calculated from
the parabolic stress-strain relationship for
concrete and is expressed as follows:
β1 =
4ε c′ − ε c
6ε c′ − 2ε c
α =
ε c′ ε c − ε c
β ε′
β1 =
α1 =
− = 0.716
− − 2
β1 =
2
= 0.738
α1 =
− = 0.716
− − 2
@Seismicisolation
@Seismicisolation
2
= 0.738
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.5b (cont.)—Procedure for flexural strengthening of an interior prestressed concrete beam with
fiber-reinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
c LQLQQJ
c PPLQQJ
‫׵‬revise estimate of c and repeat Steps 6 through 10
XQWLOHTXLOLEULXPLVDFKLHYHG
‫׵‬revise estimate of c and repeat Steps 6 through 10
XQWLOHTXLOLEULXPLVDFKLHYHG
c = 1.86 in. = 1.86 in.
c = 47 mm = 47 mm
‫׵‬the value of cVHOHFWHGIRUWKH¿QDOLWHUDWLRQLVFRUUHFW
‫ ׵‬the value of cVHOHFWHGIRUWKH¿QDOLWHUDWLRQLVFRUUHFW
Prestressing steel contribution to bending:
Mnp = 4440 kip-in. = 370 kip-ft
Mnp = 501.6 × 106 N-mm = 501.6 kN-m
FRP contribution to bending:
Mnf = 1417 kip-in. = 118 kip-ft
Mnf = 160.1 × 106 N-mm = 160.1 kN-m
ࢥMn >NLSIW NLSIW @
ࢥMn NLSIW•Mu NLSIW
ࢥMn >N1P N1P @
ࢥMn N1P•Mu = 538 kN-m
6WHS²&DOFXODWHWKHLQWHUQDOIRUFH
UHVXOWDQWVDQGFKHFNHTXLOLEULXP
)RUFHHTXLOLEULXPLVYHUL¿HGE\FKHFNLQJ
the initial estimate of cZLWK(T
F 6WHS²$GMXVWcXQWLOIRUFH
HTXLOLEULXPLVVDWLV¿HG
Steps 6 through 10 were repeated several
times with different values of c until
HTXLOLEULXPZDVDFKLHYHG7KHUHVXOWVRI
WKH¿QDOLWHUDWLRQDUH
c LQİps fps = fy NVL
İfe ffe NVLİc Į1 DQGȕ1 6WHS²&DOFXODWHÀH[XUDOVWUHQJWK
components
7KHGHVLJQÀH[XUDOVWUHQJWKLVFDOFXODWHG
XVLQJ(T J $QDGGLWLRQDO
UHGXFWLRQIDFWRUȥf = 0.85, is applied to
the contribution of the FRP system.
6WHS²&DOFXODWHGHVLJQÀH[XUDO
VWUHQJWKRIWKHVHFWLRQ
7KHGHVLJQÀH[XUDOVWUHQJWKLVFDOFXODWHG
XVLQJ(T DQG J %HFDXVH
İps !DVWUHQJWKUHGXFWLRQ
IDFWRURIࢥ VKRXOGEHXVHGSHU(T
$QDGGLWLRQDOUHGXFWLRQIDFWRU
ȥf = 0.85 is used to calculate the FRP
contribution to nominal capacity.
ࢥMn ࢥ>MnpȥfMnf]
‫׵‬the strengthened section is capable of sustaining the ‫׵‬the strengthened section is capable of sustaining the
QHZUHTXLUHGÀH[XUDOVWUHQJWK
QHZUHTXLUHGÀH[XUDOVWUHQJWK
6WHS²&KHFNVHUYLFHFRQGLWLRQRIWKH
VHFWLRQ
Calculate the cracking moment and
compare the service moment:
f r = 7.5 4000 = 474 psi = 0.474 ksi
f r = 0.6 27.6 = 3.15 N/mm 2
Mcr NLSLQ NLSIW
!Ms = 288 kip-ft
Mcr = 411,654,013 N-mm = 412 kN-mm
!Ms N1P
‫׵‬the strengthened section is uncracked at service.
‫׵‬the strengthened section is uncracked at service.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
67
Table 16.5b (cont.)—Procedure for flexural strengthening of an interior prestressed concrete beam with
fiber-reinforced polymer laminates
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
İps,s ”
İps,s ”
fps,s NVL
fps,s î5 1PP2
fps,s”fpy
fps,s NVL NVL2.
fps,s = 1238 N/mm2 1PP2 OK
fps,s”fpu
fps,s NVL NVL2.
fps,s = 1238 N/mm2 1PP2 OK
6WHS²&KHFNVWUHVVLQSUHVWUHVVLQJ
VWHHODWVHUYLFHFRQGLWLRQ
Calculate the cracking moment and
compare to service moment:
ε ps , s = ε pe +
Pe ⎛ e 2 ⎞ M s e
+
1+
Ac Ec ⎜⎝ r 2 ⎟⎠ Ec I g
&DOFXODWHWKHVWHHOVWUHVVXVLQJ(T G ⎧28,500ε ps , s for ε ps , s ≤ 0.0086
⎪
f ps , s = ⎨
0.04
⎪270 − ε − 0.07 for ε ps , s ≤ 0.0086
ps
,
s
⎩
&KHFNWKHVHUYLFHVWUHVVOLPLWVRI(T
D DQG E 6WHS²&KHFNVWUHVVLQFRQFUHWHDW
VHUYLFHFRQGLWLRQ
Calculate the cracking moment and
compare to service moment:
εc,s =
− Pe
Ac Ec
⎛ e 2 ⎞ M s yt
⎜⎝1 + r 2 ⎟⎠ − E I
c g
ε c ,s =
− ⎛ 2 ⎞ × × 1+
−
852 × 3605 ⎜⎝ 7.752 ⎟⎠ 3605 × 51,150
ε cs =
⎛ 2 ⎞
× 6 × −
1+
−
5
2⎟
⎜
× × ⎝ ⎠ × × 10
İc,s = 0.00016
İc,s = 0.00016
fc,s = Ecİc,s
fc,s SVL SVL
fc,s = 24,700 N/mm2 1PP2
fc,s”fcƍ
0.45fcƍ SVL
fc,s = 577 psi < 0.45fcƍ SVL2.
0.45fcƍ 1PP2
fc,s 1PP2 < 0.45fcƍ 1PP2
OK
6WHS²&KHFNVHUYLFHVWUHVVHVLQWKH
)53UHLQIRUFHPHQW
The stress in the FRP at service condition
FDQEHFDOFXODWHGXVLQJ(T ⎛ Ef ⎞ M y
f f , s = ⎜ ⎟ s b − ε bi E f
⎝ Ec ⎠ I
⎛ 5360 ksi ⎞ 289 kip-ft × 12 in./ft × 15.61 in.
f f ,s = ⎜
⎝ 3605 ksi ⎟⎠
511,150 in.4
− 0.00003 × 37, 700 N/mm 2
− 0.00003 × 5360 ksi
Because the section is uncracked at
service, the gross moment of inertia of the
section must be used.
⎛ 37, 700 N/mm 2 ⎞ 391.3 × 106 N/mm × 397 mm
f f ,s = ⎜
2.13 × 1010 mm 4
⎝ 24, 700 N/mm 2 ⎠⎟
ff,s = 1.41 ksi
ff,s 1PP2
0.55ffu NVL
0.55ffu 1PP2
The calculated stress in FRP should be
FKHFNHGDJDLQVWWKHOLPLWVLQ7DEOH
For carbon FRP:
ff,s”ffu
ff,s = 1.41 ksi < 0.55ffu = 47 ksi
In detailing the FRP reinforcement, the FRP should be
terminated a minimum of ƐdfFDOFXODWHGSHU(T SDVW
the point on the moment diagram that represents cracking.
The factored shear force at the termination should also be
checked against the shear force that causes FRP end peeling,
OK
ff,s 1PP2 < 0.55ffu = 322 N/mm2
OK
estimated as two-thirds of the concrete shear strength. If the
shear force is greater than two-thirds of the concrete shear
strength, FRP strips should be extended further toward the
supports. U-wraps may also be used to reinforce against
cover delamination.
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68
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.6—Shear strengthening of an interior T-beam
$UHLQIRUFHGFRQFUHWH7EHDP fcƍ= 3000 psi [20.7 N/mm2@ ORFDWHGLQVLGHRIDQRI¿FHEXLOGLQJLVVXEMHFWHGWRDQLQFUHDVH
LQ LWV OLYHORDGFDUU\LQJ UHTXLUHPHQWV $Q DQDO\VLV RI WKH
existing beam indicates that the beam is still satisfactory for
ÀH[XUDO VWUHQJWK KRZHYHU LWV VKHDU VWUHQJWK LV LQDGHTXDWH
to carry the increased live load. Based on the analysis, the
nominal shear strength provided by the concrete is Vc = 44.2
NLS N1 DQGWKHQRPLQDOVKHDUVWUHQJWKSURYLGHGE\
steel shear reinforcement is Vs NLS N1 7KXV
WKHGHVLJQVKHDUVWUHQJWKRIWKHH[LVWLQJEHDPLVࢥVn,existing =
NLSNLS NLS N1 7KHIDFWRUHG
UHTXLUHGVKHDUVWUHQJWKLQFOXGLQJWKHLQFUHDVHGOLYHORDGDW
a distance d away from the support is Vu NLS N1 Figure 16.6a shows the shear diagram with the locations where
VKHDUVWUHQJWKHQLQJLVUHTXLUHGDORQJWKHOHQJWKRIWKHEHDP
Supplemental FRP shear reinforcement is designed as
shown in Fig. 16.6b and summarized in Table 16.6a. Each
)53 VWULS FRQVLVWV RI RQH SO\ n RI D ÀH[LEOH FDUERQ
sheet installed by wet layup. The FRP system manufacturer’s reported material properties are shown in Table 16.6b.
7KHGHVLJQFDOFXODWLRQVXVHGWRDUULYHDWWKLVFRQ¿JXUDWLRQ
follow in Table 16.6c.
)LJD²6KHDUGLDJUDPVKRZLQJGHPDQGYHUVXVH[LVWLQJ
VWUHQJWK 7KH )53 UHLQIRUFHPHQW VKRXOG FRUUHFW WKH GH¿ciency shown shaded.
)LJ E²&RQ¿JXUDWLRQ RI WKH VXSSOHPHQWDO )53 VKHDU
reinforcement.
Table 16.6a—Configuration of the supplemental FRP shear reinforcement
d
22 in.
PP
dfv
16 in.
406 mm
Width of each sheet wf
10 in.
254 mm
Span between each sheet sf
12 in.
305 mm
FRP strip length
70 in.
1778 mm
Table 16.6b—Manufacturer’s reported FRP system properties
Thickness per ply tf
Ultimate tensile strength ffu*
5XSWXUHVWUDLQİfu*
Modulus of elasticity Ef
0.0065 in.
0.165 mm
550,000 psi
1PP2
0.017 in./in.
0.017 mm/mm
33,000,000 psi
227,530 N/mm2
@Seismicisolation
@Seismicisolation
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
69
Table 16.6c—Procedure for shear strengthening of an interior T-beam
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
The beam is located in an enclosed and
conditioned space and a CFRP material
ZLOOEHXVHG7KHUHIRUHSHU7DEOHDQ
HQYLURQPHQWDOUHGXFWLRQIDFWRURILV
suggested.
ffu = CEffu*
ffu NVL NVL
ffu N1PP2 N1PP2
İfu = CEİfu*
İfu İfu 6WHS²&RPSXWHWKHGHVLJQPDWHULDO
SURSHUWLHV
6WHS²&DOFXODWHWKHHIIHFWLYHVWUDLQ
OHYHOLQWKH)53VKHDUUHLQIRUFHPHQW
The effective strain in FRP U-wraps
should be determined using the bondUHGXFWLRQFRHI¿FLHQWțv7KLVFRHI¿FLHQW
FDQEHFRPSXWHGXVLQJ(T E WKURXJK H Le =
2500
nt f E f 0.58
⎛ f′ ⎞
k1 = ⎜ c ⎟
⎝ 4000 ⎠
Le =
2500
= 2.0 in.
[(1)(0.0065 in.)(33 × 106 psi)]0.58
2/3
⎛ 3000 psi ⎞
k1 = ⎜
⎝ 4000 ⎠⎟
⎛ d fv − Le ⎞
k2 = ⎜
⎟
⎝ d fv ⎠
κv =
Le =
416
= 50.8 mm
> PP × 3 N1PP 2 @0.58
2/3
⎛ 20.7 kN/mm 2 ⎞
k1 = ⎜
254
⎝
⎠⎟
= 0.825
⎛ 16 in. − 2.0 in.⎞
k2 = ⎜
⎟⎠ = 0.875
⎝
16 in.
k1k2 Le
≤ 0.75
468ε fu
κv =
LQ
= ≤ 2/3
= 0.825
⎛ 406 mm − 50.8 mm ⎞
k2 = ⎜
⎟⎠ = 0.875
⎝
406 mm
κv =
PP
= ≤ The effective strain can then be computed
XVLQJ(T D DVIROORZV
İfe țvİfu”
İfe ”
İfe ”
Afv LQ LQ LQ2
Afv PP PP PP2
ffe NVL NVL
ffe N1PP2 N1PP2
6WHS²&DOFXODWHWKHFRQWULEXWLRQRIWKH
)53UHLQIRUFHPHQWWRWKHVKHDUVWUHQJWK
The area of FRP shear reinforcement can
be computed as:
Afv = 2ntfwf
The effective stress in the FRP can be
computed from Hooke’s law.
ffe İfeEf
The shear contribution of the FRP can be
WKHQFDOFXODWHGIURP(T D Vf =
Afv f fe VLQ α + FRV α d fv
sf
Vf =
LQ2 NVL LQ
LQ
Vf =
PP 2 N1PP 2 PP
PP
Vf = 17.7 kip
@Seismicisolation
@Seismicisolation
Vf = 78.5 kN
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70
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.6c (cont.)—Procedure for shear strengthening of an interior T-beam
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
ࢥVn > @
ࢥVn NLS!Vu = 57 kip
ࢥVn > @
ࢥVn N1!Vu = 253.3 kN
‫׵‬the strengthened section is capable of sustaining
WKHUHTXLUHGVKHDUVWUHQJWK
‫׵‬the strengthened section is capable of sustaining
WKHUHTXLUHGVKHDUVWUHQJWK
6WHS²&DOFXODWHWKHVKHDUVWUHQJWKRI
WKHVHFWLRQ
The design shear strength can be
FRPSXWHGIURP(T E ZLWKȥf = 0.85
for U-wraps.
ࢥVn ࢥ Vc + VsȥfVf
@Seismicisolation
@Seismicisolation
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.7—Shear strengthening of an exterior column
$[LQ [PP VTXDUHFROXPQUHTXLUHVDQ
DGGLWLRQDONLS N1 RIVKHDUVWUHQJWK ¨Vu = 60 kip
>N1@ 7KHFROXPQLVORFDWHGLQDQXQHQFORVHGSDUNLQJ
garage and experiences a wide variation in temperature and
climate. A method of strengthening the column using FRP
is sought.
71
$Q(JODVVEDVHG)53FRPSOHWHZUDSLVVHOHFWHGWRUHWUR¿W
the column. The properties of the FRP system, as reported by
the manufacturer, are shown in Table 16.7. The design calcuODWLRQVWRDUULYHDWWKHQXPEHURIFRPSOHWHZUDSVUHTXLUHG
follow.
Table 16.7a—Manufacturer’s reported FRP system properties*
0.051 in.
1.3 mm
80,000 psi
552 N/mm2
*XDUDQWHHGUXSWXUHVWUDLQİfu*
0.020 in./in.
0.020 mm/mm
Modulus of elasticity Ef
4,000,000 psi
27,600 N/mm2
Thickness per ply tf
Guaranteed ultimate tensile strength ffu*
*
The reported properties are laminate properties.
@Seismicisolation
@Seismicisolation
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72
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.7b—Procedure for shear strengthening of an exterior column
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
ffu =CEffu*
ffu NVL NVL
ffu 1PP2 1PP2
İfu =CEİfu*
İfu İfu İfe ” İfe ” ‫׵‬XVHDQHIIHFWLYHVWUDLQRIİfe = 0.004.
‫׵‬XVHDQHIIHFWLYHVWUDLQRIİfe = 0.004.
6WHS²&RPSXWHWKHGHVLJQPDWHULDO
SURSHUWLHV
The column is located in an exterior
HQYLURQPHQWDQGDJODVV)53 *)53 material will be used. Therefore, per Table
DQHQYLURQPHQWDOUHGXFWLRQIDFWRURI
0.65 is suggested.
6WHS²&DOFXODWHWKHHIIHFWLYHVWUDLQ
OHYHOLQWKH)53VKHDUUHLQIRUFHPHQW
The effective strain in a complete
)53ZUDSFDQEHGHWHUPLQHGIURP(T
İfe ”İfu
6WHS²'HWHUPLQHWKHDUHDRI)53
UHLQIRUFHPHQWUHTXLUHG
7KHUHTXLUHGVKHDUFRQWULEXWLRQRIWKH
FRP reinforcement can be computed based
on the increase in strength needed, the
strength reduction factor for shear, and
DSDUWLDOUHGXFWLRQIDFWRUȥf IRU
completely wrapped sections in shear.
V f , reqd =
ΔVu
φ ψf
V f , reqd =
60 kip
= 74.3 kip
V f , reqd =
N1
= 330.5 kN
7KHUHTXLUHGDUHDRI)53FDQEH
GHWHUPLQHGE\UHRUJDQL]LQJ(T D 7KHUHTXLUHGDUHDLVOHIWLQWHUPVRIWKH
spacing.
Afv , reqd =
V f , reqd s f
Afv , reqd =
ε fe E f VLQ α + FRV α d f
NLS s f
NVL LQ
= s f
Afv , reqd =
N1 s f
N1PP 2 PP
= s f
6WHS²'HWHUPLQHWKHQXPEHURISOLHV
DQGVWULSZLGWKDQGVSDFLQJ
The number of plies can be determined
in terms of the strip width and spacing as
follows:
n=
Af , reqd
2t f w f
n=
s f
in w f
= sf
wf
‫׵‬XVHWZRSOLHV n FRQWLQXRXVO\DORQJWKHKHLJKW
RIWKHFROXPQ sf = wf n=
s f
PP w f
= sf
wf
‫׵‬XVHWZRSOLHV n FRQWLQXRXVO\DORQJWKHKHLJKW
RIWKHFROXPQ sf = wf @Seismicisolation
@Seismicisolation
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.8—Strengthening of a noncircular concrete
column for axial load increase
$ [ LQ [ PP VTXDUH FROXPQ UHTXLUHV
an additional 20 percent of axial load-carrying capacity.
Concrete and steel reinforcement material properties as
well as details of the cross section of the column are shown
in Table 16.8a. The column is located in an interior envi-
73
ronment, and a CFRP material will be used. A method of
strengthening the column is sought.
$FDUERQEDVHG)53FRPSOHWHZUDSLVVHOHFWHGWRUHWUR¿W
the columns. The properties of the FRP system, as reported
by the manufacturer, are shown in Table 16.8b. The design
FDOFXODWLRQV WR DUULYH DW WKH QXPEHU RI UHTXLUHG FRPSOHWH
wraps follow.
Table 16.8a—Column cross section details and material properties
fcƍ
6.5 ksi
45 MPa
fy
60 ksi
400 MPa
rc
1 in.
25 mm
Bars
12 No. 10
ࢥ
Ag
576 in.2
3716 cm2
Ast
15.24 in.2
FP2
ȡg, %
2.65
2.65
ࢥPn without FRP
2087 kip
N1
ࢥPn(req)
2504 kip
11,138 kN
Note: The column features steel ties for transverse reinforcement.
Table 16.8b—Manufacturer’s reported FRP system properties
Thickness per ply tf
Ultimate tensile strength ffu*
5XSWXUHVWUDLQİfu*
Modulus of elasticity Ef
0.013 in.
0.33 mm
550 ksi
03D
0.0167 in./in.
0.0167 mm/mm
33,000 ksi
227,527 MPa
@Seismicisolation
@Seismicisolation
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74
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.8c—Procedure for strengthening of a noncircular concrete column for axial load increase
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
ffu = CEffu*
ffu NVL NVL
ffu 03D 03D
İfu = CEİfu*
İfu LQLQ
İfu PPPP
6WHS²&RPSXWHWKHGHVLJQ)53
PDWHULDOSURSHUWLHV
The column is located in an interior
environment and a CFRP material will
EHXVHG7KHUHIRUHSHU7DEOHDQ
HQYLURQPHQWDOUHGXFWLRQIDFWRURILV
suggested.
6WHS²'HWHUPLQHWKHUHTXLUHG
PD[LPXPFRPSUHVVLYHVWUHQJWKRI
FRQ¿QHGFRQFUHWHfccƍ
fccƍFDQEHREWDLQHGE\UHRUGHULQJ(T
E f cc′ =
⎛ φPn , req
⎞
1
− f y Ast ⎟
Ag − Ast ⎜⎝ φ
⎠
f cc′ =
1
× LQ2 − LQ2
f cc′ =
⎛ 2504 kip
⎞
×⎜
− 60 ksi × 15.24 in.2 ⎟
⎝ 0.80 × 0.65
⎠
1
0.85 × (371, 612 mm 2 − 9832 mm 2 )
⎛ 11,138 kN
⎞
×⎜
− 414 MPa × 9832 mm 2 ⎟
⎝ 0.80 × 0.65
⎠
fccƍ NVL
fccƍ 03D
6WHS²'HWHUPLQHWKHPD[LPXP
FRQ¿QLQJSUHVVXUHGXHWRWKH)53
MDFNHWfƐ
fƐFDQEHREWDLQHGE\UHRUGHULQJ(T J f =
f cc′ − f c′
3.3κ a
f =
8.18 ksi − 6.5 ksi
= 1.26 ksi
× × f =
56.4 MPa − 44.8 MPa
= 8.7 MPa
0.95 × 3.3 × 0.425
where
κa =
Ae
=
Ac
⎡⎛ b ⎞
⎢⎜⎝ h ⎟⎠ h − rc
1− ⎣
Ae
Ac
⎛ b⎞
⎜⎝ ⎟⎠
h
2
ța 2 = 0.425
⎤
⎛ h⎞
+ ⎜ ⎟ b − rc 2 ⎥
⎝ b⎠
⎦ −ρ
g
3 Ag
2
1 − ρg
Ae
=
Ac
1−
[2 × (1)(24 in. − 2 × 1 in.) 2 ]
− 0.0265
3 × 576 in.2
1 − 0.0265
ța 2 = 0.425
⎡ 2 × (1)(610 mm − 2 × 25 mm) 2 ⎤⎦
1− ⎣
− 0.0265
Ae
3 × 371,612 mm 2
=
Ac
1 − 0.02265
Ae
= 0.425
Ac
SWHS²'HWHUPLQHWKHQXPEHURISOLHVn.
nFDQEHREWDLQHGE\UHRUGHULQJ(T K n=
f b2 + h2
2 E f t f ε fe
İfe țeİfu
n=
NVL LQ 2 + LQ 2
( NVL )(LQ) × −3 LQLQ
Ae
= 0.425
Ac
n=
03D PP 2 + PP 2
(03D )(PP ) × −3 PPPP
n §SOLHV
n §SOLHV
İfe îLQLQ î–3 in./in.
İfe îPPPP î–3 mm/mm
&KHFNLQJWKHPLQLPXPFRQ¿QHPHQWUDWLR
f
≥ 0.08
f c′
f 1.26 ksi
=
= > 2.
f c′ 6.5 ksi
f
f c′
=
8.7 MPa
= > 2.
44.8 MPa
@Seismicisolation
@Seismicisolation
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
75
Table 16.8c (cont.)—Procedure for strengthening of a noncircular concrete column for axial load increase
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
6WHS²9HULI\WKDWWKHXOWLPDWHD[LDO
VWUDLQRIWKHFRQ¿QHGFRQFUHWHİccu”
İccuFDQEHREWDLQHGXVLQJ(T M 0.45
⎛
f ⎛ ε fe ⎞ ⎞
ε ccu = ε c′ ⎜1.5 + 12κ b ⎜ ⎟ ⎟
f c′ ⎝ ε c′ ⎠ ⎠
⎝
where
ε cc = LQLQ
0.45
⎛
1.2 ksi ⎛ 8.8 × 10−3 in./in.⎞ ⎞
× ⎜1.5 + 12 × 0.425 ×
⎟
⎜
⎟
6.5 ksi ⎝ 0.002 in./in. ⎠ ⎠
⎝
İcc = 0.0067 in./in. < 0.01
κb =
Ae ⎛ h ⎞
⎜ ⎟
Ac ⎝ b ⎠
OK
ε cc = PPPP
0.45
⎛
8.3 MPa ⎛ 8.8 × 10−3 mm/mm ⎞ ⎞
× ⎜1.5 + 12 × 0.425 ×
⎟
⎜
⎟
44.8 MPa ⎝ 0.002 mm/mm ⎠ ⎠
⎝
İcc = 0.0067 mm/mm < 0.01
OK
0.5
țb 0.5
= 0.425
țb 0.5
= 0.425
,IWKHFDVHWKDWİccu was to be greater than
0.01, then fccƍVKRXOGEHUHFDOFXODWHGIURP
WKHVWUHVVVWUDLQPRGHOXVLQJ(T F @Seismicisolation
@Seismicisolation
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76
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.9—Strengthening of a noncircular concrete
column for increase in axial and bending forces
The column described in 16.8 is subjected to an ultimate
axial compressive load Pu NLS N1 DQG DQ
ultimate bending moment Mu NLSIW N1P e =
0.1h ,WLVVRXJKWWRLQFUHDVHORDGGHPDQGVE\SHUFHQWDW
FRQVWDQWHFFHQWULFLW\ Pu = 2470 kip, Mu NLSIW The calculations to determine moment-axial interaction
IRUWKH)53FRQ¿QHGFROXPQIROORZLQ7DEOH
Table 16.9—Procedure for strengthening of a noncircular concrete column for increase in axial and
bending forces
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
ࢥPn A NLSࢥMn A = 0 kip-ft
ࢥPn B NLSࢥMn B = 644 kip-ft
ࢥPn C NLSࢥMn C = 884 kip-ft
ࢥPn A N1ࢥMn A = 0 kN-m
ࢥPn B N1ࢥMn B = 873 kN-m
ࢥPn C N1ࢥMn C N1P
6WHS²'HWHUPLQHWKHVLPSOL¿HGFXUYH
IRUWKHXQVWUHQJWKHQHGFROXPQ n SOLHV
Points A, B, and C can be obtained by
well-known procedures, and also by using
(T ' WR ' FRQVLGHULQJȥf = 1, fccƍ fcƍE2 DQGİccu İcu = 0.003.
@Seismicisolation
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
77
Table 16.9 (cont.)—Procedure for strengthening of a noncircular concrete column for increase in axial
and bending forces
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
Point A:
Nominal axial capacity:
Point A:
Nominal axial capacity:
6WHS²'HWHUPLQHWKHVLPSOL¿HGFXUYH
IRUDVWUHQJWKHQHGFROXPQ
A wrapping system composed of six plies
will be the starting point to construct the
bilinear Curve A-B-C and then be compared
ZLWKWKHSRVLWLRQRIWKHUHTXLUHGPu and Mu.
Points A, B, and C of the curve can be
FRPSXWHGXVLQJ(T ' DQG ' ࢥPn A ࢥ fccƍ Ag – Ast fyAst
ࢥPn A î îNVLî LQ2 – 15.24 ࢥPn A î î03Dî PP2
in.2 NVLîLQ2
±PP2 03DPP2
ࢥPn A = 11,223 kN
ࢥPn A = 2523 kip
where
where
fccƍ NVL NVL
fccƍ 03D 03D
fccƍ NVL
fccƍ 03D
fl =
ࢥPn B,C ࢥ A yt 3 + B yt 2 + C yt D ™Asifsi]
ࢥMn B,C ࢥ E yt 4 + F yt 3 + G yt 2 + H yt + I ™Asifsidi
7KHFRHI¿FLHQWVA, B, C, D, E, F, G, H,
and I of the previous expressions are given
E\(T ' A=
−b Ec − E2
12 f c′
B=
2
⎛ ε ccu ⎞
⎜⎝
⎟
c ⎠
2
in.⎞
⎛
× × NVL × × LQ × ⎜ × ⎟
⎝
in.⎠
LQ 2 + LQ
2
Point B:
Nominal axial capacity:
Point B:
Nominal axial capacity:
−24 in.(4595 ksi − 190.7 ksi) 2 ⎛ 0.0042 in./in.⎞
⎜⎝
⎟⎠
12 × 6.5 ksi
22 in.
2
LQ NVL − NVL ⎛ LQLQ⎞
⎜⎝
⎟⎠
2
22 in.
= 10.17 ksi
B=
E=
−b Ec − E2
16 f c′
h ⎞ E − E2
⎛
F = b⎜c − ⎟ c
⎝
2 ⎠ 12 f c′
2
LQ × LQ × NVL
2
î LQLQ NLS
bcE2
ε ccu
2
2
⎛ ε ccu ⎞
⎜⎝ c ⎟⎠
D = 24 in. × 22 in. × 6.5 ksi +
2
2
fƐ = 8.67 MPa
C = –24 in. × 6.5 ksi = –156 kip/in.
D = bf c′ +
PP 2 + PP
fƐ = 1.26 ksi
= −0.22 kip/in.3
C = bfcƍ
mm ⎞
⎛
× × 03D × × PP × ⎜ × ⎟
⎝
mm ⎠
ࢥPn B = 0.65[–0.22 kip/in.3 LQ 3 + 10.17 ksi
ࢥPn B = 0.65[–6.003 × 10–5 kN/mm3 PP 3 + 70.14
LQ 2±NLSLQ LQ NLS@ × 10–3 kN/mm2 PP 2±N1PP PP in.2 NVL LQ2 NVL LQ2 NVL @
16,215 kN] + 3277 mm2 03D PP2 03D PP2 NVL
ࢥPn B = 2210 kip
ࢥPn B N1
where
where
A=
b Ec − E2 ⎛ ε ccu ⎞
⎜⎝ c ⎟⎠
2
fl =
A=
−PP 03D − 03D
× 03D
2
⎛ PPPP ⎞
⎝⎜
⎠⎟
PP
2
= −6.003 × 10 −5 kN/mm3
B=
600 mm(31, 685 MPa − 1315 MPa ) ⎛ 0.0042 mm/mm ⎞
⎜⎝
⎟⎠
2
559 mm
= 70.14 × 10 −3 kN/mm 2
C = –610 mm × 44.84 MPa = –27.32 kN/mm
D = PPîPPî03D
PP × PP × 03D
+
2
î PPPP = N1
2
b Ec − E2 ⎛ ε ccu ⎞
⎛ ε ccu ⎞
⎜⎝
⎟ +
⎜⎝
⎟
3
c ⎠
c ⎠
⎛b
h ⎞ E − E2 ⎛ ε ccu ⎞ ⎞
⎛
G = − ⎜ f c′ + b ⎜ c − ⎟ c
⎜⎝
⎟
⎝
2⎠
2
c ⎠ ⎟⎠
⎝2
h⎞
⎛
H = bf c′ ⎜ c − ⎟
⎝
2⎠
I=
bc 2
h ⎞ bc 2 E2
⎛
f c′ − bcf c′ ⎜ c − ⎟ +
(ε ccu )
⎝
2
2⎠
3
−
bcE2
2
h⎞
⎛
⎜⎝ c − ⎟⎠ (ε ccu )
2
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.9 (cont.)—Procedure for strengthening of a noncircular concrete column for increase in axial
and bending forces
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
Key parameters of the stress-strain model:
yt = c
)RUWKHFDOFXODWLRQRIWKHFRHI¿FLHQWVLWLVQHFHVVDU\WR )RUWKHFDOFXODWLRQRIWKHFRHI¿FLHQWVLWLVQHFHVVDU\WR
compute key parameters from the stress-strain model:
compute key parameters from the stress-strain model:
ε′t
ε ccu
yt = 22 in. ×
for Point B
⎧d
⎪
ε ccu
c=⎨
⎪d ε + ε for Point C
ccu
⎩ sy
ε t′ =
E2 =
ε t′ =
f cc′ − f c′
ε ccu
Ae ⎛ h ⎞
⎜ ⎟
Ac ⎝ b ⎠
7.31 ksi − 6.5 ksi
= 190.7 ksi
0.0042 in./in.
2 × 44.8 MPa
= 0.003 mm/mm
31, 685 MPa − 1315 MPa
E2 =
50.4 MPa − 44.8 MPa
= 1315 MPa
0.0042 mm/mm
fccƍ 03D 03D 03D
0.45
⎛
⎛ 0.58 ksi ⎞ ⎛ 0.004 in./in.⎞ ⎞
× ⎜1.5 + 12 × 0.425 ⎜
⎟
⎜
⎟
⎝ 6.5 ksi ⎠ ⎝ 0.002 in./in.⎠ ⎟⎠
⎝
ε ccu = 0.002 mm/mm
0.45
⎛
⎛ 03D ⎞ ⎛ PPPP ⎞ ⎞
× ⎜1.5 + 12 × 0.425 ⎜
⎟ ⎝⎜
⎟ ⎟
⎝
⎠
⎠
44.8
MPa
0.002
mm/mm
⎝
⎠
İccu = 0.0042 in./in.
İccu = 0.0042 mm/mm
ța țb = 0.425
ța țb = 0.425
2
0.5
ψ f E f nt f ε fe
b2
ε t′ =
ε ccu = 0.002 in./in.
İfe PLQ țİİfu
0.003 mm/mm
= 389 mm
0.0042 mm/mm
c PP
fccƍ NVL NVL NVL
0.45
⎛
f ⎛ ε fe ⎞ ⎞
ε ccu = ε c′ ⎜1.5 + 12κ b ⎜ ⎟ ⎟
f c′ ⎝ ε c′ ⎠ ⎠
⎝
κb =
yt = 559 mm ×
2 × 6.5 ksi
= 0.003 in./in.
NVL − NVL
E2 =
fccƍ fcƍțafl
Ae ⎛ b ⎞
⎜ ⎟
Ac ⎝ h ⎠
0.003 in./in.
= 15.33 in.
0.0042 in./in.
c = 22 in.
2 f c′
Ec − E2
κa =
&DOFXODWLRQLQ6,PHWULFXQLWV
f =
h2
Notes: The designer should bear in mind
that, for the case of pure compression, the
HIIHFWLYHVWUDLQLQWKH)53İfe, is limited
E\țİİfu and, in the case of combined axial
DQGEHQGLQJE\İfe PLQ țİİfu × × NVL × × LQ × LQLQ
LQ 2 + LQ
2
&KHFNLQJWKHPLQLPXPFRQ¿QHPHQWUDWLR
fƐ/fcƍ NVLNVL •2.
f =
× × 03D × × PP × PPPP
PP 2 + PP
2
&KHFNLQJWKHPLQLPXPFRQ¿QHPHQWUDWLR
fƐ/fcƍ 03D03D •2.
The strains in each layer of steel are determined
by similar triangles in the strain distribution. The
corresponding stresses are then given by:
fs1 İs1Es LQLQîNVLĺNVL
fs2 İs2Es LQLQîNVLĺNVL
fs3 İs3Es LQLQîNVL NVL
fs4 İs4Es LQLQîNVL NVL
The strains in each layer of steel are determined
by similar triangles in the strain distribution. The
corresponding stresses are then given by:
fs1 İs1Es PPPPî03Dĺ03D
fs2 İs2Es PPPPî03Dĺ03D
fs3 İs3Es = 0.0013 mm/mm × 200,000 MPa = 257 MPa
fs4 İs4Es = 0 mm/mm × 200,000 MPa = 0 MPa
Nominal bending moment:
Nominal bending moment:
ࢥMn B = 0.65[–4.502 × 10–5 kN/mm3 PP 4 +
ࢥMn B = 0.65[–0.166 kip/in.3 LQ 4NVL 62.01 × 10–3 kN/mm3 PP 3±N1PP LQ 3±NLSLQ LQ 2 + 1560 kip
PP 2N1 PP N1PP@
LQ NLSLQ@LQ2 NVL LQ 3277 mm2 03D PP PP2 2.54 in.2 NVL LQ ±LQ2 NVL LQ
03D PP ±PP2 03D PP
ࢥMn B = 682 kip-ft
ࢥMn B N1P
where
where
E=
−LQ NVL − NVL 2 ⎛ LQLQ⎞
⎜⎝
⎟⎠
16 × 6.5 ksi
22 in.
= – 0.166 kip/in.3
2
E=
−PP 03D − 03D
16 × 44.8 MPa
2
2
⎛ 0.0042 mm/mm ⎞
–5
3
× ⎜
⎟⎠ = –0.452 × 10 kN/mm
⎝
PP
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
79
Table 16.9 (cont.)—Procedure for strengthening of a noncircular concrete column for increase in axial
and bending forces
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
F = PP PP±PP
F = LQ LQ±LQ
2
×
NVL − NVL
⎛ LQLQ⎞
×⎜
⎟⎠
⎝
12 × 6.5 ksi
22 in.
2
03D − 03D 2 ⎛ PPPP ⎞
×⎜
⎝
⎠⎟
× 03D
PP
PP 03D − 03D
+
3
⎛ 0.0042 mm/mm ⎞
2
−3
×⎜
⎟⎠ = 62.01 × 10 kN/mm
⎝
PP
2
×
LQ NVL − NVL ⎛ LQLQ⎞
×⎜
⎟⎠
⎝
3
22 in.
= NVL
+
G = NVLîLQLQ LQ±LQ
G = 03DîPPPP PP±PP
⎛ NVL − NVL ⎞ ⎛ LQLQ⎞
×⎜
⎝
⎠⎟ ⎝⎜
⎠⎟
2
22 in.
⎛ 31, 685 MPa − 1315 MPa ⎞ ⎛ 0.0042 mm/mm ⎞
×⎜
⎟⎠ ⎜⎝
⎟⎠
⎝
PP
= ±NLSLQ
= –31.48 kN/mm
H NVLîLQ LQ±LQ NLS
H 03DîPP PP±PP N1
I NVLîLQî >LQ@2 ±NVL LQ±
LQ îLQîLQNVLîLQî >
in.]2 LQLQ ±NVLîLQî LQ
LQ±LQ LQLQ NLSLQ
I 03DîPPî >PP@2@ ±03D
PP±PP î PP PP 03D
îPPî >PP@2@ PPPP ±
03DîPPî PP PP±PP
PPPP N1PP
The distances from each layer of steel reinforcement
to the geometric centroid of the cross section are:
The distances from each layer of steel reinforcement
to the geometric centroid of the cross section are:
d1 = 10 in.
d2 = d3 = 3.3 in.
d1 = 254 mm
d2 = d3 = 85 mm
Point C:
Nominal axial capacity:
ࢥPnI >±NLSLQ3 LQ 3NVL LQ 2±NLSLQ LQ NLS@LQ2
NVL LQ2 NVL LQ2 ±NVL 5.08 in.2 ±NVL
Point C:
Nominal axial capacity:
ࢥPn C = 0.65[–1.33 ×10–4 kN/mm3 PP 3 +
104.41 × 10–3 kN/mm2î PP 2 – 27.32 kN/
PP PP N1@PP2 03D + 1315 mm2 03D PP2 ±03D 3277 mm2 ±03D
ࢥPnI = 1320 kip
ࢥPn C = 5870 kN
where
where
A=
−LQ NVL − NVL 2 ⎛ LQLQ⎞
⎜⎝
⎟
12 × 6.5 ksi
14.78 in. ⎠
2
A=
−LQ NVL − NVL ⎛ LQLQ⎞
⎜⎝
⎟
2
14.78 in. ⎠
= 15.14 ksi
2
2
⎛ 0.0042 mm/mm ⎞
−4
2
×⎜
⎟⎠ = 1.33 × 10 kN/mm
⎝
375 mm
±NLSLQ3
B=
−PP 03D − 03D
12 × 44.8 MPa
B=
−PP 03D − 03D
2
⎛ 0.0042 mm/mm ⎞
−3
2
× ⎜
⎟⎠ = –104.41 × 10 kN/mm
⎝
375 mm
C = –24 in. × 6.5 ksi = –156 kip/in.
C = –610 mm × 44.8 MPa = –27.32 kN/mm
D = 24 in. × 14.78 in. × 6.5 ksi
LQ × LQ × NVL
+
2
î LQLQ NLS
D = 610 mm × 375 mm × 44.8 MPa
610 mm × 375 mm × 1315 MPa
+
2
î PPPP N1
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80
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.9 (cont.)—Procedure for strengthening of a noncircular concrete column for increase in axial
and bending forces
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,PHWULFXQLWV
)RUWKHFDOFXODWLRQRIWKHFRHI¿FLHQWVLWLVQHFHVVDU\
to compute key parameters from the stress-strain
model:
)RUWKHFDOFXODWLRQRIWKHFRHI¿FLHQWVLWLVQHFHVVDU\
to compute key parameters from the stress-strain
model:
0.0042 in./in.
⎛
⎞
c = 22 in. × ⎜
⎝ 0.0021 in./in. + 0.0042 in./in.⎟⎠
0.0042 mm/mm
⎛
⎞
c = 560 mm × ⎜
⎝ 0.0021 mm/mm + 0.0042 mm/mm ⎟⎠
= 373 mm
= 14.67 in.
yt = 14.64 in.
0.003 in./in.
= 10.5 in.
0.0042 in./in.
yt = 373 mm
The strains in each layer of steel are determined
by similar triangles in the strain distribution. The
corresponding stresses are then given by:
fs1 İs1Es LQLQîNVLĺNVL
fs2 İs2Es LQLQîNVL NVL
fs3 İs3Es ±î–4LQLQîNVL ±NVL
fs4 İs4Es ±LQLQîNVL ±NVL
0.003 in./in.
= 266 mm
0.0042 in./in.
The strains in each layer of steel are determined
by similar triangles in the strain distribution. The
corresponding stresses are then given by:
fs1 İs1Es PPPPî03Dĺ03D
fs2 İs2Es = 0.0018 mm/mm × 200,000 MPa = 350 MPa
fs3 İs3Es ±î–4 mm/mm × 200,000 MPa = –31.8 MPa
fs4 İs4Es = –0.0021 mm/mm × 200,000 MPa = –414 MPa
Nominal bending moment:
Nominal bending moment:
ࢥMn & = 0.65[–0.37 kip/in.3 LQ 4 + 11.46 ksi
ࢥMn C >±î–5 kN/mm3 PP 4î
LQ 3±NLSLQ LQ 2NLS 10–3 kN/mm2 PP 3±N1PP PP 2 +
LQ NLSLQ@LQ2 NVL LQ N1 PP N1PP@PP2
in.2 NVL LQ ±LQ2 ±NVL 03D PP PP2 ±03D LQ ±LQ2 ±NVL LQ
PP ±PP2 ±03D PP
ࢥMn C NLSIW
ࢥMn C = 1345 kN-m
where
E=
where
−LQ NVL − NVL 2 ⎛ LQLQ⎞
⎝⎜ 14.78 in. ⎠⎟
16 × 6.5 ksi
2
= –0.37 kip/in.3
E=
−PP 03D − 03D
16 × 44.8 MPa
2
⎛ PPPP ⎞
⎜⎝
⎟⎠
375 mm
2
±î−5 N1PP3
F = LQ LQ±LQ
2
NVL − NVL ⎛ LQLQ⎞
⎝⎜ 14.78 in. ⎠⎟
12 × 6.5 ksi
LQ NVL − NVL
+
3
⎛ 0.0042 in./in.⎞
×⎜
= 11.46 ksi
⎝ 14.78 in. ⎠⎟
F = PP PP±PP
2
×
G = ±NVLîLQLQ LQ±LQ
⎛ NVL − NVL ⎞ ⎛ LQLQ⎞
×⎜
⎟⎠ ⎜⎝
⎟
⎝
2
14.78 in. ⎠
= –120.08 kip/in.
03D − 03D 2 ⎛ PPPP ⎞
⎝⎜
⎠⎟
12 × 44.8 MPa
375 mm
PP 03D − 03D
+
3
⎛ 0.0042 mm/mm ⎞
×⎜
= × −3 N1PP 2
⎝
⎠⎟
375 mm
2
×
G = ±03DîPPPP PP±PP
⎛ 31,681 MPa − 1315 MPa ⎞ ⎛ 0.0042 mm/mm ⎞
×⎜
⎝
⎠⎟ ⎝⎜
⎠⎟
2
375 mm
= –21.03 kN/mm
H NVLîLQ LQ±LQ NLS
H 03DîPP PP±PP N1
I NVLîLQî >LQ@2 ±NVL LQ±LQ LQ LQ NVLîLQî
>LQ@2 LQLQ ±NVLîLQî
LQ LQ±LQ LQLQ
= 11,643 kip-in.
I 03DîPPî >PP@2 ±03D
PP±PP î PP PP 03DîPPî >PP@2 PPPP ±
03DîPPî PP PP±
PP PPPP N1PP
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
81
Table 16.9 (cont.)—Procedure for strengthening of a noncircular concrete column for increase in axial
and bending forces
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
6WHS²&RPSDULVRQRIVLPSOL¿HG
SDUWLDOLQWHUDFWLRQGLDJUDPZLWK
UHTXLUHGPu and Mu
&DOFXODWLRQLQ6,PHWULFXQLWV
The following table summarizes the axial and bending The following table summarizes the axial and bending
QRPLQDOFDSDFLWLHV XQVWUHQJWKHQHGDQGVWUHQJWKHQHG QRPLQDOFDSDFLWLHV XQVWUHQJWKHQHGDQGVWUHQJWKHQHG for Points A, B, and C. These points are plotted in the for Points A, B, and C. These points are plotted in the
IROORZLQJ¿JXUH
IROORZLQJ¿JXUH
Point
A
B
C
n = 0 plies
XQVWUHQJWKHQHG
PHPEHU
ࢥMn,
ࢥPn,
kip
kip-ft
2087
0
1858
644
884
n = 6 plies
ࢥPn,
ࢥMn,
kip
kip-ft
2523
0
2210
682
1320
Point
A
B
C
@Seismicisolation
@Seismicisolation
n = 0 plies
XQVWUHQJWKHQHG
PHPEHU
ࢥMn,
ࢥPn,
kN
kN-m
0
8264
873
4128
n = 6 plies
ࢥPn,
ࢥMn,
kN
kN-m
11,223
0
5870
1345
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82
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.10—Plastic hinge confinement for seismic
strengthening
7KLV H[DPSOH LOOXVWUDWHV WKH GHVLJQ RI DQ )53 UHWUR¿W WR
enhance the plastic rotation capacity of a nonductile reinforced concrete column. In this example, the column cannot
HI¿FLHQWO\ UHVLVW VHLVPLF ORDGV IRU WZR UHDVRQV WKH WLH
VSDFLQJGRHVQRWFRQIRUPWRFXUUHQWVHLVPLFGHVLJQFRGHV
DQG WKHWLHVGRQRWSURMHFWLQWRWKHFRUHDQGXQGHUVHLVPLF
loads may open once the cover concrete begins to spall. The
DIRUHPHQWLRQHG GH¿FLHQFLHV LQGLFDWH WKDW WKH FROXPQ PD\
KDYHLQDGHTXDWHVKHDUVWUHQJWKLQDGHTXDWHFRQ¿QHPHQWRI
WKH SODVWLF KLQJH UHJLRQ DQG LQDGHTXDWH FODPSLQJ RI ODS
VSOLFHV ,Q DGGLWLRQ WKH GHVLJQHU VKRXOG HQVXUH DGHTXDWH
resistance against buckling of the main longitudinal reinIRUFHPHQW ,Q WKLV H[DPSOH WKH GH¿FLHQF\ XQGHU FRQVLGHUDWLRQ LV LQDGHTXDWH SODVWLF URWDWLRQ FDSDFLW\ ZKLFK FDQ EH
HQKDQFHG E\ FRQ¿QHPHQW RI WKH SODVWLF KLQJH UHJLRQ ZLWK
FRP. A seismic analysis has already determined that the
FROXPQLVFDSDEOHRIUHVLVWLQJWKHUHTXLUHGVHLVPLFPRPHQWV
7KXVWKHUHLVQRQHHGWRLQFUHDVHWKHÀH[XUDOFDSDFLW\RIWKH
section. This example is limited in scope to the FRP design
UHTXLUHPHQWV DQG GRHV QRW FRYHU WKH VHLVPLF DQDO\VLV
ASCE/SEI 41 is used as the base standard for this example.
The column, which is to be part of a lateral load-resisting
system, is illustrated in Fig. 16.10a. Expected material proper-
ties and other relevant information are listed in Table 16.10a.
From a seismic analysis, the column should be capable of
GHYHORSLQJDSODVWLFURWDWLRQșp = 0.025 rad. The axial load
on the column, including gravity plus seismic loads, is Pu =
NLS N1 7KLVSODVWLFURWDWLRQGHPDQGH[FHHGVWKH
limiting value of 0.015 stipulated in ASCE/SEI 41 numerical
acceptance criteria for reinforced concrete columns that do
not conform to current seismic design codes. The concrete
and reinforcing steel strain limitations of ASCE/SEI 41 as
listed in Table 16.10b should not be exceeded.
The column is strengthened with CFRP laminates having
the composite properties listed in Table 16.10c and bonded
DURXQG WKH FROXPQ XVLQJ WKH ZHW OD\XS WHFKQLTXH *ODVV
)53 *)53 KRZHYHU FDQ VLPLODUO\ EH XVHG LI GHVLUHG
The design process was initiated by considering a wrapping system composed of three plies. After two iterations,
WKH ¿QDO ZUDSSLQJ V\VWHP ZDV IRXQG WR UHTXLUH ¿YH SOLHV
2QO\WKHFDOFXODWLRQVXVHGWRYHULI\WKH¿QDOFRQ¿JXUDWLRQ
are provided. These calculations are shown in Table 16.10d.
Figure 16.10b shows the moment curvature analysis of the
DVEXLOWDQGUHWUR¿WUHFWDQJXODUVHFWLRQV7KHPRPHQWFXUYDture analysis results show the as-built ultimate curvature
FDSDFLW\ LV VLJQL¿FDQWO\ ORZHU WKDQ WKH UHTXLUHG FXUYDWXUH
demand.
)LJD²$VEXLOWFROXPQGHWDLOV
)LJE²0RPHQWFXUYDWXUHDQDO\VLV
Table 16.10a—Column material properties
4000 psi
27.6 MPa
3605 ksi
25 GPa
Longitudinal reinforcing steel: yield strength fy
44,000 psi
303 MPa
Modulus of elasticity of steel Es
NVL
200 GPa
Concrete strength fcƍ
Concrete elastic modulus
Ec = f c′ SVL Ec = f c′ 03D Longitudinal reinforcing steel: yield strain İy
Column height between plastic hinges L
Distance to extreme tension steel d
0.0015
0.0015
10 ft
3.05 m
14.625 in.
371 mm
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
83
Table 16.10b—Maximum usable strain levels (ASCE/SEI 41)
Strain limits
&RPSUHVVLYH FRQFUHWH
7HQVLOH VWHHO
&RPSUHVVLYH VWHHO
8QFRQ¿QHGVHFWLRQV
&RQ¿QHGVHFWLRQVSHU
0.003
İccu
0.005
0.05
Limited by the concrete
0.02
Table 16.10c—Manufacturer’s reported composite properties
Thickness per ply tf
Ultimate tensile strength
5XSWXUHVWUDLQİfu*
Modulus of elasticity, Ef
ffu*
0.023 in.
0.584 mm
155 ksi
1072 MPa
0.015
0.015
NVL
64.3 GPa
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84
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.10d—Procedure for designing plastic hinge confinement for seismic strengthening
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
6WHS²)53V\VWHPGHVLJQPDWHULDO
SURSHUWLHV
İfu = CEİfu*
İfu”î CE The column is located in an interior space.
7KHUHIRUHSHU7DEOHDQHQYLURQPHQWDO
UHGXFWLRQIDFWRURILVXVHG
țe = 0.55
İfe ”țİİfu
İfe ”î ‫׵‬İfe = 0.04
‫׵‬İfe = 0.04
Lp = 2 + 0.0003 ×44,000 × 0.75 = 12 in.
Lp îî LQ
6WHS²3ODVWLFKLQJHOHQJWK
In FRP jacketed columns, the plastic hinge
length is:
1RWH8VHDPD[LPXPJDSEHWZHHQWKH)53DQGWKHFROXPQEDVHRILQ PP
Lp = g + 0.0003fydEƐ SVLDQGLQ
Lp = g + 0.044fydEƐ 03DDQGPP
6WHS²3UHOLPLQDU\FDOFXODWLRQV
b = h LQ PP
From 12.1.2:
D = h2 + b2
κa =
Ae ⎛ b ⎞
⎜ ⎟
Ac ⎝ h ⎠
κb =
Ae
Ac
D = 406.42 + 406.42 = 575 mm
Ae/Ac = 0.62
Ae/Ac = 0.62
2
2
⎛A⎞
κ a = 0.62 ⎜ e ⎟ = 0.62
⎝ Ac ⎠
h
b
κ b = 0.62
where Ae/Ac is calculated as:
⎡⎛ b⎞
⎛ h⎞
2
⎢ ⎜⎝ h ⎟⎠ h − rc + ⎜⎝ b ⎟⎠ b − rc
1− ⎢
3 Ag
⎢
⎢⎣
Ae
=
Ac
1 − ρg
D = 162 + 162 = 22.63 in.
ța = 0.62
16
= 0.62
16
țb = 0.62
İcƍ 2
⎤
⎥
⎥ − ρg
⎥
⎥⎦
İcƍ h/b = 1.00
1RWH)RUUHFWDQJXODUPHPEHUVSODVWLFKLQJHFRQ¿QHPHQWE\MDFNHWLQJLVQRWUHFRPPHQGHGIRUPHPEHUV
featuring side aspect ratios, h/b, greater than 1.5, or face dimensions, b or hH[FHHGLQJLQ PP XQOHVVWHVWLQJGHPRQVWUDWHVWKHLUHIIHFWLYHQHVV 6WHS²&RQ¿QLQJFRQFUHWHPRGHO
YDULDEOHV
8VLQJWKHWULDOGHVLJQRI¿YHSOLHV
FRPSXWHWKHFRQ¿QHGFRQFUHWHPRGHO
parameters listed in the following:
f =
2 E f t f n f ε fe
fl =
D
× × × × = 380 psi
22.63
fl =
2 × 64,300 × 0.584 × 5 × 0.004
= 2.61 MPa
575
ȥf IRUIXOO\ZUDSSHGVHFWLRQV
ȥf fccƍ fcƍȥfțafl
fccƍ îîî SVL
fccƍ îîî 03D
0.45
⎛
f ⎛ ε fe ⎞ ⎞
ε ccu = ε c′ ⎜1.50 + 12κ b ⎜ ⎟ ⎟
f c′ ⎝ ε′c ⎠ ⎠
⎝
0.45
⎛
380 ⎛ 0.004 ⎞ ⎞
ε ccu = 0.002 ⎜1.50 + 12 × 0.62 ×
⎜⎝
⎟⎠ ⎟
4000
0.002
⎝
⎠
0.45
⎛
2.61 ⎛ 0.004 ⎞ ⎞
ε ccu = 0.002 ⎜1.50 + 12 × 0.62 ×
⎜⎝
⎟⎠ ⎟
27.60 0.002
⎝
⎠
= ≤ = ≤ İccu is limited to 0.01 to prevent excessive cracking and the resulting loss of concrete integrity
1RWH7KHH[SUHVVLRQVSUHVHQWHGSUHYLRXVO\DUHXVHGLQFRQMXQFWLRQZLWKDPRPHQWFXUYDWXUH Mࢥ DQDO\VLVSURJUDPWRREWDLQWKH\LHOGDQGXOWLPDWHFXUYDWXUH7KHVHFXUYDWXUHV
are presented in Steps 5 and 6.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
85
Table 16.10d (cont.)—Procedure for designing plastic hinge confinement for seismic strengthening
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
6WHS²2XWSXWIURPMࢥDQDO\VLV
SURJUDPREWDLQWKHQHXWUDOD[LVDW
\LHOGLQJRIORQJLWXGLQDOUHLQIRUFHPHQW
cy,frp
Neutral axis:
cy,frp = 5.34 in.
Neutral axis:
cy,frp = 136 mm
6WHS²2XWSXWIURPMࢥDQDO\VLV
SURJUDPREWDLQWKHQHXWUDOD[LVDW
XOWLPDWHcu,frp
Neutral axis:
cu,frp LQ
1RWH<LHOGVWUDLQRIORQJLWXGLQDOUHLQIRUFHPHQWİy Neutral axis:
cu,frp = 50 mm
1RWH7KHXOWLPDWHFRQFUHWHFRPSUHVVLYHVWUDLQLVFRPSXWHGSHU6WHSİccu 1. Concrete compression strain:
İccu 2. Steel tension strain:
⎛d
⎞
ε s = ε ccu ⎜ − 1⎟
⎝ cu ⎠
6WHS²&RPSXWHWKH\LHOGFXUYDWXUH
φ y , frp =
εy
⎛ 371 ⎞
ε s = ⎜
− = < ⎝ 136 ⎟⎠
From a MࢥDQDO\VLVWKH\LHOGFXUYDWXUHLV
From a MࢥDQDO\VLVWKH\LHOGFXUYDWXUHLV
φ y , frp =
d − c y , frp
6WHS²&RPSXWHWKHXOWLPDWH
FXUYDWXUHFDSDFLW\
φu , frp =
⎛ 14.625 ⎞
ε s = ⎜
− ⎟ = < ⎝ 5.34
⎠
0.0015
= 0.000163/in.
14.625 − 5.34
From a MࢥDQDO\VLVWKHXOWLPDWHFXUYDWXUHLV
ε ccu
cu , FRP
φu , frp =
φ y , frp =
0.0015
= 0.0064/m
371 − 136
From a MࢥDQDO\VLVWKHXOWLPDWHFXUYDWXUHLV
= 0.0025/in.
φu , frp =
0.0049
= 0.099/m
50
6WHS²&RPSXWHWKHXOWLPDWH
FXUYDWXUHGHPDQG
φD =
θp
Lp
+ y , frp
φD =
6WHS²9HULI\GHVLJQ
ࢥDࢥu,frp
6WHS²/HQJWKRIFRQ¿QHGUHJLRQlo
7UDQVYHUVHUHLQIRUFHPHQWDVVSHFL¿HG
per Section 18.7 of ACI 318-14 shall be
provided over a length lo
0.025
+ 0.000163 = 0.0022/in.
12
φD =
0.025
+ 0.0064 = 0.084/m
0.305
ࢥD = 0.0022/in. < 0.0025/in. OK
ࢥD PP2.
⎧16 in.
⎪⎪120 / 2
o ≥ ⎨
= 10 in.
⎪ 6
⎪⎩18 in.
⎧406.4 mm
⎪⎪ 3050/2
o ≥ ⎨
= 254 mm
⎪ 6
⎪⎩457 mm
lo!Lp LQ PP
Design summary:
&RPSOHWHO\ZUDSWKHVHFWLRQZLWK¿YHWUDQVYHUVHSOLHV
&RQ¿QLQJMDFNHWVKRXOGH[WHQGDWOHDVWLQ PP EH\RQGWKHMRLQWLQWHUIDFH
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86
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.11—Lap-splice clamping for seismic
strengthening
7KLV H[DPSOH LOOXVWUDWHV WKH GHVLJQ RI DQ )53 UHWUR¿W WR
improve the seismic performance of a reinforced concrete
column that is constructed with a lap splice in a region of
plastic rotations. Material properties, details, and other
relevant information are provided in Table 16.11a and Fig.
16.11. The column is strengthened with CFRP laminates
having the composite properties listed in Table 16.11b and
ERQGHG DURXQG WKH FROXPQ XVLQJ WKH ZHW OD\XS WHFKQLTXH
Glass FRP, however, can similarly be used if desired.
7KH¿QDOZUDSSLQJV\VWHPZDVIRXQGWRUHTXLUH¿YHSOLHV
2QO\WKHFDOFXODWLRQVXVHGWRYHULI\WKH¿QDOFRQ¿JXUDWLRQ
are provided. These calculations are shown in Table. 16.11c.
)LJ²'HWDLORIODSVSOLFHLQDSODVWLFKLQJHUHJLRQ
Table 16.11a—Column material properties
4000 psi
27.6 MPa
3605 ksi
25 GPa
Longtudinal reinforcing steel: yield strength fy
44,000 psi
303.4 MPa
Modulus of elasticity of steel Es
NVL
200 GPa
Concrete strength fcƍ
Concrete elastic modulus
Ec = f c′ SVL
Ec = f c′ 03D
/RQJLWXGLQDOUHLQIRUFLQJVWHHO\LHOGVWUDLQİy
Column height between plastic hinges, L
Distance to extreme tension steel, d
0.0015
0.0015
10 ft
3.05 m
14.625 in.
371 mm
Table 16.11b—Manufacturer’s reported composite properties
Thickness per ply tf
0.08 in.
2 mm
Ultimate tensile strength
143 ksi
03D
0.010
0.010
NVL
*3D
Rupture strain
Modulus of elasticity Ef
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87
Table 16.11c—Procedure for designing lap-splice clamping for seismic strengthening
3URFHGXUH
6WHS²&RPSXWHWKHWHQVLOHVWUHVV
WKDWH[LVWLQJVSOLFHFDQGHYHORS $&,
6HFWLRQ
⎛c K ⎞
40 d λ f c′ ⎜ b tr ⎟
⎝ db ⎠
LQDQGSVL
fs =
3 db ψ t ψ e ψ s
⎛c K ⎞
3.33 d λ f c′ ⎜ b tr ⎟
⎝ db ⎠
PPDQG03D
fs =
3 db ψ t ψ e ψ s
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
s = 12 in.
n=1
Longitudinal bars in the potential plane of splitting
s = 305 mm
n=1
K tr =
40 × 1 × 0.11
= 0.37 in.
12 × 1
cb + K tr
+ + + =
= 2.24 ≤ 2.50
db
1.00
3HU(T D RI$&,WKHYDOXH
cannot be greater than 2.5.
40 Atr
K tr =
sn
ȥt ȥe ȥs = 1.00
Ȝ QRUPDOZHLJKWFRQFUHWH
Ktr =
40 × 1× 71
= PP
305 × 1
cb + K tr
+ + + =
= 2.24 ≤ 2.50
db
25.4
cb + K tr
db
40 × 20.0 × 1.0 4000 × 2.24
3 × 1.0 × 1.0 × 1.0 × 1.0
= SVL ≤ SVL
fs =
3.33 × 508 × 1.0 27.6 × 2.24
3 × 25.4 × 1.0 × 1.0 × 1.0
= 260 MPa ≤ 303 MPa
fs =
Note: Computed stress fs does not reach fy, longitudinal bar yield strength, and as such lap splice must be clamped.
6WHS²6WUHVVFRUUHVSRQGLQJWRSXOORXW
FDSDFLW\RIVSOLFH
fs ≤
fs ≤
33 d λ f c′
db ψ t ψ e ψ s
db ψ t ψ e ψ s
Ɛprov = 20dEƐ = 20 × 25.4 = 508 mm
Pullout capacity of splice:
Pullout capacity of splice:
fs =
LQDQGSVL
2.75 d λ f c′
Ɛprov = 20dEƐ = 20 × 1.0 = 20 in.
33 × 20.0 × 4000
= 41,742 psi
1.0 × 1.0 × 1.0 × 1.0
fs =
2.75 × 508 × 27.6
= 03D
25.4 × 1.0 × 1.0 × 1.0
PPDQG03D
6WHS²&RPSXWHWKHUHTXLUHGMDFNHW
WKLFNQHVVtj
nt f = ×
D
NVLDQGLQ
Ef
nt f = ×
D
03DDQGPP
Ef
D LQ PD[LPXPGLPHQVLRQLQDUHFWDQJXODUPHPEHU
D = 610 mm
Ef NVL
Ef 03D
t j = 218 ×
24
= 0.38 in.
t j = ×
610
= PP
6WHS²&RPSXWHWKHUHTXLUHGQXPEHU
RISOLHVn
n = tj/tf
tf = 0.08 in.
tf = 2 mm
n ¿YHSOLHV
n ¿YHSOLHV
Design summary:
&RPSOHWHO\ZUDSWKHVHFWLRQZLWK¿YHWUDQVYHUVHSOLHV
&RQ¿QLQJMDFNHWVKRXOGH[WHQGDWOHDVWIXOOKHLJKWRIODSVSOLFHWKDWLVLQ PP
8VLQJ¿YHSOLHVRIWKH)53VSHFL¿HGUHVXOWVLQDVSOLFHFDSDFLW\RISVL 03D ZKLFKLVFRQWUROOHGE\WKHPD[LPXPSXOORXWFDSDFLW\FDOFXODWHG
in Step 2.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.12—Seismic shear strengthening
This example illustrates the main steps in calculating the
DPRXQWRI)53UHTXLUHGIRUWKHVKHDUVWUHQJWKHQLQJRIDUHLQforced concrete member. The member used in this example
is illustrated in Fig. 16.12. Column material properties are
VKRZQLQ7DEOHDWKHFRQ¿JXUDWLRQRIWKH)53VKHDU
reinforcement is described in Table 16.12b, and the CFRP
laminate material properties are listed in Table 16.12c.
ASCE/SEI 41 is used as the standard for this example. Glass
)53 *)53 FDQVLPLODUO\EHXVHGLIGHVLUHG&DOFXODWLRQV
IRUGHWHUPLQLQJWKH)53UHTXLUHGDVVKRZQLQ7DEOHG
)LJ²$VEXLOWFROXPQGHWDLOV
Table 16.12a—Column material properties
4000 psi
27.6 MPa
3605 ksi
25 GPa
Longtudinal reinforcing steel: yield strength fy
44,000 psi
303.4 MPa
Modulus of elasticity of steel Es
NVL
200 GPa
Concrete strength fcƍ
Concrete elastic modulus
Ec = f c′ SVL
Ec = f c′ 03D
/RQJLWXGLQDOUHLQIRUFLQJVWHHO\LHOGVWUDLQİy
Column height between plastic hinges, L
Distance to extreme tension steel, d
Ultimate axial load Pu
0.0015
0.0015
10 ft
3.05 m
14.625 in.
371 mm
75 kip
333.62 kN
Table 16.12b—Configuration of supplemental FRP shear reinforcement
Minimum section dimension
16 in.
406 mm
dfy JRYHUQHGE\PLQLPXPVHFWLRQGLPHQVLRQ
16 in.
406 mm
Width wf
8 in.
203 mm
Spacing sf IXOOFRYHUDJH
8 in.
203 mm
Table 16.12c—Manufacturer’s reported composite properties
Thickness per ply tf
Ultimate tensile strength ffu*
5XSWXUHVWUDLQİfu*
Modulus of elasticity Ef
0.023 in.
0.584 mm
155 ksi
1072 MPa
0.015
0.015
NVL
64.3 GPa
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
89
Table 16.12d—Procedure for seismic shear strengthening
'HVLJQVWHSV
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
6WHS²&RPSXWHWKHSUREDEOHPRPHQW
FDSDFLW\RIWKHPHPEHUMpr
From a MࢥDQDO\VLVWKHSUREDEOHPRPHQWFDSDFLW\LV
Mpr = 322 kip-ft
From a MࢥDQDO\VLVWKHSUREDEOHPRPHQWFDSDFLW\LV
Mpr = 437 kN-m
3HULQFDOFXODWLQJWKHSUREDEOH
PRPHQWࢥ DQGȥf = 1 are used.
Notes:
,QVHLVPLFDSSOLFDWLRQVWKHVKHDUGHVLJQSURFHVVLQLWLDWHVZLWKWKHFDOFXODWLRQRIWKHSUREDEOHPRPHQW
capacity of the section.
0RPHQWMpr is computed at both top and bottom ends of the member.
6WHS²2EWDLQWKH\LHOGDQGXOWLPDWH
FXUYDWXUHIURPDMࢥDQDO\VLV
Yield curvature:
ࢥy,frp = 0.000163/in.
Yield curvature:
ࢥy,frp = 0.0064/m
Ultimate curvature:
ࢥu,frp LQ
Ultimate curvature:
ࢥu,frp = 0.074/m
Plastic hinge length:
Plastic hinge length:
Lp = 2 + 0.0003 × 44,000 × 0.75 = 12 in.
Lp îî PP
Note: Use a maximum gap between the FRP and the
column base of 2 in.
Note: Use a maximum gap between the FRP and the
column base of 50.8 mm.
<LHOGGHÀHFWLRQ
<LHOGGHÀHFWLRQ
6WHS²&RPSXWHWKHGLVSODFHPHQW
GXFWLOLW\DQGUHGXFWLRQIDFWRUk
In FRP jacketed columns, the plastic hinge
OHQJWKLV (T Lp = g + 0.0003fydb
fy is in ksi and db is in inches
Lp = g + 0.044fydb
fy is in MPa and db is in mm
In this example:
L
= LQ PP
2
<LHOGGHÀHFWLRQ¨y,frp:
Leff =
Δ y , frp =
2
eff
φ y , frp L
2
Δ y , frp =
3
3ODVWLFGHÀHFWLRQ¨p,frp:
Δ p , frp
Δy =
0.0065 × 15242
= 5.1 mm
3 × 1000
3ODVWLFGHÀHFWLRQ
Lp ⎞
⎛
= φu − φ y L p ⎜ Leff − ⎟
2⎠
⎝
3ODVWLFGHÀHFWLRQ
12 ⎞
− ⎞
⎛
⎛
305 ⎜1524 −
Δ p , frp = − × ⎜ − ⎟ = LQ Δ p , frp =
⎟ = 28.6 mm
⎝
⎝
2⎠
1000
2 ⎠
'LVSODFHPHQWGXFWLOLW\ȝ¨:
μΔ = 1 +
0.000163 × 60
= 0.20 in.
3
Displacement ductility:
Δp
μΔ = 1 +
Δy
Shear reduction factor per ASCE/SEI 41
⎧μ Δ ≤ k = ⎪
× − μ Δ
⎪
⎨ ≤ μ Δ ≤ k = +
4
⎪
⎪⎩μ Δ > k = 6WHS²&RPSXWHWKHVKHDUGHVLJQ
IRUFHVu
Displacement ductility:
1.13
= 6.7
0.20
μΔ = 1 +
28.6
= 6.7
5.1
Reduction factor:
Reduction factor:
k = 0.70
k = 0.70
,QWKLVH[DPSOHZLWKWKHH[FHSWLRQRIWKHHDUWKTXDNHIRUFHVWKHUHDUHQRDSSOLHGXQLIRUPORDGVRQWKHPHPEHU
as such:
Wu = 0.00
From Step 1, the probable moment capacity is:
Mpr,top = Mpr,bot NLSIW N1P
Design shear force:
Per ACI 318-14 Section 18.7.6:
Vu =
M pr ,top + M pr ,bot
L
±
wu L
2
Vu =
322 + 322
± 0 = 64.4 kip
120/12
Design shear force:
Vu =
@Seismicisolation
@Seismicisolation
437 + 437
± 0 = 286 kN
3.05
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.12d (cont.)—Procedure for seismic shear strengthening
'HVLJQVWHSV
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
Concrete contribution to shear capacity:
Concrete contribution to shear capacity:
Vc = 0
Vc = 0
Steel contribution to shear capacity:
Steel contribution to shear capacity:
6WHS²&DOFXODWHWKHFRQFUHWHVcDQG
VWHHOFRQWULEXWLRQVs
Concrete contribution, Vc:
Per ACI 318-14 Section 18.7.6.2.1, and
because:
M pr , r + M pr ,l
n
⎛w ⎞ 1
≥⎜ u n⎟ ⇒
⎝ 2 ⎠2
Vc = 0
Steel contribution Vs
Vs = Ash f y
d
s
Vs = 2 × 0.20 × 44 ×
14.625
= 21.4 kip
12
Vs = 2 × 129 × 303.4 ×
371.475
= 95.2 kN
305
Combined concrete and steel contribution:
k Vc +Vs NLS
Combined concrete and steel contribution:
k Vc +Vs N1
5HTXLUHG)53IRUFH
5HTXLUHG)53IRUFH
6WHS²&DOFXODWHWKHUHTXLUHG)53
IRUFHVf
V f ,R
⎡Vu
⎤
⎢ φ − k Vc + Vs ⎥
⎣
⎦
=
ψf
V f ,R
⎡ 64.4
⎤
⎢ 1.00 − ⎥⎦
=⎣
= 45.26 kip
V f ,R
⎡ 286
⎤
⎢1.00 − 66.6⎥⎦
=⎣
= 201.3 kN
3HU$6&(6(,ࢥ For completely wrapped members, Table
UHFRPPHQGVȥf 6WHS²&DOFXODWHWKHHIIHFWLYHVWUHVVffe.
For fully wrapped members, the effective
VWUDLQLVFRPSXWHGXVLQJ(T İfe = 0.75CEİfu*”
Effective strain:
İfe îî ”
Effective strain:
İfe îî ”
Effective stress:
ffe î NVL
Effective stress:
ffe = 0.004 × 64,300 = 257 MPa
Area per ply:
Afv = 2 × 0.023 × 8 = 0.37 in.2
Area per ply:
Afv = 2 × 0.584 × 203 = 237 mm2
Force per ply:
Force per ply:
CE The column is located in an interior space.
7KHUHIRUHSHU7DEOHDQHQYLURQPHQWDO
UHGXFWLRQIDFWRURILVXVHG
The effective FRP stress can be computed
from Hooke’s law:
ffe İfeEf
6WHS²&DOFXODWHWKHQXPEHURISOLHVnf
Area of a single ply for a fully wrapped
PHPEHU (T D Afv = 2tfwf
The shear contribution of the FRP can be
WKHQFDOFXODWHGIURP(T VLQ α + FRV α d fv
V f = Afv f fe
sf
V f = 0.37 × 37.3
= 27.6 kip
8
V f = 237 × 257
Number of plies:
n fv =
V f ,R
Vf
45.26
=
= PLQLPXP
27.6
= 122 kN
203
Number of plies:
n fv =
V f ,R
Vf
=
201.3
= PLQLPXP
122
Design summary: Completely wrap the section with two transverse plies
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
16.13—Flexural and shear seismic strengthening
of shear walls
7KLV H[DPSOH LOOXVWUDWHV WKH XVH RI DQ )53 UHWUR¿W WR
LQFUHDVHWKHVKHDUDQGÀH[XUDOVWUHQJWKRIDQH[LVWLQJFDQWLlevered concrete wall. The shear strengthening is achieved
by installing horizontally oriented FRP on one face of the
ZDOO 7KH ÀH[XUDO VWUHQJWKHQLQJ LV DFKLHYHG E\ LQVWDOOLQJ
multiple layers of vertically oriented FRP on both faces of
the wall near the wall ends. Details for anchorage of the FRP
WRWKHIRXQGDWLRQDUHQRWDGGUHVVHG&DUERQ)53 &)53 LV
XVHG LQ WKLV H[DPSOH *ODVV )53 *)53 FDQ VLPLODUO\ EH
used if desired.
The example incorporates the following two major phases:
'HWHUPLQH WKH VKHDU DQG ÀH[XUDO FDSDFLW\ RI WKH
existing wall
'HVLJQWKH)53WRDFKLHYHWKHUHTXLUHGVWUHQJWK
91
Details of the wall and relevant information are provided
in Fig. 16.13a and Table 16.13a. The wall is assumed to be
an ordinary shear wall. The wall is strengthened with FRP
having the composite properties listed in Table 16.13b. A
factored axial load, PuRINLS N1 LVDVVXPHGLQDGGLtion to the lateral force. ASCE/SEI 41 is assumed to be the
standard used as the basis for the rehabilitation.
This example illustrates a manual calculation approach for
the design of FRP strengthening of a shear wall. A moment
curvature analysis of the existing and repaired wall, shown
in Fig. 16.13b, is used to assess the accuracy of the manual
DSSURDFK 7KH UHDVRQDEO\ JRRG DJUHHPHQW RI WKH ÀH[XUDO
results from the design example with those from a momentcurvature analysis validates the illustrative example. The
design calculations are shown in Table 16.13c.
)LJD²&RQFUHWHZDOOGHWDLOV
)LJ E²0RPHQWFXUYDWXUH DQDO\VLV IRU VKHDU ZDOO
example.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.13a—As-built shear wall properties and demands
Concrete strength
Longitudinal reinforcing steel yield strength
Modulus of elasticity of steel
Longitudinal reinforcing yield strain
Shear wall height h
Shear wall length
Shear wall thickness
Existing wall reinforcement
+RUL]RQWDO1RDWLQ PP RQFHQWHU !ȡt = 0.0015
9HUWLFDO1RDWLQ PP RQFHQWHU !ȡl ȡb = 0.0027
Axial factored load Pu
Ultimate shear demand Vu
Ultimate moment demand at wall base Mu
Asw DUHDRIZDOOZHEVWHHO !DUHDRIIRXU1REDUV
QHJOHFWLQJRQHEDUZLWKLQWKHFRPSUHVVLRQ]RQH
2500 psi
17.23 MPa
40.0 ksi
275.8 MPa
NVL
200 GPa
0.0014 in./in.
0.0014 mm/mm
10 ft
3000 mm
60.0 in.
1500 mm
6 in.
150 mm
—
—
12 kip
53.4 kN
52 kip
232 kN
260 kip-ft
348 kN-m
0.8 in.2
500 mm2
Table 16.13b—Manufacturer’s reported composite properties
0.023 in.
Thickness per ply tf
Ultimate tensile strength
5XSWXUHVWUDLQİfu*
Modulus of elasticity Ef
ffu*
0.575 mm
140 ksi
03D
0.012 in./in.
0.012 mm/mm
NVL
66.2 GPa
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
93
Table 16.13c—Procedure for flexural and shear seismic strengthening of shear walls
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
6WHS²&RPSXWHH[LVWLQJZDOOFDSDFLW\
Shear capacity:
Shear capacity per ACI 318:
Vc = 2λ f c′tw d fv
Vc =
Vc =
× × 1000
0.167bw d f c′
Vc =
(0.167 × 0.8 × 1500)
Av f v d fv
Vsw
s
Vn = Vc + Vsw
0.8 × 60
= 0.11 × 40, 000 ×
12
Vsw = 17.6 kip
Vn = 28.8 kip + 17.6 kip
Vn = 46.4 kip
17.23
1000
Vc = 28.8 kip
1000
Vsw =
Vc = 124.8 kN
Vsw =
71 × 275.8 × 0.8 ×
1500
305
1000
Vsw = 77.0 kN
Vn = 124.8 kN + 77.0 kN
Vn = 201.8 kN
ࢥVn = 201.8 kN < Vu = 232 kN
8VLQJࢥ IRUVKHDU SHU$6&(6(, Flexural capacity:
$TXLFNPHWKRGWRDVVHVVWKHÀH[XUDO
capacity is shown in the following.
Assume that all web steel in the wall
yields. This includes all the longitudinal
reinforcement except for the one bar that
is adjacent to the compression face, that is,
four No. 4 bars can be considered to yield.
a=
Asw f y + Pu
ࢥVn = 46.4 kip < Vu = 52 kip
0.8 in. × 40 ksi + 12 kip
= 3.45 in.
0.85 × 2.5 ksi × 6 in.
2
a=
0.85 f c′tw
Mn Aswfy + Pu d – a
where d = Lw/2
⎛ 500 mm 2 × 275.8 MPa ⎞
⎜⎝
⎟⎠ + 53.4 kN
1000
= 87.1 mm
a=
⎛ 0.85 × 17.23 MPa × 150 mm ⎞
⎜⎝
⎟⎠
1000
d = Lw/2 = 30 in.
Mn = 104 kip-ft
d = 750 mm
Mn = 135.1 kN-m
ࢥMn = 104 kip-ft < Mu = 260 kip-ft
ࢥMn = 135.1 kN-m < Mu = 348 kN-m
8VLQJࢥ It can be observed that the wall does not
KDYHDGHTXDWHFDSDFLW\
6WHS²)53GHVLJQPDWHULDOSURSHUWLHV
For interior exposure for carbon FRP: CE Use environmental reduction factors from
7DEOH
3HU
ffu = CEffu*
İfu = CEİfu*
ffu = 133 ksi
İfu = 0.0114 in./in.
ffu 03D
İfu = 0.0114 mm/mm
)RURQHOD\HURI)53İfd = 0.0088
)RUWZROD\HUVRI)53İfd = 0.0062
)RUWKUHHOD\HUVRI)53İfd = 0.0051
)RURQHOD\HURI)53İfd = 0.0088
)RUWZROD\HUVRI)53İfd = 0.0062
)RUWKUHHOD\HUVRI)53İfd = 0.0051
6WHS²)OH[XUDOVWUHQJWKHQLQJ
6WHSD²&RPSXWHWKHGHERQGLQJVWUDLQ
OLPLWİfd
This is the limit for the effective strain in
the FRP.
3HU(T ε fd = 0.
ε fd = 0.41
f c′
≤ ε fu LQOE
nE f t f
f c′
≤ ε fu
nE f t f
SI
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94
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.13c (cont.)—Procedure for flexural and shear seismic strengthening of shear walls
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
Flexural design involves iteration to
DFKLHYHHTXLOLEULXPDFURVVWKHVHFWLRQ
8VXDOO\WKH¿UVWVWHSLVWRDVVXPHWKHGHSWK
of the neutral axis c.
Use the available information to assist with an
assumption for the depth of the neutral axis c.
$VVXPHWKDWWKHÀH[XUDOVWUHQJWKHQLQJZLOO
UHTXLUHWKUHHOD\HUVRILQ PP ZLGH
strips on each side of the wall at each end.
Assume that the effective strain is at the
centroid of the FRP area. Knowing the
maximum effective strain in the FRP,
compute the force in the FRP
Tf = CEAfİfdEf
&DOFXODWLRQLQ6,XQLWV
wf = 8 in.
nf = 3
tf = 0.023 in.
Af WZRVLGHVî Af = 1.104 in.2
Tf NVL NLS
wf = 200 mm
nf = 3
tf = 0.575 mm
Af PP2
Tf =
()()( 03D )
1000
= N1
Depth of corresponding compression block:
a=
Asw f y + Pu + T f
0.85 f c′tw
Compute an estimate of the depth of the
neutral axis, c:
Check actual strain at centroid of FRP area
and corresponding force in the FRP:
It is observed that the force in the FRP
does not agree with that based on the initial
assumption. However, the above steps
provide a reasonable starting point for an
assumption for c.
a = 7.05 in.
a = 177.2 mm
c = a/0.85 = 8.3 in.
c = a/0.85 = 208.5 mm
W f /2 ⎞
⎛
ε fe CG = ε fd ⎜ +
= ⎝ c + 1 − Lw ⎟⎠
W f /2
⎛
⎞
ε fe CG = ε fd ⎜ +
= ⎝ c + 25.4 − Lw ⎠⎟
Corresponding force in FRP,
Tf = CEAfİfeCGEf = 42.32 kip
Corresponding force in FRP,
Tf = CEAfİfeCGEf = 182.1 kN
Assume c = 8.0 in.
Assume c = 200 mm
İc = 0.0008
İcİcu = 0.003 OK
İc = 0.0008
İcİcu = 0.003 OK
İsc = 0.007
where dƍ LQ
İscİy = 0.0014
İsc = 0.007
where dƍ PP
İscİy = 0.0014
⎛ε ⎞
ε st1 = ⎜ c ⎟ (14.5 + 1 − 8.0 )
⎝ c⎠
⎛ε ⎞
ε st1 = ⎜ c ⎟ (362.5 + 25 − 200 )
⎝ c⎠
İst1 İy
İst1 İy
Similarly,
İst2 !İy
İst3 !İy
İst4 !İy
İfeCG = 0.0047
Similarly,
İst2 !İy
İst3 !İy
İst4 !İy
İfeCG = 0.0047
Tf = 42.34 kip
Tsw îîîî
= 28.35 kip
Tf = 182.5 kN
Tsw = 125 × 0.00075 × 200,000 + 3 × 125 × 275.8
= 122.175 kN = 122.2 kN
Compute concrete strain at extreme
FRPSUHVVLRQVXUIDFHSHU(T D ⎛
⎞
1
ε c = ε fd ⎜
≤ ε cu
⎝ Lw c − 1⎟⎠
Compute strain in the bar in the
compression zone:
⎛ε ⎞
ε sc = ⎜ c ⎟ (c − d ′ )
⎝ c⎠
Compute strain in the bars in the tension
zone:
Compute strain at centroid of FRP area:
Recompute total tensile force components
at the above determined strain levels:
Recalculate depth of compression block
and depth to neutral axis:
,WHUDWHDVUHTXLUHGWRUHDFKFRQYHUJHQFH
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
95
Table 16.13c (cont.)—Procedure for flexural and shear seismic strengthening of shear walls
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
6WHSE²&DOFXODWHWKHVWUDLQVDQG
IRUFHFRPSRQHQWVLQFRQFUHWH)53DQG
UHLQIRUFLQJVWHHO
a = 6.48 in.
c = 7.63 in.
a = 163 mm
c PP
Force in the bar in the compression zone:
Final value of the depth of the neutral axis is
achieved after iteration.
c = 7.648 in.
a = 6.5 in.
İc İcu
c PP
a = 162.4 mm
İc İcu
İsc İy
İsc İy
Csc îî NLS
Csc = 125 × 0.00066 × 200 = 16.5 kN
Strains and forces in bars in tensile zone:
Strain and force in FRP:
İst1
İst2
İst3
İst4
)URPHTXLOLEULXPFRPSUHVVLYHIRUFHLQ
concrete:
6WHSF²&DOFXODWHWKHPRPHQWFDSDFLW\
RIWKHVHFWLRQ
Compute lever arm for different force
components:
Nominal moment capacity, Mn:
Per Section 10.2.10, include reduction
IDFWRUIRU)53FRQWULEXWLRQȥ İy
!İy
!İy
!İy
İst1
İst2
İst3
İst4
İy
!İy
!İy
!İy
Ts1 = 4.52 kip
Ts2 = Ts3 = Ts4 = 8.0 kip
™Ts = 28.52 kip
Ts1 N1
Ts2 = Ts3 = Ts4 = 34.48 kN
™Ts N1
İfeCG = 0.0047
Tf = 42.37 kip
İfeCG = 0.0047
Tf = 182.5 kN
Cc ™Ts + Tf + Pu + Csc NLS
Cc ™Ts + Tf + Pu + Csc N1
Bar in compression:
d1 = c –1 in. = 7.648 – 1 = 6.65 in.
Bar in compression:
d1 = c – 25 = 166 mm
Concrete compression:
Concrete compression:
a⎞
6.5
⎛
c − ⎟ = 7.648 −
= 4.4 in.
⎝⎜
2⎠
2
a⎞
⎛
c − ⎟ = PP
⎝⎜
2⎠
First bar in tension:
First bar in tension:
LQLQ±c LQ
PPPP±c PP
Second bar in tension: 22.35 in.
Third bar in tension: 36.85 in.
Fourth bar in tension: 51.35 in.
6HFRQGEDULQWHQVLRQPP
7KLUGEDULQWHQVLRQPP
Fourth bar in tension: 1284 mm
FRP:
Lw – c – Wf/2 – 1 in. = 47.35 in.
FRP:
Lw – c – Wf/2 – 25 mm = 1184 mm
Pu:
Lw/2 – c = 22.35 in.
Pu:
Lw/2 – c PP
Mn îîî
× 22.35 + 8 × 36.85 + 8 × 51.35 + 0.85 × 42.37 ×
47.35 + 12 × 22.35 = 272.2 kip-ft
Mn = 353 kN·m
ࢥMn NLSIW!Mu = 260 kip-ft
ࢥMn!Mu ‫׵‬OK
ࢥMn N1āP!Mu = 348 kN·m
ࢥMn!Mu ‫׵‬OK
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96
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table 16.13c (cont.)—Procedure for flexural and shear seismic strengthening of shear walls
3URFHGXUH
&DOFXODWLRQLQLQOEXQLWV
&DOFXODWLRQLQ6,XQLWV
From Step 1, Vn* = 46.4 kip
From Step 1, Vn N1
6WHS²6KHDUVWUHQJWKHQLQJ
3HU(T E Vf is the shear contribution of FRP and is
computed in accordance with Chapter 11.
6WHSD²&DOFXODWHVf
Because the FRP is only on one side of the
ZDOOSHU(T F Since the FRP will be face-bonded to the
wall, the effective FRP strain will be:
İfe țvİfu”
For one layer of the FRP:
Le LQ
k1 =0.731
k2 țv = 0.2
İfe = 0.2 × 0.014 = 0.0028
ffe î NVL
İfe = 0.2 × 0.014 = 0.0028
ffe = 0.0028 × 66.2 = 0.185 GPa
It is assumed that FRP is installed over the full
height of the wall and not in discrete strips.
dfv = 0.8Lw = 48 in.
Vf îîîî NLS
dfv = 0.8Lw = 1200 mm
Vf îîîî N1
5HGXFWLRQIDFWRUIRU)53VKHDUFRQWULEXWLRQȥf = 0.85.
ȥfVf NLS
ȥf Vf = 81.5 kN
6KHDUFDSDFLW\RIWKHUHWUR¿WWHGZDOO
ࢥVn NLS
ࢥVn NLS!Vu = 52 kip
ࢥVn!Vu ‫׵‬OK
Mn = 272.2 kip-ft
ࢥVn N1
ࢥVn N1!Vu = 232 kN
ࢥVn!Vu ‫׵‬OK
Mn = 353 kN·m
6KHDUFRUUHVSRQGLQJWRWKHQRPLQDOÀH[XUDOVWUHQJWK
VM nom = 272.2 kip-ft/10 ft = 27.2 kip
The shear strength of the wall is:
Vn = 65.3 kip
Vn•VM nom ‫׵‬OK
VM nom = 353 kN·m/3 m = 117.1 kN
The shear strength of the wall is:
Vn = 284.6 kN
Vn•VM nom ‫׵‬OK
8VH(T E F G DQG H WRFRPSXWHțv.
Corresponding tensile stress in the FRP:
Per ACI 318-14, Section 11.5.4.2, dfv is
taken as 0.8Lw.
Compute shear capacity of FRP
VWUHQJWKHQHGZDOOXVLQJࢥ 6WHSE²&RPSXWHWKHVKHDU
FRUUHVSRQGLQJWRWKHQRPLQDOÀH[XUDO
VWUHQJWK6HH6HFWLRQ
Note: The FRP for shear strengthening
could be optimized by using horizontal
strips rather than full coverage. For
anchorage of shear FRP see Section
13.6.3.1.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
CHAPTER 17—REFERENCES
&RPPLWWHHGRFXPHQWVDUHOLVWHG¿UVWE\GRFXPHQWQXPEHU
and year of publication followed by authored documents
listed alphabetically.
American Concrete Institute (ACI)
$&, ²&RGH 5HTXLUHPHQWV IRU 'HWHUPLQLQJ
Fire Resistance of Concrete and Masonry Construction
Assemblies
ACI 224.1R-07—Causes, Evaluation, and Repair of
Cracks in Concrete Structures
$&,²%XLOGLQJ&RGH5HTXLUHPHQWVIRU6WUXFWXUDO
Concrete and Commentary
ACI 364.1R-07—Guide for Evaluation of Concrete Structures before Rehabilitation
$&, 5²*XLGH IRU 6HLVPLF 5HKDELOLWDWLRQ RI
Existing Concrete Frame Buildings and Commentary
ACI 437R-03—Strength Evaluation of Existing Concrete
Buildings
ACI 440R-07—Report on Fiber-Reinforced Polymer
)53 5HLQIRUFHPHQWIRU&RQFUHWH6WUXFWXUHV
ACI 440.3R-12—Guide Test Methods for Fiber-ReinIRUFHG 3RO\PHUV )53V IRU 5HLQIRUFLQJ RU 6WUHQJWKHQLQJ
Concrete Structures
ACI 440.7R-10—Guide for the Design and Construction
of Externally Bonded Fiber-Reinforced Polymer Systems
for Strengthening Unreinforced Masonry Structures
$&,²6SHFL¿FDWLRQIRU&DUERQDQG*ODVV)LEHU
5HLQIRUFHG3RO\PHU )53 0DWHULDOV0DGHE\:HW/D\XSIRU
External Strengthening of Concrete and Masonry Structures
$&, ²6WDQGDUG 6SHFL¿FDWLRQ IRU 5HSDLULQJ
&RQFUHWHZLWK(SR[\0RUWDUV 5HDSSURYHGE\
ACI 546R-14—Guide to Concrete Repair
$&,²&RGH5HTXLUHPHQWVIRU(YDOXDWLRQ5HSDLU
and Rehabilitation of Concrete Buildings and Commentary
American National Standards Institute (ANSI)
$16, ==²+D]DUGRXV :RUNSODFH
Chemicals - Hazard Evaluation and Safety Data Sheet and
Precautionary Labeling Preparation
American Society of Civil Engineers (ASCE)
ASCE 7-10—Minimum Design Loads for Buildings and
Other Structures
$6&(6(,²6HLVPLF5HKDELOLWDWLRQDQG5HWUR¿WRI
Existing Buildings
ASTM International
ASTM C1583/C1583M-13—Standard Test Method for
Tensile Strength of Concrete Surfaces and the Bond Strength
or Tensile Strength of Concrete Repair and Overlay MateULDOVE\'LUHFW7HQVLRQ 3XOORII0HWKRG
$670 '²7HVW 0HWKRG IRU 'HÀHFWLRQ 7HPSHUDture of Plastics Under Flexural Load in the Edgewise Position
$670 '²6WDQGDUG 7HVW 0HWKRG IRU &RHI¿FLHQW
of Linear Thermal Expansion of Plastics Between –30°C
and 30°C with a Vitreous Silica Dilatometer
97
$670 '²6WDQGDUG 7HVW 0HWKRGV IRU )OH[XUDO
Properties of Unreinforced and Reinforced Plastics and
Electrical Insulating Materials
ASTM D2240-15—Standard Test Method for Rubber
Property—Durometer Hardness
$670 ' ²6WDQGDUG 3UDFWLFH IRU )XVLRQ
RI3RO\ 9LQ\O&KORULGH 39& &RPSRXQGV8VLQJD7RUTXH
Rheometer
ASTM D2584-11—Standard Test Method for Ignition
Loss of Cured Reinforced Resins
$670 '²6WDQGDUG 7HVW 0HWKRGV IRU 7HQVLOH
Compressive, and Flexural Creep and Creep-Rupture of
Plastics
$670 ''0²6WDQGDUG 7HVW 0HWKRG IRU
Tensile Properties of Polymer Matrix Composite Materials
ASTM D3171-15—Standard Test Methods for Constituent Content of Composite Materials
ASTM D3418-15—Standard Test Method for Transition
Temperatures and Enthalpies of Fusion and Crystallization
of Polymers by Differential Scanning Calorimetry
$670 ''0²6WDQGDUG 7HVW 0HWKRG IRU
Tension-Tension Fatigue of Polymer Matrix Composite
Materials
ASTM D4476/D4476M-14—Standard Test Method for
Flexural Properties of Fiber Reinforced Pultruded Plastic
Rods
$670''0 ²6WDQGDUG7HVW0HWKRG
for Tensile Properties of Fiber Reinforced Polymer Matrix
Composite Bars
ASTM D7337/D7337M-12—Standard Test Method for
Tensile Creep Rupture of Fiber Reinforced Polymer Matrix
Composite Bars
ASTM D7522/D7522M-15—Standard Test Method for
Pull-Off Strength for FRP Bonded to Concrete Substrate
$670''0 ²6WDQGDUG7HVW0HWKRG
for Determining Tensile Properties of Fiber Reinforced
Polymer Matrix Composites Used for Strengthening of Civil
Structures
ASTM D7616/D7616M-11—Standard Test Method for
Determining Apparent Overlap Splice Shear Strength Properties of Wet Lay-Up Fiber-Reinforced Polymer Matrix
Composites Used for Strengthening Civil Structures
ASTM D7617/D7617M-11—Standard Test Method for
Transverse Shear Strength of Fiber-Reinforced Polymer
Matrix Composite Bars
ASTM E84-16—Standard Test Method for Surface
Burning Characteristics of Building Materials
ASTM E328-13—Standared Test Methods for Stress
Relaxation Tests for Materials and Structures
ASTM E831-14—Standard Test Method for Linear
Thermal Expansion of Solid Materials by Thermomechanical Analysis
$670 ( ²6WDQGDUG 7HVW 0HWKRG IRU
Assignment of the Glass Transition Temperatures by Differential Scanning Calorimetry
ASTM E1640-13—Standard Test Method for Assignment
of the Glass Transition Temperature by Dynamic Mechanical Analysis
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98
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
$670(²7HVW0HWKRGIRU'LVWRUWLRQ7HPSHUDture in Three-Point Bending by Thermomechanical Analysis
Code of Federal Regulations (CFR)
CFR 16 Part 1500-2015—Hazardous Substances and ArtiFOHV$GPLQLVWUDWLRQDQG(QIRUFHPHQW5HJXODWLRQV
&)5²7UDQVSRUWDWLRQ
International Code Council (ICC)
,&& $& ²$FFHSWDQFH &ULWHULD IRU &RQFUHWH
and Reinforced and Unreinforced Masonry Strengthening
8VLQJ([WHUQDOO\%RQGHG)LEHU5HLQIRUFHG3RO\PHU )53 Composite Systems
International Concrete Repair Institute (ICRI)
,&5,5²*XLGHIRU8VLQJ,Q6LWX7HQVLOH3XOO
Off Tests to Evaluate Bond of Concrete Surface Materials
ICRI 310.2R-2013—Selecting and Specifying Concrete
Surface Preparation for Sealers, Coatings, Polymer Overlays, and Concrete Repair
Authored documents
$$6+72³/5)'%ULGJH'HVLJQ6SHFL¿FDWLRQV´
third edition, American Association of State Highway and
7UDQVSRUWDWLRQ2I¿FLDOV:DVKLQJWRQ'&
$LHOOR0$*DODWL1DQG7HJROD/$³%RQG
Analysis of Curved Structural Concrete Elements Strengthened using FRP Materials,” Fifth International Symposium
on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-5), Cambridge-Thomas Telford, London,
pp. 680-688.
$QWRQRSRXORV & 3 DQG 7ULDQWD¿OORX 7 & “Analysis of FRP-Strengthened RC Beam-Column Joints,”
Journal of Composites for Construction, V. 6, No. 1, pp.
41-51. doi: $6&( $SLFHOOD)DQG,PEURJQR0³)LUH3HUIRUPDQFH
of CFRP-Composites Used for Repairing and Strengthening
Concrete,” Proceedings of the 5th ASCE Materials Engineering Congress, Cincinnati, OH, pp. 260-266.
$UGXLQL 0 DQG 1DQQL $ ³%HKDYLRU RI 3UH
Cracked RC Beams Strengthened with Carbon FRP Sheets,”
Journal of Composites for Construction, V. 1, No. 2, pp.
63-70. doi: $6&( %DOVDPR$0DQIUHGL*0ROD(1HJUR3DQG3URWD
A., 2005, “Seismic Rehabilitation of a Full-Scale RC Structure using GFRP Laminates,” 7th International Symposium
on Fiber-Reinforced (FRP) Polymer Reinforcement for
Concrete Structures, SP-230, C. K. Shield, J. P. Busel, S. L.
Walkup, and D. D. Gremel, eds., American Concrete Institute, Farmington Hills, MI, pp. 1325-1344.
Bank, L. C., 2006, Composites for Construction: Structural Design with FRP Materials, John Wiley & Sons,
Hoboken, NJ, 560 pp.
%HODUEL$%DH6$\RX$.XFKPD'0LUPLUDQ$
and Okeil, A., 2011, “Design of FRP Systems for Strengthening Concrete Girders in Shear,” NCHRP Report 678,
National Cooperative Highway Research Program, 130 pp.
%LDQFR 9 0RQWL * DQG %DUURV - $ 2 “Design Formula to Evaluate the NSM FRP Strips Shear
Strength Contribution to a RC Beam,” Composites.
Part B, Engineering 9 SS GRL 10.1016/j.
FRPSRVLWHVE
Binici, B., and Ozcebe, G., 2006, “Seismic Evaluation
RI ,Q¿OOHG 5HLQIRUFHG &RQFUHWH )UDPHV 6WUHQJWKHQHG ZLWK
FRPS,” Proceedings of the 8th U.S. National Conference on
Earthquake Engineering(DUWKTXDNH(QJLQHHULQJ5HVHDUFK
Center, San Francisco, CA, 10 pp.
%LVE\/$*UHHQ0)DQG.RGXU9.5D
³)LUH (QGXUDQFH RI )LEHU5HLQIRUFHG 3RO\PHU&RQ¿QHG
Concrete Columns,” ACI Structural Journal, V. 102, No. 6,
1RY'HFSS
%LVE\/$*UHHQ0)DQG.RGXU9.5E
“Response to Fire of Concrete Structures that Incorporate
FRP,” Progress in Structural Engineering and Materials, V.
1RSSGRLSVH
%RXVLDV67ULDQWD¿OORX7)DUGLV06SDWKLV/DQG
2¶5HJDQ % ³)LEHU5HLQIRUFHG 3RO\PHU 5HWUR¿Wting of Rectangular Reinforced Concrete Columns with or
without Corrosion,” ACI Structural Journal, V. 101, No. 4,
July-Aug., pp. 512-520.
Bousselham, A., and Chaallal, O., 2006, “Behavior of
Reinforced Concrete T-Beams Strengthened in Shear with
Carbon Fiber-Reinforced Polymer—An Experimental
Study,” ACI Structural Journal, V. 103, No. 3, May-June,
SS
%UDFFL-00DQGHU-%DQG5HLQKRUQ$0D
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
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$6&( 'H /RUHQ]LV / /XQGJUHQ . DQG 5L]]R $ “Anchorage Length of Near-Surface-Mounted FRP Bars for
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
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Structures (FRPRCS-3), V. 1, Japan Concrete Institute,
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
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External FRP Reinforcement,” Concrete International, V.
1R-XQHSS
1DQQL$ %DNLV & ( %RRWKE\ 7 ( /HH< - DQG
)ULJR(/³7HQVLOH5HLQIRUFHPHQWE\)536KHHWV
Applied to RC,” 9C/1-8, ICE 97 International Composites
Exposition1DVKYLOOH71-DQSS&WR
1DSRODQR / 0HQQD & $VSURQH ' 3URWD $ DQG
Manfredi, G., 2015, “LCA-Based Study on Structural
5HWUR¿W2SWLRQVIRU0DVRQU\%XLOGLQJV´The International
Journal of Life Cycle Assessment, V. 20, No. 1, pp. 23-35.
doi: 10.1007/s11367-014-0807-1
1DWLRQDO5HVHDUFK&RXQFLO³/LIH3UHGLFWLRQ0HWKodologies for Composite Materials,” Committee on Life
Prediction Methodologies for Composites, NMAB-460,
National Materials Advisory Board, Washington, DC, 75 pp.
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and Flexural Strengthening of R/C Beams with Carbon Fiber
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Concrete Columns using Carbon Fiber,” MS thesis, UniverVLW\RI:DVKLQJWRQ6HDWWOH:$SS
Nowak, A. S., and Szerszen, M. M., 2003, “Calibration
RI'HVLJQ&RGHIRU%XLOGLQJV $&, 3DUW²6WDWLVWLFDO
Models for Resistance,” ACI Structural Journal, V. 100, No.
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2GDJLUL70DWVXPRWR.DQG1DNDL+³)DWLJXH
and Relaxation Characteristics of Continuous Aramid Fiber
Reinforced Plastic Rods,” Third International Symposium
on Non-Metallic (FRP) Reinforcement for Concrete Structures (FRPRCS-3), V. 2, Japan Concrete Institute, Tokyo,
Japan, pp. 227-234.
2NHLO $ 0 %LQJRO < DQG $ONKUGDML 7 “Analyzing Model Uncertainties for Concrete Beams Flexurally Strengthened with FRP Laminates,” Proceedings of
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:DVKLQJWRQ'&SS &'520
2UWRQ6/-LUVD-2DQG%D\UDN2³'HVLJQ
Considerations of Carbon Fiber Anchors,” Journal of
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$6&( 2UWRQ 6 / -LUVD - 2 DQG %D\UDN 2 ³&)53
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Collapse,” ACI Structural Journal, V. 106, No. 5, Sept.-Oct.,
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3DOPLHUL $ 0DWWK\V 6 DQG 7DHUZH / ³)LUH
Testing of RC Beams Strengthened with NSM Reinforcement,” 10th International Symposium on Fiber-Reinforced
Polymer Reinforcement for Concrete Structures (FRPRCS-
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
10), SP-275, American Concrete Institute, Farmington Hills,
0, &'520
3DPSDQLQ 6 %RORJQLQL ' DQG 3DYHVH $ ³3HUIRUPDQFH%DVHG6HLVPLF5HWUR¿W6WUDWHJ\IRU([LVWLQJ
Reinforced Concrete Frame Systems Using Fiber-Reinforced Polymer Composites,” Journal of Composites for
Construction, V. 11, No. 2, pp. 211-226. doi: 10.1061/
$6&( 3DQWHOLGHV & 3 *HUJHO\ - 5HDYHOH\ / ' DQG
9ROQ\\ 9 $ ³5HWUR¿W RI 5& %ULGJH 3LHU ZLWK
CFRP Advanced Composites,” Journal of Structural Engineering 9 1R SS GRL 10.1061/
$6&( 3DQWHOLGHV & 3 &O\GH & DQG 5HDYHOH\ / ' “Rehabilitation of R/C Building Joints with FRP Composites,” 12th World Conference on Earthquake Engineering,
$XFNODQG1HZ=HDODQG &'520
3DQWHOLGHV&3$ODPHGGLQH)6DUGR7DQG,PEVHQ
5³6HLVPLF5HWUR¿WRI6WDWH6WUHHW%ULGJHRQ,QWHUstate 80,” Journal of Bridge Engineering9 1R SS
333-342. doi: $6&( 3DQWHOLGHV&32NDKDVKL<DQG5HDYHOH\/'
“Seismic Rehabilitation of Reinforced Concrete Frame Interior Beam-Bolumn Joints with FRP Composites,” Journal of
Composites for Construction, V. 12, No. 4, pp. 435-445. doi:
$6&( 3DUN5DQG3DXOD\7Reinforced Concrete Structures, Wiley, 800 pp.
3DWHUVRQ-DQG0LWFKHOO'³6HLVPLF5HWUR¿WRI
Shear Walls with Headed Bars and Carbon Fiber Wrap,”
Journal of Structural Engineering 9 1R SS
606-614. doi: $6&( Prestressed/Precast Concrete Institute, 2004, PCI Design
Handbook Precast and Prestressed Concrete, sixth edition,
Prestressed/Precast Concrete Institute, Chicago, IL, 750 pp.
Pellegrino, C., and Modena, C., 2002, “Fiber Reinforced
Polymer Shear Strengthening of Reinforced Concrete Beams
with Transverse Steel Reinforcement,” Journal of Composites for Construction, V. 6, No. 2, pp. 104-111. doi: 10.1061/
$6&( 3HVVLNL 6 3 &RQOH\ & + *HUJHO\ 3 DQG:KLWH 5
1³6HLVPLF%HKDYLRURI/LJKWO\5HLQIRUFHG&RQFUHWH
Column and Beam-Column Joint Details,” NCEER Report
1RSS
3HVVLNL 6 +DUULHV . $ .HVWQHU - 6DXVH 5 DQG
Ricles, J. M., 2001, “The Axial Behavior of Concrete
&RQ¿QHG ZLWK )53 -DFNHWV´ Journal of Composites for
Construction, V. 5, No. 4, pp. 237-245. doi: 10.1061/
$6&( 3RUWHU0/0HKXV-<RXQJ.$2¶1HLO()DQG
%DUQHV % $ ³$JLQJ IRU )LEHU 5HLQIRUFHPHQW LQ
Concrete,” Proceedings of the Third International Symposium on Non-Metallic (FRP) Reinforcement for Concrete
Structures, Japan Concrete Institute, Sapporo, Japan.
3ULHVWOH\ 0 6HLEOH ) DQG &DOYL * Seismic
'HVLJQDQG5HWUR¿WRI%ULGJHV, John Wiley and Sons, New
York, 704 pp.
103
3URWD $ 1DQQL $ 0DQIUHGL * DQG &RVHQ]D (
2004, “Selective Upgrade of Underdesigned Reinforced
Concrete Beam-Column Joints Using Carbon Fiber-Reinforced Polymers,” ACI Structural Journal, V. 101, No. 5,
6HSW2FWSS
5HHG&(3HWHUPDQ5-DQG5DVKHHG+$
“Evaluating FRP Repair Method for Cracked Prestressed
Concrete Bridge Members Subjected to Repeated Loadings
3KDVH ´KTRAN Report No. K-TRAN: KSU-01-2, Kansas
Department of Transportation, Topeka, KS, 106 pp.
5LWFKLH37KRPDV'/X/DQG&RQQHOH\*
“External Reinforcement of Concrete Beams Using Fiber
Reinforced Plastics,” ACI Structural Journal, V. 88, No. 4,
-XO\$XJSS
5REHUWV 7 0 DQG +DML.D]HPL + ³7KHRUHWical Study of the Behavior of Reinforced Concrete Beams
Strengthened by Externally Bonded Steel Plates,” Proceedings of the Institute of Civil Engineers, Part 2, V. 87, No.
SS
5RFFD6*DODWL1DQG1DQQL$³([SHULPHQWDO
Evaluation of FRP Strengthening of Large-Size Reinforced
Concrete Columns,” Report No. UTC-142, University of
Missouri-Rolla, MO.
5RFFD 6 *DODWL 1 DQG 1DQQL$ ³5HYLHZ RI
'HVLJQ *XLGHOLQHV IRU )53 &RQ¿QHPHQW RI 5HLQIRUFHG
Concrete Columns of Noncircular Cross Sections,” Journal
of Composites for Construction, V. 12, No. 1, Jan.-Feb., pp.
GRL $6&( Rosenboom, O. A., and Rizkalla, S. H., 2006, “Behavior
of Prestressed Concrete Strengthened with Various CFRP
Systems Subjected to Fatigue Loading,” Journal of Composites for Construction91R1RY'HFSS
doi: $6&( 5RVWDV\)6³%RQGLQJRI6WHHODQG*)533ODWHV
in the Area of Coupling Joints. Talbrucke Kattenbusch,”
Research Report1R)HGHUDO,QVWLWXWHIRU0DWHULDOV7HVWLQJ%UDXQVFKZHLJ*HUPDQ\ LQ*HUPDQ
5RVWDV\ ) 6 ³2Q 'XUDELOLW\ RI )53 LQ$JJUHVsive Environments,” Third International Symposium on
Non-Metallic (FRP) Reinforcement for Concrete Structures
)535&6 9-DSDQ&RQFUHWH,QVWLWXWH7RN\R-DSDQ
pp. 107-114.
5R\ODQFH0DQG5R\ODQFH2³(IIHFWRI0RLVWXUH
on the Fatigue Resistance of an Aramid-Epoxy Composite,”
Organic Coatings and Plastics Chemistry, V. 45, American
Chemical Society, Washington, DC, pp. 784-788.
6DDGDWPDQHVK + (KVDQL 0 5 DQG -LQ / “Seismic Strengthening of Circular Bridge Pier Models with
Fiber Composites,” ACI Structural Journal 9 1R 1RY'HFSS
6DEQLV*06KURII$&DQG.DKQ/)HGV
“Seismic Rehabilitation of Concrete Structures,” SP-160,
American Concrete Institute, Farmington Hills, MI, 318 pp.
6DWR < 8HGD 7 .DNXWD < DQG 7DQDND 7 “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.,
pp. 621-627.
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104
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
6DXVH 5 +DUULHV . $ :DONXS 6 / 3HVVLNL 6
and Ricles, J. M., 2004, “Flexural Behavior of Concrete
Columns with Carbon Fiber Composite Jackets,” ACI Structural Journal, V. 101, No. 5, Sept.-Oct., pp. 708-716.
6HLEOH ) 3ULHVWOH\ 0 - 1 +HJHPLHU * $ DQG
,QQDPRUDWR ' ³6HLVPLF 5HWUR¿W RI 5& &ROXPQV
with Continuous Carbon Fiber Jackets,” Journal of Composites for Construction, V. 1, No. 2, pp. 52-62. doi: 10.1061/
$6&( 6H]HQ+:KLWWDNHU$6(OZRRG.-DQG0RVDODP
K. M., 2003, “Performance of Reinforced Concrete BuildLQJV GXULQJ WKH $XJXVW .RFDHOL 7XUNH\ (DUWKTXDNH DQG 6HLVPLF 'HVLJQ DQG &RQVWUXFWLRQ 3UDFWLFH LQ
Turkey,” Journal of Engineering Structures, V. 25, No. 1,
pp. 103-114. doi: 6 6KDUDI 0 + 6RXGNL . $ DQG 9DQ 'XVHQ 0
2006, “CFRP Strengthening for Punching Shear of Interior Slab-Column Connections,” Journal of Composites
for Construction, V. 10, No. 5, pp. 410-418. doi: 10.1061/
$6&( 6KDULI $ $O6XODLPDQL * %DVXQEXO , %DOXFK 0
DQG *KDOHE % ³6WUHQJWKHQLQJ RI ,QLWLDOO\ /RDGHG
Reinforced Concrete Beams Using FRP Plates,” ACI Structural Journal91R0DU$SUSS
Sheikh, S., and Yau, G., 2002, “Seismic Behavior of
&RQFUHWH &ROXPQV &RQ¿QHG ZLWK 6WHHO DQG )LEHU5HLQforced Polymers,” ACI Structural Journal 9 1R Jan.-Feb., pp. 72-80.
Silva, P. F., and Ibell, T. J., 2008, “Evaluation of Moment
Redistribution in Continuous FRP-Strengthened Concrete
Structures,” ACI Structural Journal, V. 105, No. 6, Nov.'HFSS
6LOYD3)(UHFNVRQ1-DQG&KHQ*³6HLVPLF
5HWUR¿W RI %ULGJH -RLQWV LQ WKH &HQWUDO 86 ZLWK &)53
Composites,” ACI Structural Journal, V. 104, No. 2, Mar.Apr., pp. 207-217.
6RXGNL . $ DQG *UHHQ 0 ) ³)UHH]H7KDZ
Response of CFRP Wrapped Concrete,” Concrete International91R$XJSS
6SRHOVWUD 0 5 DQG 0RQWL * ³)53
&RQ¿QHG &RQFUHWH 0RGHO´ Journal of Composites for
Construction, V. 3, No. 3, pp. 143-150. doi: 10.1061/
$6&( Suppliers of Advanced Composite Materials AssociaWLRQSACMA Recommended Methods (SRM) Manual,
Suppliers of Advanced Composite Materials Association,
Arlington, VA.
Szerszen, M. M., and Nowak, A. S., 2003, “Calibration of
'HVLJQ &RGH IRU %XLOGLQJV $&, 3DUW ²5HOLDELOLW\
Analysis and Resistance Factors,” ACI Structural Journal,
91R0D\-XQHSS
7HQJ-*&KHQ-)6PLWK67DQG/DP/
FRP Strengthened RC Structures, John Wiley & Sons, West
Sussex, UK, 266 pp.
7HQJ-*6PLWK67<DR-DQG&KHQ-)
“Intermediate Crack Induced Debonding in RC Beams and
Slabs,” Construction & Building Materials, V. 17, No. 6-7,
pp. 447-462. doi: 6 7HQJ - * /X ; =<H / 3 DQG -LDQJ - - “Recent Research on Intermediate Crack Induced Debonding
in FRP Strengthened Beams,” Proceedings of the 4th International Conference on Advanced Composite Materials for
Bridges and Structures, Calgary, AB, Canada.
7RXWDQML + ³6WUHVV6WUDLQ &KDUDFWHULVWLFV RI
&RQFUHWH &ROXPQV ([WHUQDOO\ &RQ¿QHG ZLWK $GYDQFHG
Fiber Composite Sheets,” ACI Materials Journal91R
0D\-XQHSS
7ULDQWD¿OORX7&³6KHDU6WUHQJWKHQLQJRI5HLQIRUFHG
Concrete Beams Using Epoxy-Bonded FRP Composites,” ACI
Structural Journal91R0DU$SUSS
:DOODFH - : ³6HLVPLF 'HVLJQ RI 5& 6WUXFWXUDO :DOOV 3DUW , 1HZ &RGH )RUPDW´ Journal of Structural Engineering, V. 121, No. 1, pp. 75-87. doi: 10.1061/
$6&( :DQJ1DQG(YDQV-7³&ROODSVHRI&RQWLQXRXV
Fiber Composite Beam at Elevated Temperatures,” Composites,
V. 26, No. 1, pp. 56-61. doi: 3Wang, Y. C., and Restrepo, J. I., 2001, “Investigation
of Concentrically Loaded Reinforced Concrete Columns
&RQ¿QHG ZLWK *ODVV )LEHU5HLQIRUFHG 3RO\PHU -DFNHWV´
ACI Structural Journal91R0D\-XQHSS
:LOOLDPV%.%LVE\/$.RGXU9.5*UHHQ0
)DQG&KRZGKXU\(³)LUH,QVXODWLRQ6FKHPHVIRU
FRP-Strengthened Concrete Slabs,” Composites. Part A,
Applied Science and Manufacturing, V. 37, No. 8, pp. 11511160. doi: 10.1016/j.compositesa.2005.05.028
:ROI 5 DQG 0LHVVOHU + - ³+/96SDQQJOLHGHU
in der Praxis,” Erfahrungen Mit Glasfaserverbundstaben
Beton, V. 2, pp. 47-51.
:X : ³7KHUPRPHFKDQLFDO 3URSHUWLHV RI )LEHU
5HLQIRUFHG 3ODVWLFV )53 %DUV´ 3K' GLVVHUWDWLRQ :HVW
9LUJLQLD8QLYHUVLW\0RUJDQWRZQ:9SS
Xian, G., and Karbhari, V. M., 2007, “Segmental Relaxation of Water-Aged Ambient Cured Epoxy,” Journal of
Polymer Degradation and Stability91RSS
GRL10.1016/j.polymdegradstab.2007.06.015
<DPDJXFKL 7 .DWR < 1LVKLPXUD 7 DQG 8RPRWR
7 ³&UHHS 5XSWXUH RI )53 5RGV 0DGH RI $UDPLG
Carbon and Glass Fibers,” Third International Symposium
on Non-Metallic (FRP) Reinforcement for Concrete Structures )535&6 9 -DSDQ &RQFUHWH ,QVWLWXWH 7RN\R
-DSDQSS
Youssef, M. N., 2003, “Stress Strain Model for Concrete
&RQ¿QHGE\)53&RPSRVLWHV´3K'GLVVHUWDWLRQ8QLYHUVLW\
of California-Irvine, Irvine, CA, 310 pp.
=KDQJ&/LQ:;$EXGXGGLQ0DQG&DQQLQJ/
2012, “Environmental Evaluation of FRP in UK Highway
Bridge Deck Replacement Applications Based on a Comparative LCA Study,” Advanced Materials Research, V. 374,
pp. 43-48.
=XUHLFN$+(OOLQJZRRG%51RZDN$60HUW]
'5DQG7ULDQWD¿OORX7&³5HFRPPHQGHG*XLGH
6SHFL¿FDWLRQ IRU WKH 'HVLJQ RI ([WHUQDOO\ %RQGHG )53
Systems for Repair and Strengthening of Concrete Bridge
Elements,” 1&+53 5HSRUW , Transportation Research
%RDUG:DVKLQJWRQ'&SS
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
105
EDUVZLWK¿EHUYROXPHVRIDSSUR[LPDWHO\WRSHUFHQW
3URSHUWLHVDUHEDVHGRQJURVVODPLQDWHDUHD Table A.3 presents ranges of tensile properties for CFRP,
*)53DQG$)53ODPLQDWHVZLWK¿EHUYROXPHVRIDSSUR[Lmately 40 to 60 percent. Properties are based on grossODPLQDWHDUHD 7KHSURSHUWLHVDUHVKRZQIRUXQLGLUHFtional, bidirectional, and +45/–45-degree fabrics. Table A.3
DOVRVKRZVWKHHIIHFWRIYDU\LQJWKH¿EHURULHQWDWLRQRQWKH
0-degree strength of the laminate.
Table A.4 gives the tensile strengths of some commercially available FRP systems. The strength of unidirectional
ODPLQDWHVLVGHSHQGHQWRQ¿EHUW\SHDQGGU\IDEULFZHLJKW
These tables are not intended to provide ultimate strength
values for design purposes.
APPENDIX A—MATERIAL PROPERTIES OF
CARBON, GLASS, AND ARAMID FIBERS
Table A.1 presents ranges of values for the tensile properWLHVRIFDUERQJODVVDQGDUDPLG¿EHUV7KHWDEXODWHGYDOXHV
DUHEDVHGRQWKHWHVWLQJRILPSUHJQDWHG¿EHU\DUQVRUVWUDQGV
in accordance with suppliers of SACMA Recommended
0HWKRG5 Suppliers of Advanced Composite MateULDOV$VVRFLDWLRQ 7KHVWUDQGVRU¿EHU\DUQVDUHLPSUHJnated with resin, cured, and then tested in tension. The tabuODWHGSURSHUWLHVDUHFDOFXODWHGXVLQJWKHDUHDRIWKH¿EHUVWKH
resin area is ignored. Hence, the properties listed in Table A.1
are representative of unidirectional FRP systems whose propHUWLHVDUHUHSRUWHGXVLQJQHW¿EHUDUHD 4.3.1 Table A.2 presents ranges of tensile properties for carbon
)53 &)53 JODVV)53 *)53 DQGDUDPLG)53 $)53 Table A.1—Typical tensile properties of fibers used in FRP systems
Elastic modulus
Fiber type
3
10 ksi
Ultimate strength
GPa
ksi
MPa
Rupture strain, minimum, %
300 to 550
WR
1.2
Carbon
General purpose
32 to 34
220 to 240
High-strength
32 to 34
220 to 240
550 to 700
WR
1.4
Ultra-high-strength
32 to 34
220 to 240
WR
4820 to 6200
1.5
High-modulus
50 to 75
340 to 520
250 to 450
1720 to 3100
0.5
Ultra-high-modulus
75 to 100
WR
200 to 350
1380 to 2400
0.2
E-glass
10 to 10.5
WR
WR
1860 to 2680
4.5
S-glass
12.5 to 13
WR
500 to 700
3440 to 4140
5.4
Glass
Aramid
General purpose
10 to 12
WR
500 to 600
3440 to 4140
2.5
High-performance
16 to 18
110 to 124
500 to 600
3440 to 4140
1.6
Table A.2—Tensile properties of FRP bars with fiber volumes of 50 to 70 percent
FRP system description
Elastic modulus,
103NVL *3D
8OWLPDWHWHQVLOHVWUHQJWKNVL 03D
Rupture strain, %
High-strength carbon/epoxy
WR WR
WR WR
1.2 to 1.8
E-glass/epoxy
WR WR
WR WR
1.6 to 3.0
High-performance aramid
WR WR
WR WR
2.0 to 3.0
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106
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Table A.3—Tensile properties of FRP laminates with fiber volumes of 40 to 60 percent
Elastic modulus
FRP system description
¿EHURULHQWDWLRQ
Property at 0 degrees 3URSHUW\DWGHJUHHV
103NVL *3D
Ultimate tensile strength
Property at 0 degrees
3URSHUW\DWGHJUHHV
103NVL *3D
NVL 03D
NVL 03D
Rupture strain
at 0 degrees, %
High-strength carbon/epoxy,
degrees
0
WR WR
WR WR
WR WR
WR WR
1.0 to 1.5
WR WR
WR WR
WR WR
WR WR
1.0 to 1.5
+45/–45
WR WR
WR WR
WR WR
WR WR
1.5 to 2.5
WR WR
WR WR
WR WR
WR WR
1.5 to 3.0
E-glass/epoxy, degrees
0
WR WR
WR WR
WR WR
WR WR
2.0 to 3.0
+45/–45
WR WR
WR WR
WR WR
WR WR
2.5 to 3.5
High-performance aramid/epoxy,
degrees
0
WR WR
WR WR
WR WR
WR WR
2.0 to 3.0
WR WR
WR WR
WR WR
WR WR
2.0 to 3.0
+45/–45
WR WR
WR WR
WR WR
WR WR
2.0 to 3.0
Notes:
)53FRPSRVLWHSURSHUWLHVDUHEDVHGRQ)53V\VWHPVKDYLQJDQDSSUR[LPDWH¿EHUYROXPHRISHUFHQWDQGDFRPSRVLWHWKLFNQHVVRILQ PP ,QJHQHUDO)53EDUVKDYH
¿EHUYROXPHVRIWRSHUFHQWSUHFXUHGV\VWHPVKDYH¿EHUYROXPHVRIWRSHUFHQWDQGZHWOD\XSV\VWHPVKDYH¿EHUYROXPHVRIWRSHUFHQW%HFDXVHWKH¿EHUYROXPH
LQÀXHQFHVWKHJURVVODPLQDWHSURSHUWLHVSUHFXUHGODPLQDWHVXVXDOO\KDYHKLJKHUPHFKDQLFDOSURSHUWLHVWKDQODPLQDWHVFUHDWHGXVLQJWKHZHWOD\XSWHFKQLTXH
=HURGHJUHHVUHSUHVHQWVXQLGLUHFWLRQDO¿EHURULHQWDWLRQ
=HURGHJUHHV RU±GHJUHHV UHSUHVHQWV¿EHUEDODQFHGLQWZRRUWKRJRQDOGLUHFWLRQVZKHUHGHJUHHVLVWKHGLUHFWLRQRIORDGLQJDQGGHJUHHVLVQRUPDOWRWKHGLUHFWLRQ
of loading.
Tension is applied to 0-degree direction. All FRP bar properties are in the 0-degree direction.
Table A.4—Ultimate tensile strength* of some commercially available FRP systems
Ultimate strength†
Fabric weight
)53V\VWHPGHVFULSWLRQ ¿EHUW\SHVDWXUDWLQJUHVLQIDEULFW\SH
General purpose carbon/resin unidirectional sheet
High-strength carbon/resin unidirectional sheet
High-modulus carbon/resin unidirectional sheet
General-purpose carbon/resin balanced sheet
3
oz/yd
3
g/m
lb/in.
kN/mm
6
200
2600
500
12
400
3550
620
7
230
1800
320
300
4000
700
18
620
5500
300
3400
600
300
1000
180
27
4100
720
10
350
1300
230
E-glass/balanced fabric
300
680
120
Aramid/resin unidirectional sheet
12
420
4000
700
E-glass/resin unidirectional sheet
‡
‡
High-strength carbon/resin precured, unidirectional laminate
70
2380
3300
E-glass/vinyl ester precured, unidirectional shell
50‡
1700‡
1580
*Values shown should not be used for design.
†
Ultimate tensile strength per unit width of sheet or fabric.
‡
Precured laminate weight.
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
APPENDIX B—SUMMARY OF STANDARD TEST
METHODS
Table B provides a summary of test methods for the shortand long-term mechanical and durability testing of FRP
rods and sheets. The recommended test methods are based
on the knowledge gained from research results and literature worldwide and include those methods described in ACI
440.3R that have not yet been adopted by ASTM.
107
Durability-related tests use the same test methods but
UHTXLUH DSSOLFDWLRQVSHFL¿F SUHFRQGLWLRQLQJ RI VSHFLPHQV
Acceptance of the data generated by the listed test methods
FDQEHWKHEDVLVIRU)53PDWHULDOV\VWHPTXDOL¿FDWLRQDQG
DFFHSWDQFH IRUH[DPSOHACI 440.8 Table B—Test methods for FRP material systems
Property
$670WHVWPHWKRG V
ACI 440.3R test
method
Summary of differences
Test methods for sheets, prepreg, and laminates
D2538
Surface hardness
D2240
—
No ACI methods developed
D3418
&RHI¿FLHQWRIWKHUPDO
expansion
'
—
No ACI methods developed
Glass-transition temperature
E1640
—
No ACI methods developed
—
No ACI methods developed
Volume fraction
D3171
D2584
Sheet to concrete adhesion
GLUHFWWHQVLRQSXOORII
D7522/D7522M
L.1*
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found in the ASTM method
Tensile strength and modulus
''0RU
D7565/D7565M, as
appropriate
L.2*
ACI method provides methods for calculating tensile strength and
PRGXOXVRQJURVVFURVVVHFWLRQDODQGHIIHFWLYH¿EHUDUHDEDVLV6HFWLRQ
3.3.1 is used to calculate design values.
Lap shear strength
D7616/D7616M
L.3*
$&,PHWKRGSURYLGHVVSHFL¿FUHTXLUHPHQWVIRUVSHFLPHQSUHSDUDWLRQ
Test methods for FRP bars
Cross-sectional area
D7205/D7207M
B.1*
Two options for bar area are provided in ASTM D7205/D7205M
QRPLQDODQGDFWXDO ZKHUHDVRQO\QRPLQDODUHDLVXVHGLQ$&,5
Method B.1
Longitudinal tensile strength
and modulus
D7205/D7205M
B.2*
Strain limits for calculation of modulus are different in the two methods.
D7617/D7617M
*
The ACI method focuses on dowel action of bars and does not overlap
with existing ASTM methods that focus mainly on beam shearing failure
PRGHV%DUVKHDUVWUHQJWKLVRIVSHFL¿FFRQFHUQIRUDSSOLFDWLRQVZKHUH
FRP rods are used to cross construction joints in concrete pavements.
Shear strength
B.4
Durability properties
—
B.6
Fatigue properties
''0
B.7
Creep properties
D7337/D7337M
B.8*
Relaxation properties
Flexural tensile properties
Flexural properties
&RHI¿FLHQWRIWKHUPDO
expansion
'
E328
—
'
D4476/D4476M
E831
'
No existing ASTM test methods available.
%
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$&,PHWKRGVDOVRUHTXLUHVSHFL¿FFDOFXODWLRQVWKDWDUHQRWSURYLGHGLQWKH
ASTM methods.
B.11
No existing ASTM test methods available.
—
No ACI methods developed.
—
No ACI methods developed.
—
No ACI methods developed.
—
No ACI methods developed.
E1356
Glass-transition temperature
E1640
D648
(
Volume fraction
D3171
*
Test method in ACI 440.3R is replaced by reference to appropriate ASTM method.
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108
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
APPENDIX C—AREAS OF FUTURE RESEARCH
Future research is needed to provide information in areas
that are still unclear or are in need of additional evidence
to validate performance. The list of topics presented in this
appendix provides a summary.
D 0DWHULDOV
L0HWKRGVRI¿UHSURR¿QJ)53VWUHQJWKHQLQJV\VWHPV
ii. Behavior of FRP-strengthened members under
elevated temperatures
iii. Behavior of FRP-strengthened members under cold
temperatures
iv. Fire rating of concrete members strengthened with
FRP systems
Y(IIHFWRIGLIIHUHQWFRHI¿FLHQWVRIWKHUPDOH[SDQVLRQ
between FRP systems and member substrates
vi. Creep-rupture behavior and endurance times of FRP
systems
vii. Strength and stiffness degradation of FRP systems
in harsh environments
E )OH[XUHD[LDOIRUFH
i. Compression behavior of noncircular members
wrapped with FRP systems
ii. Behavior of members strengthened with FRP systems
oriented in the direction of the applied axial load
iii. Effects of high concrete strength on behavior of
FRP-strengthened members
iv. Effects of lightweight concrete on behavior of FRPstrengthened members
Y0D[LPXPFUDFNZLGWKDQGGHÀHFWLRQSUHGLFWLRQDQG
control of concrete reinforced with FRP systems
YL /RQJWHUP GHÀHFWLRQ EHKDYLRU RI FRQFUHWH ÀH[XUDO
members strengthened with FRP systems
F 6KHDU
i. Effective strain of FRP systems that do not completely
wrap around the section
ii. Use of FRP systems for punching shear reinforcement in two-way systems
G 'HWDLOLQJ
i. Anchoring of FRP systems
7KHGHVLJQJXLGHVSHFL¿FDOO\LQGLFDWHVWKDWWHVWPHWKRGV
are needed to determine the following properties of FRP:
D %RQG FKDUDFWHULVWLFV DQG UHODWHG ERQGGHSHQGHQW
FRHI¿FLHQWV
E &UHHSUXSWXUHDQGHQGXUDQFHWLPHV
F )DWLJXHFKDUDFWHULVWLFV
G &RHI¿FLHQWRIWKHUPDOH[SDQVLRQ
H 6KHDUVWUHQJWK
I &RPSUHVVLYHVWUHQJWK
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EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
APPENDIX D—METHODOLOGY FOR
COMPUTATION OF SIMPLIFIED P-M INTERACTION
DIAGRAM FOR NONCIRCULAR COLUMNS
$[LDO ORDGPRPHQW P-M LQWHUDFWLRQ GLDJUDPV PD\ EH
GHYHORSHGE\VDWLVI\LQJVWUDLQFRPSDWLELOLW\DQGIRUFHHTXLOLErium using the model for the stress strain behavior for FRPFRQ¿QHG FRQFUHWH SUHVHQWHG LQ (T F WKURXJK H )RUVLPSOLFLW\WKHSRUWLRQRIWKHXQFRQ¿QHGDQGFRQ¿QHG30
diagrams corresponding to compression-controlled failure can
be reduced to two bilinear curves passing through the following
SRLQWV )LJ 7KHIROORZLQJRQO\PDNHVUHIHUHQFHWRWKH
FRQ¿QHGFDVHEHFDXVHWKHXQFRQ¿QHGFDVHLVDQDORJRXV D 3RLQW$ SXUHFRPSUHVVLRQ DWDXQLIRUPD[LDOFRPSUHVVLYHVWUDLQRIFRQ¿QHGFRQFUHWHİccu
E 3RLQW % ZLWK D VWUDLQ GLVWULEXWLRQ FRUUHVSRQGLQJ WR
zero strain at the layer of longitudinal steel reinforcement
QHDUHVWWRWKHWHQVLOHIDFHDQGDFRPSUHVVLYHVWUDLQİccu on
the compression face
F 3RLQW & ZLWK D VWUDLQ GLVWULEXWLRQ FRUUHVSRQGLQJ WR
EDODQFHG IDLOXUH ZLWK D PD[LPXP FRPSUHVVLYH VWUDLQ İccu
DQGD\LHOGLQJWHQVLOHVWUDLQİsy at the layer of longitudinal
steel reinforcement nearest to the tensile face
)RUFRQ¿QHGFRQFUHWHWKHYDOXHRIࢥPn corresponding to
3RLQW$ ࢥMnHTXDOV]HUR LVJLYHQLQ(T D DQG E while the coordinates of Points B and C can be computed as:
⎡ A yt 3 + B yt
φPn B C = φ ⎢
⎣ + D + ∑ Asi f si
φM n B C
2
+ C yt ⎤
⎥
⎦
⎡ E yt 4 + F yt 3 + G yt 2 ⎤
= φ⎢
⎥ ⎣ + H yt + I + ∑ Asi f si di ⎦
'
'
where
−b Ec − E2
A=
12 f c′
B=
2
⎛ ε ccu ⎞
⎜⎝
⎟
c ⎠
2
'D
b Ec − E2 ⎛ ε ccu ⎞
⎜⎝ c ⎟⎠
2
'E
C = –bfcƍ
D = bcf c′ +
'F
bcE2
ε ccu 2
−b Ec − E2
E=
16 f c′
2
⎛ ε ccu ⎞
⎜⎝ c ⎟⎠
'G
2
⎡ ⎛
h ⎞ Ec − E2 2 ⎛ ε ccu ⎞
⎢b ⎜ c − ⎟
⎜
⎟
⎝
2 ⎠ 12 f c′ ⎝ c ⎠
F=⎢
⎢ b E −E ⎛ε ⎞
2
c
ccu
⎢+
⎜⎝
⎟
3
c ⎠
⎣⎢
'H
2
⎤
⎥
⎥
⎥
⎥
⎦⎥
'I
109
Fig. D.1—Strain distributions for Points B and C for simpli¿HGLQWHUDFWLRQGLDJUDP
⎛b
h ⎞ E − E2 ⎛ ε ccu ⎞ ⎞
⎛
G = ⎜ f c′ + b ⎜ c − ⎟ c
⎜⎝
⎟ ⎝
2⎠
2
c ⎠ ⎟⎠
⎝2
'J
h⎞
⎛
H = bf c′ ⎜ c − ⎟ ⎝
2⎠
'K
⎡ bc 2
h ⎞ bc 2 E2
⎛
f
bcf
c
−
−
ε ccu
′
′
⎢
⎟+
c
c ⎜
⎝
2
2⎠
3
⎢
I=
⎢ bcE2 ⎛
h⎞
⎢−
⎜⎝ c − ⎟⎠ ε ccu
2
2
⎣
⎤
⎥
⎥
⎥
⎥
⎦
'L
,Q (T 'D WKURXJK 'L c is the distance from the
H[WUHPHFRPSUHVVLRQ¿EHUWRWKHQHXWUDOD[LV )LJ' DQG
LW LV JLYHQ E\ (T ' 7KH SDUDPHWHU yt represents the
vertical coordinate within the compression region measured
from the neutral axis position and corresponds to the transiWLRQVWUDLQİtƍ (T ' >UHIHUWR)LJ'@ for Point B
⎧d
⎪
ε ccu
c=⎨
for Point C
⎪d ε + ε
ccu
⎩ sy
yt = c
ε t′
ε ccu
'
'
where fsi is the stress in the i-th layer of longitudinal steel
reinforcement. The values are calculated by similar triangles
from the strain distribution corresponding to Points B and
C. Depending on the neutral axis position c, the sign of fsi
will be positive for compression and negative for tension. A
ÀRZFKDUWLOOXVWUDWLQJWKHDSSOLFDWLRQRIWKHSURSRVHGPHWKodology is shown in Fig. D.2.
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110
EXTERNALLY BONDED FRP SYSTEMS FOR STRENGTHENING CONCRETE STRUCTURES (ACI 440.2R-17)
Fig. D.2—Flowchart for application of methodology.
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MCPOL Licensed to: McMaster University Library
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As ACI begins its second century of advancing concrete knowledge, its original chartered purpose
remains “to provide a comradeship in finding the best ways to do concrete work of all kinds and in
spreading knowledge.” In keeping with this purpose, ACI supports the following activities:
· Technical committees that produce consensus reports, guides, specifications, and codes.
· Spring and fall conventions to facilitate the work of its committees.
· Educational seminars that disseminate reliable information on concrete.
· Certification programs for personnel employed within the concrete industry.
· Student programs such as scholarships, internships, and competitions.
· Sponsoring and co-sponsoring international conferences and symposia.
· Formal coordination with several international concrete related societies.
· Periodicals: the ACI Structural Journal, Materials Journal, and Concrete International.
Benefits of membership include a subscription to Concrete International and to an ACI Journal. ACI
members receive discounts of up to 40% on all ACI products and services, including documents, seminars
and convention registration fees.
As a member of ACI, you join thousands of practitioners and professionals worldwide who share
a commitment to maintain the highest industry standards for concrete technology, construction,
and practices. In addition, ACI chapters provide opportunities for interaction of professionals and
practitioners at a local level to discuss and share concrete knowledge and fellowship.
American Concrete Institute
38800 Country Club Drive
Farmington Hills, MI 48331
Phone: +1.248.848.3700
Fax: +1.248.848.3701
www.concrete.org
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MCPOL Licensed to: McMaster University Library
38800 Country Club Drive
Farmington Hills, MI 48331 USA
+1.248.848.3700
www.concrete.org
The American Concrete Institute (ACI) is a leading authority and resource
worldwide for the development and distribution of consensus-based
bcM]QMaQbM]QcRPV]WPMZaRb^daPRb͜RQdPMcW^]MZ_a^UaM\b͜M]QPRacWŬPMcW^]b
for individuals and organizations involved in concrete design, construction,
and materials, who share a commitment to pursuing the best use of concrete.
Individuals interested in the activities of ACI are encouraged to explore the
ACI website for membership opportunities, committee activities, and a wide
variety of concrete resources. As a volunteer member-driven organization,
ACI invites partnerships and welcomes all concrete professionals who wish to
be part of a respected, connected, social group that provides an opportunity
for professional growth, networking and enjoyment.
9
781945
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487590
MCPOL Licensed to: McMaster University Library