wabo mbrace design guide

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ENGINEERINGDESIGN

GUIDELINES

Wabo®MBrace

Composite Strengthening System

Third Edition

May 2002

Watson Bowman Acme Corp.

95 Pineview Drive Amherst, New York 14228

Phone: (716) 691-7566Fax: (716) 691-9239

Website: www.wbacorp.com



Preface

The development of advanced polymers has led to the use of composite materials inmany industries including aerospace, automotive, defense, and shipbuilding. In the

past, economic factors and lack of an adequate knowledge base limited their use in theconstruction industry. However, a decreasing trend of raw materials and manufacturingcosts have made these materials economically competitive with more traditionalconstruction materials. In addition, there now exist a wide number of research andconstruction projects that have expanded the knowledge base for using composites inconstruction.

Development of composite products for use in construction has led to the introduction of composite structural shapes, composite bars and grids for concrete reinforcement, andcomposite tendons for prestressed concrete. However, at the forefront of thesetechnologies is the use of externally bonded composite materials for strengtheningexisting concrete structures. The most important characteristics of composite materials

in this application are: predominace of labor and shut-down costs as opposed to materialcosts, time and site constraints, and log-term durability.

Externally bonded composite or fiber reinforced polymer (FRP) materials wereintroduced as an alternative to steel plate bonding in 1982. The initial research of premanufactured FRP plate bonding began in Switzerland. FRP plate bonding wasdeveloped analogous to steel plate bonding. In contrast to steel, FRP is lighter, easier toinstall, and non-corrosive. Further development of this concept was done in Japanwhere the FRP material was “cast-in-place” from its two components, fiber and polymer.

The Japanese development of this technology and of FRP materials in 1985 has directlyled to the key components used in the Wabo®MBrace Composite Strengthening System.

The increasing consideration and usage of the system on strengthening projects areindicators of the benefits of FRP technology.

Hundreds of technical papers and several proceedings related to externally bonded FRPreinforcement are available. In fact, ASCE has begun a new publication entitled Journal

of Composites in Construction that deals exclusively with externally bonded FRP andother composite material systems. ACI Committee 440 now serves to establishstandardized design criteria, testing procedures, and quality control measures for FRP inconcrete structures. This committee’s work is presently available as a state-of-the-artreport. However, draft documents for design and construction codes are currently beingcirculated through the committee and should be available in the near future.

This design guide seeks to condense much of the current literature and conform to therecommendations of ACI in order to provide the engineer with useful design reference.It is envisioned that this guide will supplement future design codes, and through periodicupdates, reflect the most current research on externally bonded FRP reinforcement.



Copyright, 2002, Watson Bowman Acme Corp.

Watson Bowman Acme Corp95 Pineview Drive

Amherst, New York 14228, USA(716) 691-7566

This document is intended for use by only structural design and analysis professionals.Those persons using these guidelines must have sufficient knowledge and experienceregarding the design, construction and repair of concrete structures, and be sufficientlyfamiliar with minimum design standards and codes. This document does not, nor is itintended to, replace formal training with respect to the design, construction or repair of concrete structures.

The equations and design procedures presented herein are considered as the mostcurrent available in the technical literature. The referenced technical literature has beenpeer reviewed by technical Journals, Associations and Conference organizers and theauthors assume no responsibility for referenced conclusions.

While every attempt has been made to verify and validate the contents and informationcontained in this document, no guarantee or warranty, either expressed or implied(including the warranties of merchantability or fitness of purpose), is offered regardinguniversal adaptation of the equations and procedures presented herein. It is theresponsibility of the structural design and analysis professional to substantiate their conclusions drawn from the equations and procedures presented in this guide. Theauthors will not be held accountable for the conclusions, interpretations,recommendations or analyses of others using these guidelines.

Printed in U.S.A #114871



For additional information, visit the Watson Bowman Acme website at www.wbacorp.comor contact your local Watson Bowman Acme Composite Specialist.

Technical and Application Inquires:

Mr. Steve TyslBridge & Wabo® A-P-ECompsoite SpecialistWatson Bowman Acme CorpTel: (216) [email protected]

Mr. Will GoldComposite EngineeringSpecialistWatson Bowman Acme CorpTel: (216) 622-2690

[email protected]

Tel: (216) 622-2690Mr. Robert Snider Parking & ArchitecturalComposite SpecialistWatson Bowman Acme CorpTel: (281)[email protected]

http://www.wbacorp.com/

http://www.wbacorp.com/



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Chapter 1 Format

1.1 SCOPE 1-2

1.2 PHILOSOPHY OF THE MANUAL 1-2

1.3 ORGANIZATION OF THE MANUAL 1-2



Wabo®MBrace Composite Strengthening System Design Guide

05/30/021-2

Chapter 1 Format

1.1 Scope

This document is a guide to the engineering design of the Wabo ®MBrace CompositeStrengthening System. The guide addresses strengthening of concrete structures using

externally bonded Wabo®

MBrace Carbon Fiber Reinforced Polymer (CFRP) and GlassFiber Reinforced Polymer (GFRP) reinforcement.

An effort has been made to cover all types of strengthening that have been sufficientlydeveloped and tested for use in construction. This includes flexural strengthening, shear strengthening, and improving the ductility of compression members1. Design provisionsfor using the system to strengthen unreinforced, conventionally reinforced, andprestressed concrete structures are given.

The material presented is specific in that it only addresses the unique considerationsthat must be made when designing with the Wabo®MBrace System. The guide does notdeal with such issues as existing condition assessment, structural analysis, or traditionalconcrete design. These issues should be understood by the reader and are covered in

great detail elsewhere2,3,4

.

1.2 Philosophy of the Manual

This guide is intended for use by structural engineers and other technical professionalsfor the design of strengthening systems using the Wabo®MBrace family of products. Themanual presents simple design procedures and equations to cover the most commonaspects of strengthening with the Wabo®MBrace System.

In addition to the analytical design topics, more general information is included regardingtypical applications, the nature and behavior of the materials used in the system, and theinstallation procedures. This information is provided to give the engineer a physicalunderstanding of the system and so the engineer can make informed judgements on itsuse.

Where possible, the procedures, equations, and notation used in this manual areconsistent with those found in ACI 318-955.

1.3 Organization of the Guide

The manual is organized into four major parts:

Part 1 presents general information about this guide and definitions of the terms that areused throughout the guide.

Part 2 is a general description of the Wabo®MBrace System and its applications. Thissection presents information that will help the reader understand the physical aspects of the Wabo®MBrace technology. This section also serves as a source for the physical andmechanical properties of the materials used in the Wabo®MBrace strengthening system.



Chapter 1 Format

05/30/02 1-3

Part 3 presents the procedures and equations used for designing with the Wabo®MBracestrengthening system. Additional comment is made on the underlying theories andprinciples that form these procedures and equations. Each chapter of this section dealswith a different strengthening concern. At the beginning of each chapter, a definition of all notation used for the equations presented in the chapter is given. Design examplesare provided at the end of each chapter as aid to those not familiar with the design

process.

Part 4 addresses engineering practice. This section includes standard specificationsand general information.

The appendices include several design aids. These include tables giving typical areasof CFRP reinforcement, flexural strengthened resistance factors, development lengthsfor various sheet configurations, and strengthened column interaction diagrams. A listand brief description of recently completed projects that utilize the Wabo®MBrace is alsogiven in the appendix.

1 Nanni, A. (1995), "Concrete Repair with Externally Bonded FRP Reinforcement:Examples from Japan," Concrete International , v. 17, no. 6, June, pp. 22-26.

2 Emmons, P., (1993), Concrete Repair and Maintenance Illustrated , R.S. MeansCompany, Kingston, MA, 295 pg.

3 West, H., (1993), Fundamentals of Structural Analysis, J.W. Wiley and Sons, NewYork, NY, 698 pg.

4 Nilson, A., (1997), Design of Concrete Structures 12 th Ed., McGraw-Hill, New York, NY,780 pg.

5 ACI 318 (1995), “Building Codes and Requirements for Reinforced Concrete,” American Concrete Institute, Farmington Hills, MI, 369 pg.



Chapter 2 Definitions




05/30/022-2


Auto-ignition temperature — temperature at which a material willspontaneously ignite (does not need an ignition source). This is typically amuch higher temperature than the flash point.

Composites — composites are here defined as a matrix of polymeric materialreinforced by fibers with a discernable aspect ratio of length to thickness.

Concrete substrate the concrete surface to which the FRP is bonded.

Coverage — the area that a given volume of resin can cover.

Debonding — Failure resulting from the FRP laminate detaching from theconcrete substrate at the bond line.

Delamination — any of several failure modes resulting from the FRP laminateprogressively detaching from the concrete member along the direction of thefibers. Note that this does not necessarily imply a failure along the bond line;

the failure could result from rupture of the concrete in the vicinity of thelaminate. Also peeling .

Dry fiber sheet —a flexible sheet composed of several filaments of the fiber material arranged with a common orientation in a flat plane. This is theconfiguration of all fiber reinforcement systems used in the Wabo®MBraceComposite System. Also unidirectional sheet , fiber sheet or, simply, sheet .

Durability — the ability of a material or system to maintain its physical andmechanical properties over time.

Fiber orientation—the orientation of the filaments in a dry fiber sheet. If theorientation is expressed as an angle, this angle is taken with respect to thestrengthened members longitudinal axis.

Fiber sheet — see Dry fiber sheet .

Fibers — the load carrying elements in a composite material with a highlyoriented, defect free micro structure. The Wabo®MBrace CompositeStrengthening System is available in varieties of carbon or glass fibers.

Filament —a thread-like portion of the fiber material; this is the smallest unit of a fibrous material.

Flash point — Temperature at which a material will ignite in the presence of an ignition source (i.e., flame or spark).

Glass transition temperature — Temperature at which a polymer material

transforms from a brittle (or glassy) state to a softened (or rubbery) state.

Laminate — the final composite system after all components have beeninstalled and cured.

Peeling — see Delamination.

Ply — a unit of FRP material consisting of one layer of dry fiber sheet.




05/30/02 2-3

Pot life — the length of time after adding hardener to an epoxy resin that the resincan no longer be rolled or troweled. Also working time (for Wabo ®MBrace resins)

Primer — the first epoxy resin coat used to fill the concrete pore structure and toprovide adequate bond to the concrete substrate.

Putty — a thick, paste-like epoxy which is used to fill surface defects in the concretesubstrate.

Rehabilitation restoring the structural capacity of a damaged element to a itscapacity before the damage/degradation.

Resins — the composite material matrix that binds the fibers together, allows loadtransfer between fibers, and protects the fibers from the environment. TheWabo®MBrace Composite Strengthening System uses thermosetting epoxy resins.

Retrofit increasing the structural capacity of an element in good condition toaccommodate a change in loading.

Saturant — the epoxy resin that is used to impregnate the dry fiber sheet. Sheet — see Dry fiber sheet .

Topcoat — a finish coat used to protect the composite material from UV exposure,chemical splash, and abrasion. The topcoat also serves an aesthetic purpose bymimicking the color of the concrete substrate.

Tow — multi-filament strands of carbon or glass fiber.

Unidirectional sheet — see Dry fiber sheet .

Working time — see Pot life.



5/02 3-1

3The Wabo

® MBrace

System

3.1 General Description

3.2 Material Components

3.2.1 Wabo®MBrace

Primer

3.2.2 Wabo®MBrace Putty

3.2.3 Wabo®MBrace

Saturant

3.2.4 Wabo®

MBrace Fiber Reinforcement

3.2.5 Wabo®MBrace

Topcoat,Wabo

®MBrace ATX ,

and Wabo®MBrace

Topcoat FRL

3.3 Applications and Use

3.4 Installation Procedures

3.5 References

Chapter 3

The Wabo ® MBrace CompositeStrengthening System

3.1 General Description

The Wabo®MBrace System is comprised of four basiccomponents that, when combined, form a high-strength fiberreinforced polymer (FRP) laminate. The FRP laminate maybe used as external reinforcement for strengthening existingconcrete and masonry structures. This technology offers a

cost-effective alternative to conventional strengtheningtechniques such as steel plate bonding, steel jackets, sectionenlargement, and other techniques. The fibers are bondedby the use of three epoxy-based resins. The resins used areWabo®MBrace Primer, Wabo®MBrace Putty andWabo®MBrace Saturant. An optional final layer of eitherWabo®MBrace Topcoat, Wabo®MBrace ATX orWabo®MBrace Topcoat FRL may be used. The componentsof the Wabo®MBrace System are illustrated in Fig. 3.1 andare described in the following section.

3.2 Material Components

3.2.1 Wabo®MBrace Primer

Wabo®MBrace Primer is essential in providing an adequatesurface for bonding the Wabo®MBrace fibers and resins tothe base concrete. This first coat is a 100% solids epoxy basedmaterial with a relatively low viscosity. The viscosity of theWabo®MBrace Primer is formulated to penetrate the pore

Putty

1stResin Coat

2nd Resin Coat

Fiber Reinforcem ent

Topcoat

Prim er

Figure 3.1 – Components of the Wabo® MBrace

Composite Strengthening System



Wabo®MBrace Composite Strengthening System Engineering Design Guidelines

5/023-2

structure of the concrete. It is standard practice to prepare the concrete substrate bysandblasting the concrete surface to open the pore structure of the concrete.Wabo®MBrace Primer is typically applied using a short or medium nap roller.

3.2.2 Wabo®MBrace Putty

Wabo®MBrace Putty is a thick, paste-like epoxy that is used to fill bug holes and surface

defects up to 1/4 inch (5 mm) deep. The primary purpose of the putty is to provide asmooth, level bond surface in order to maximize the contact area of the FRP to theconcrete. Wabo®MBrace Putty can also be used for leveling and patching small holes. Ifthe base concrete has deep holes or large areas of damage, the defective concrete areashould be chipped out to reveal sound material and replaced with repair mortar. If theconcrete substrate is level and in good condition, the putty may not be required.Wabo®MBrace Putty is typically applied with a trowel.

3.2.3 Wabo®MBrace Saturant

Wabo®MBrace Saturant is the polymer matrix component of the FRP laminate. It is usedto impregnate the dry fibers. The saturant maintains the fibers in their intendedorientation and distributes stress among the fibers. The saturant also protects the fibersfrom abrasion and environmental effects.

The saturant is a bisphenol A epoxy resin. It is formulated to quickly wet the fibers andhold the tow sheet in place while the Wabo®MBrace System cures. The viscosity ofWabo®MBrace Saturant allows easy handling and overhead application of the fiber sheet.Wabo®MBrace Saturant is typically applied with a medium nap roller.

3.2.4 Wabo®MBrace Fiber Reinforcement

High strength fibers are the key load carryingcomponent of the Wabo®MBrace CompositeStrengthening System. The Wabo®MBraceSystem is available with high strength carbonfibers, high modulus carbon fibers, E-glassfibers, or Aramid fibers. Each of these fibers

has high strength to weight and stiffness toweight ratios. The fibers are assembled into astandard unidirectional sheet supplied innominal 20 in (500 mm)widths.

The tensile behavior of each of the fibers usedin the Wabo®MBrace system are compared in the graph. Detailed mechanical propertiesof both the fibers and epoxyresins are provided in Chapter4.

0

100

200

300

400

500

600

0 0.005 0.01 0.015 0.02 0.025

Strain (in/in)

S t r e s s

( k



Chapter 3 The Wabo®MBrace Composite Strengthening System

5/02 3-3

3.2.4.1 Wabo®MBrace Carbon Fibers

Wabo®MBrace carbon fibers are manufactured by pyrolizing polyacrylonitrile (PAN)

based precursor fibers at temperatures near 2700 F (1500 C). The result of thepyrolization process is a highlyaligned, cross-linked chain ofcarbon atoms. The exactmechanical properties of thefibers, including the tensilemodulus of elasticity, can beadjusted by altering several,carefully controlled variablesduring the manufacturingprocess. The carbon fiber

filaments are assembled intountwisted tows that are then used to create a continuous unidirectional sheet. Highstrength carbon fibers compose the CF 130, 145, and 160 unidirectional sheets, and highmodulus carbon fibers are used for the CF 530 unidirectional sheet.

3.2.4.2 Wabo®MBrace Glass Fibers

Wabo®MBrace glass fibers aremanufactured by drawing moltenglass through a die or a bushing.The resulting “E” type glassfilaments are grouped into towsthat are then assembled into thecontinuous EG 900 unidirectional

sheet.

E-glass fibers are high strength but low stiffness. They, therefore, have very highelongation capacity.

3.2.4.3 Wabo®MBrace Aramid Fibers

Aramid fibers are manufactured by polymerization of amine and carboxcylic acid. Theresult is an ultra-high molecular weight aromatic polyamide (aramid). The aramidmaterial is then spun into individual filaments. The aramid fibers are woven into the

continuous AK 60 unidirectional sheet.

Aramid fibers have high strength,excellent toughness, and are resistant to

impact and abrasion. Aramid may beused in lieu of carbon fiber in situationswhere a non-conductive material isneeded. Aramid does degrade underexposure to ultraviolet light and shouldbe protected. In addition, aramid

fibers absorb moisture which can lead to a reduction in their tensile properties. Sincearamid is an organic compound, aramid fibers are sensitive to temperature extremes.

Typical aramid fibers have a usable temperature range of +/- 350 F.

Carbon Fiber Properties

Very high strength and stiffness

Excellent moisture and chemical resistance

Highly resistant to fatigue and creep rupture

Thermally stable up to 3500 F

Low impact resistance

Conductive

Susceptible to galvanic corrosion

Glass Fiber Properties

High strength, low stiffness

Sensitive to moisture and alkalinity

Low resistance to fatigue and creep rupture

Soften at temperatures over 1500 F

Highly insulative

Aramid Fiber Properties

High strength

Excellent chemical resistance

Resistant to fatigue and creep rupture Usable temperature range +/- 350 F

Excellent impact resistance

Low conductivity

Sensitive to UV exposure and moisture




5/023-4

3.2.4.4 Custom Fiber Architectures

Other fiber architectures such as hybrid sheets using two or more fiber types, plain weavefabrics, and sheets with specific fiber areal weights may be available for specialapplications. Contact an Wabo®MBrace service representative for more information.

3.2.5 Wabo®MBrace Topcoat, Wabo®MBrace ATX , and Wabo®MBrace Topcoat FRL

The final component to the Wabo®MBrace Strengthening System is one of three finishcoats that are specified as an option. These products provide protection from ultravioletlight (UV), chemical splash, and abrasion. Wabo®MBrace Topcoat FRL providesadditional resistance to smoke generation and flame spread. The Topcoat FRL enables thesystem to achieve a Class I (Class A) fire resistance per ASTM E841. Other topcoat systemsmay be used for specific environmental exposure conditions. All topcoats mimic the colorof concrete, so they are also used to provide a uniform color to repaired concretemembers.

3.3 Applications and Use

The Wabo®MBrace Composite Strengthening System was developed as a cost-effectivealternate to conventional strengthening techniques. The high strength fiber sheets can beinstalled quickly and easily on flat surfaces, around columns or beams, and in areas withlimited access. The system has been used and tested for increasing the flexural capacity ofbeams, slabs and columns, the shear capacity of beams, columns and walls and theductility of columns.

Increases in flexural capacity are achieved by bonding the system to the tension face of amember in bending. Shear capacity may be improved by wrapping the systemtransversely around a member or orienting fibers perpendicular to potential shear cracks.

The ductility of columns may be enhanced by confining the column by wrapping thesystem completely around the column in the hoop direction.

3.4 Installation Procedures

The Wabo®MBrace Composite Strengthening System is installed exclusively by aninternational network of selected contractors. The contractors within the network areexperienced and receive additional training in concrete repair and strengtheningtechniques, product information, installation methods and quality control measures.

Figure 3.2 –Wabo® MBrace installation before and after the application of Topcoat

ATX



Chapter 3 The Wabo®MBrace Composite Strengthening System

5/02 3-5

The installation procedures are provided to give the reader a general understanding of thesteps involved in construction*. The Wabo®MBrace composite strengthening system caneasily be installed on properly prepared, sound concrete surfaces in a series of eight steps.The system is installed using “wet lay-up” techniques. That is, the fiber materials areplaced on the surface dry and then impregnated with epoxy resins in place to form theFRP laminate.

Step 1: Stabilizing the Concrete Substrate

Prior to installing the Wabo®MBrace composite strengthening system the concretesubstrate must be prepared to accept the system. The integrity of the system depends onthe quality and strength of the concrete as well as the bond between the FRP and theconcrete. Cracks, spalls and corroding reinforcing steel need to be repaired prior toinstalling the Wabo®MBrace System.

Spalls and other types of damage should be removed and patched with suitable repair

mortars such as Master Builders Emaco R320 or Emaco R350 surface renovation

mortars. If repairs using form and pour techniques are required, the use of Emaco S88-

CA, Emaco S77-CR or Emaco S66-CR structural repair mortar is recommended.

All cracks greater that 0.010 inch (0.25 mm) in width and subject to movement (thermal,

vibration, etc.) should be epoxy injected using Master Builders SCB injection technology.

Corroding reinforcing steel should be cleaned (or replaced) before installing theWabo®MBrace System. FRP systems, like conventional strengthening techniques are notintended to resist or arrest the enormous and incalculable expansive forces generated bycontinuing corrosion of the reinforcing steel.

Step 2: Surface Preparation

The surface of the concrete should be free of loose and unsound materials. All laitance,dust, dirt, oil, curing compound, etc. should be removed. Mechanical abrasion techniques(e.g. abrasive blasting, grinding), water blasting or other approved methods should beused to open the pore structure of the concrete prior to applying the Wabo ®MBraceprimer. The surface should be profiled to a minimum ICRI CSP 3 surface texture.

Step 3: Application of Wabo®MBrace Primer

The Wabo®MBrace primer is applied to the properly prepared concrete surface using ashort or medium nap roller.

Step 4: Application of Wabo®MBrace Putty

The Wabo®MBrace putty is applied to the primed surface using a trowel. The puttyshould be used to fill any surface defects; complete coverage is not necessary. The puttymay be applied immediately after priming the surface without waiting for the primer tocure.

Step 5: Application of First Coat of Wabo®MBrace Saturant

The Wabo®MBrace saturant is applied to the primed and puttied surface with a mediumnap roller. The saturant can be installed immediately after application of the primer andputty (before cure) or long after the application of the primer and putty. If the saturant is

installed after cure of the putty and primer, the surface should be wiped clean with a drycloth. (Solvents should not be used to clean the surface.)

The saturant is blue in color and should be applied to a thickness of 18 to 22 mils. Thevolume of saturant used depends on the FRP sheet used.

* More detailed information regarding the installation process as well as construction specificationsare available from Master Builders.




5/023-6

Step 6: Application of Wabo®MBrace Fiber Sheet

The fiber sheets should be measured and pre-cut prior to installing on the surface. Thesheet is placed on the concrete surface and gently pressed into the saturant. Prior toremoving the backing paper, a squeegee or trowel may be used to remove any air bubbles.After the backing paper is removed a ribbed roller is rolled in the direction of the fibers tofacilitate impregnation by separating the fibers. The ribbed roller should never be used in

a direction transverse to the fibers since fibers could be damaged. Streaks of blue coloredsaturant should be visible on the fiber sheet after rolling.

Step 7: Application of Second Coat of Wabo®MBrace Saturant

A second coat of saturant is applied immediately after placing and rolling the fiber sheet.The second coat of saturant is applied to the FRP sheet with a medium nap roller to athickness of 18 to 22 mils. More saturant is required for the Wabo ®MBrace Wabo®MBraceEG 900 sheets because they are thicker than the carbon sheets.

Step 8: Application of Additional Fiber Plies

If required, additional fiber plies may be installed by re-saturating the surface after thesecond saturant coat is applied and repeating Steps 4, 5 and 6. This process should berepeated for as many plies as are necessary. After completion of this step, the fiber sheetlayers are completely encapsulated in laminate form.

Step 9: Application of Wabo®MBrace Finish Coats (Optional)

After the saturant has cured tack free, one of the Wabo®MBrace finish coats may beapplied for protection or aesthetic purposes.

3.5 References

1 ASTM E84 Test Method for Surface Burning Characteristics of Building Materials, Vol. 04.07.



Chapter 4 Technical Data

4.1 PHYSICAL PROPERTIES 4-2

4.2 COVERAGE 4-3

4.3 ENGINEERING PROPERTIES 4-4

4.4 FIBER SELECTION GUIDELINES 4-6

4.5 REFERENCES 4-8




05/30/024-2


4.1 Physical Properties

This section is presented to acquaint the user to the physical appearance and handling

properties of Wabo®

MBrace resins. In general, the Wabo®

MBrace resins are easy to mix

and apply. All are formulated for both over-head and side-wall applications and provideadequate time for application.

While the Wabo®

MBrace resins are formulated with the applicator in mind, some people

may be sensitive to the epoxy resins and curing agents contained within. As with mostchemicals, proper ventilation, as well as eye and skin protection should be provided.

Material Data Safety Sheets (MSDS) are always provided with each shipment of

Wabo®

MBrace resins. These should be kept on file at the job-site and referred to in caseof an accident.

Table 4.1 – Master Table of Physical Properties for Wabo® MBrace Resins

Wabo®MBrace Primer Wabo

®MBrace Putty Wabo

®MBrace Saturant

Color

Part A

Part B

Mixed

Amber

Clear

Amber

Tan

Charcoal

Tan (see Note 5)

Blue

Clear

Blue

Solids 100% 100% 100%

VOC content 0.89 lb/gal (107 g/L) 0.74 lb/gal (89 g/L) 0.17 lb/gal (20 g/L)

Mix ratio by volume

Part A/Part B

3/1 3/1 3/1

Mix ratio by mass

(weight) Part A/Part B

100/30 100/30 100/34

Mixed viscosity at 25 C

(77 F)

400 cps (see Note 1) 45,000 cps 1,350 cps

Working time at 25 C(77 F) 20 minutes (see Note 2) 40 minutes 45 minutes

Flash point

Part A

Part B204 F (95 C)

200 F (93 C)

210 F (99 C)

200 F (93 C)

230 F (110 C)

200 F (93 C)

Clean-up T-410 (see Note 3),Methyl ethyl ketone, or

Acetone

T-410,Methyl ethyl ketone, or

Acetone

T-410,Methyl ethyl ketone, or

Acetone

Shelf life 18 months (see Note 4) 18 months 18 months

Note 1: The viscosity of fluids is measured in centipoise (cps) and is relative to the viscosity of water. For

comparison, water has a viscosity of 1 cps, motor oil has a viscosity of 500 cps, pancake syrup is 2,500 cps,catsup is 50,000 cps and peanut butter is 250,000 cps.

Note 2: Working time is based on a 1 gal (3.8 L) sample.

Note 3: T-410 is available through Master Builders, Inc. Note 4: When stored in original, sealed containers at 72 F (20 C). Note 5: Thoroughly mixed material has no color streaks.

Typical of many fluids, Wabo®

MBrace resins show reduced viscosity with increasing

temperature. In addition, increased temperatures accelerate the cure of epoxy. Becausethese two properties are dependent on temperature, substantial differences in the working

time or pot life are expected. Such behavior is depicted in Table 4.2. In Table




05/30/02 4-3

4.2, the reported viscosity is the initial mixed viscosity of the resin and hardener (Part Aand Part B) stored and mixed at the respective temperature. As the epoxy reaction

advances and the temperature of the mixed components rises, the viscosity will increase

until full cure. The working time is the length of time after which the resin can no longer

be easily rolled or troweled. Table 4.2 – Temperature vs. Viscosity

Temperature Mixed Viscosity (cps)Wabo®MBrace

Primer

Wabo®MBrace Putty Wabo®MBrace

Saturant

50 F (10 C) 1,200 74,000 2,500

77 F (25 C) 400 45,000 1,600

90 F (32 C) 200 33,000 900

Note: Based on a standard Brookfield method.

Table 4.3 – Temperature vs. Working Time

Temperature Working Time (min)Wabo®MBrace

Primer


Saturant50 F (10 C) 75 95 200

77 F (25 C) 20 40 45

90 F (32 C) 10 15 15

Note: Based on 1 gal (3.8 L) sample.

It is common practice to mix only the amount of material needed to coat a given area

within the applicator’s ability. Working times can be extended by spreading the material

immediately after mixing and by keeping materials out of direct sunlight in warmweather. In extreme warm weather cases, the resins can be cooled prior to mixing by

immersing unopened containers in ice water.

4.2 Coverage

In general, the area that a particular volume of resin can cover (coverage) is dependent on

the surface texture and porosity of the substrate. Additionally, the viscosity of the resin

will also control the amount of penetration and thus, the overall coverage. Because of thevariability of field conditions, coverage is presented as a typical range of values.

Table 4.4 – Typical Resin Coverage

Surface Texture Cured

Rough Smooth Thickness

Product Type of Application ft2/gal

(m2/L)

ft2/gal

(m2/L)

mils (mm)

Wabo®MBrace Primer First coat – roller 200 (4.9) 250 (6.1) 3 (0.07)Wabo®MBrace Putty Filler coat – trowel 6 (0.15) 12 (0.29) VariesWabo®MBrace Saturant

(CF 130 and CF 530)Saturation and

Subsequent coats – roller

Not

applicable

55 (1.3)

(total)

20 (0.5)

(total)

Note 1: 1 mil = 0.001 in.

Note 2: Coverage of EG 900 is 27 ft2/gal (0.65 m2/L)




05/30/024-4

4.3 Engineering Properties

The overall engineering or mechanical properties of the Wabo®MBrace composite system

are greatly influenced by the fibers. For typical design purposes, only the tensile strength

and tensile modulus of the fiber is considered. These values are determined by tensile

testing of FRP specimens1. Ultimate strength is determined by using the net area of the

fiber embedded in cured saturant. Design strength is determined by reducing the averageultimate strength by three standard deviations. The stress-strain curve for Wabo

®MBrace

fibers are typical of fiber reinforced polymers and show linear behavior up to ultimatestress followed by brittle failure. For example, the stress-strain curve for Wabo

®MBrace

CF 130, a carbon fiber reinforced epoxy, is shown in Figure 4.1. The stress in Figure 4.1

was computed using the net fiber area.

Table 4.5 – Design Values for Wabo® MBrace Fibers

Wabo®MBrace Fiber

Ultimate

Strength

ksi (MPa)

Design

Strength

ksi (MPa)

Tensile

Modulus

ksi (MPa)

CF 130 High Tensile Carbon 620 (4275) 550 (3790) 33,000 (228,000)CF 530 High Modulus Carbon 584 (4027) 510 (3517) 54,000 (372,000)

EG 900 E-Glass 251 (1730) 220 (1517) 10,500 (72,400)

0

100

200

300

400

500

600

700

0 0.005 0.01 0.015 0.02

Strain

S t r e s s

( k s i )

Figure 4.1 – Representative stress-strain curve from tensile test data,Wabo

® MBrace CF 130 carbon fiber.

The design numbers should be further reduced by appropriate factors depending if LRFD

or ASD methods are used.

With regard to the design assumption that bond between the composite and concrete

substrate is “perfect”, it is necessary for all materials within the bond line to be stronger




05/30/02 4-5

and more resilient than the concrete. For this reason, the tensile, compressive and flexural properties of the neat resins are presented. Also, for those interested in performing micro-

mechanical design and analysis, these values can be used for the constitutive materials

properties. Please note that micro-mechanical treatment of the Wabo®

MBrace System is

beyond the scope of this manual. For additional information, contact your Watson

Bowman Acme Composite Specialist.The term “neat resins” refers to a sample of cured epoxy resin with no reinforcing fiber

materials present. For testing, neat resins are mixed, cast into sheets and allowed to cure.

After full cure is achieved, typically 7 days at 72 F (20 C) and 40% relative humidity,samples are machined from the sheets and tested to determine particular engineering

properties.

Because of the viscoelastic behavior of the Wabo®

MBrace resins, the temperature andstrain rates during testing are important parameters that greatly influence the strength and

stiffness of the constitutive materials. Therefore, to provide repeatable results, testing is

performed according to appropriate ASTM standards.

Table 4.6 – Tension: Neat Resin Properties ASTM D-6382

Wabo®MBrace

Primer


Saturant

Maximum Stress

psi (MPa)

2500 (17.2) 2200 (15.2) 8000 (55.2)

Stress at Yield

psi (MPa)

2100 (14.5) 1900 (13.1) 7800 (53.8)

Stress at Rupture

psi (MPa)

2500 (17.2) 2100 (14.5) 7900 (54.5)

Strain at Max. Stress 0.400 0.060 0.030

Strain at Yield 0.040 0.020 0.025

Strain at Rupture 0.400 0.070 0.035

Elastic Modulus

psi (MPa)

104,000 (715) 260,000 (1790) 440,000 (3035)

Poisson’s Ratio 0.48 0.48 0.40

Note: Properties determined at 72 F (20 C) and 40% relative humidity.




05/30/024-6

Table 4.7 – Flexure: Neat Resin Properties ASTM D-7903

Wabo®MBrace

Primer

Wabo®MBrace

Putty

Wabo®MBrace

Saturant

Maximum Stress psi (MPa) 3500 (24.1) 4000 (27.6) 20,000 (138)

Stress at Yield psi (MPa) 3500 (24.1) 3800 (26.2) 20,000 (138)

Stress at Rupture psi (MPa)

Large deformationwith no rupture. 3700 (25.5) 18,000 (124)

Strain at Max. Stress 0.060 0.060 0.042

Strain at Yield 0.050 0.040 0.038

Strain at Rupture Large deformation

with no rupture. 0.070 0.050

Flexural Modulus psi (MPa) 86,300 (595) 130,000 (895) 540,000 (3724)


Table 4.8 – Compression: Neat Resin Properties ASTM D-6954

Wabo®MBrace

Primer

Wabo®MBrace

Putty

Wabo®MBrace

Saturant

Maximum Stress psi (MPa) 4100 (28.3) 3300 (22.8) 12,500 (86.2)

Stress at Yield psi (MPa) 3800 (26.2) 3300 (22.8) 12,500 (86.2)

Strain at Max.Stress 0.100 0.100 0.050

Strain at Yield 0.040 0.050 0.050

Compressive

Modulus, psi (MPa) 97,000 (670) 156,000 (1075) 380,000 (2620)


4.4 Fiber Selection Guidelines

Three different reinforcing fibers are available with the Wabo®MBrace Composite

Strengthening System – CF 130, CF 530, and EG 900. Each strengthening application

should be carefully evaluated to determine the most appropriate reinforcing fiber. Factors

to consider in selecting a fiber type include the type of loading (sustained or event),environmental exposure conditions, and project economics. The intent of this section is to present the engineer with some general guidelines that will aid in selecting an appropriate

reinforcing fiber.

Carbon fibers, such as those used in CF 130 and CF 530 reinforcement, possess highstrength, high modulus and are unaffected by typical environmental exposure conditions.




05/30/02 4-7

Carbon fiber has also been shown to resist high stresses for sustained periods withoutfailing due to creep rupture

*. E-glass fibers used in EG 900 reinforcement allow for a

reduced material cost, but possess lower strength and modulus than carbon fibers. E-glass

fibers also do not exhibit the superior long-term behavior of carbon fibers. In general, E-

glass fibers have been shown to degrade over time when exposed to moisture and other

environmental conditions. Eventually, E-glass fibers will fail due to creep rupture atsustained stresses greater than 30% of ultimate. To provide a safeguard against

environmental and creep degradation, duration and environmental strength reductionfactors, CD and CE are applied to the design values. These reduction factors limit the

allowable stress to levels that environmental and sustained stress effects are no longer a

concern. These values are tabulated in Table 6.1.1. The tabulated strength reductionfactors are determined by long term durability testing of FRP tensile specimens without

protective coatings. Therefore, designs using these strength reduction factors will be

conservative.

The high strength, high modulus and negligible creep rupture behavior make carbonfibers ideal for flexural and shear strengthening applications. Because fibers used for

these applications typically carry high levels of sustained stress, E-glass fibers will

require large strength reduction factors to prevent creep rupture. In most cases this resultsin repairs that lack efficiency in materials use and project economics. In contrast, the

excellent resistance to environmental exposures makes carbon fiber ideal for applications

in harsh environments.

The two carbon fiber types available (CF 130 and CF 530) give the engineer the ability toselect a material with either very high strength or very high modulus. Due to its higher

strength and higher elongation at failure, CF 130 is best used when the ultimate behavior

of a concrete element needs to be improved. In applications where serviceability(deflection, allowable stresses, etc.) is the main concern, CF 530 may be a more

appropriate choice due to its higher modulus. However, since bonded FRP reinforcementin general do not dramatically effect serviceability, CF 130 will be best suited for the

majority of applications.

E-glass fibers are ideal for “event” loading conditions (seismic, blast, etc.) where the lack

of sustained stresses in the fiber eliminate problems with creep rupture. For theseconditions, low cost EG 900 fiber is most appropriate. In harsh environments, redundant

use of material and protective coatings can compensate for environmental degradation of

the E-glass fibers over time.

* Creep rupture is a phenomenon unique to FRP materials. Sustained, long-term stresses can cause certain

fibers to fail suddenly after a passage of time. The duration to cause failure is dependent on the magnitude

of the sustained stress, with higher stresses shortening the time to failure. The phenomenon is similar to

fatigue in metals except that the stresses are constant rather than cyclic. In fact, creep rupture is also knownas static fatigue since the sustained load vs. time curves resemble classic S-N curves.




05/30/024-8

4.5 References

1 ASTM D-3039, Test Method for Tensile Properties of Polymer Matrix Composite

Materials, Vol. 15.03.

2 ASTM D-638, Test Method for Tensile Properties of Plastics, Vol. 08.01.

3 ASTM D-790, Test Method for Flexural Properties of Unreinforced and Reinforced

Plastics and Electrical Insulating Materials. Vol. 08.01.

4 ASTM D-695, Test Method for Compressive Properties of Rigid Plastics, Vol. 08.01.



Chapter 5 Durability

5.1 GENERAL 5-2

5.2 ENVIRONMENTAL EXPOSURE 5-2

5.3 CHEMICAL EXPOSURE 5-3

5.4 FIRE 5-3

5.4.1 Surface Flammability 5-4

5.4.2 Structural Fire Ratings 5-4

5.5 REFERENCES 5-4




05/30/025-2


5.1 General

At room temperature, moisture, atmospheric chemicals, solvents, bases and weak acids

do not affect bare carbon fiber 1. Oxidizing agents and temperatures above

660 F (350 C)2 can also degrade bare carbon fiber. In the presence of an epoxy matrix,the carbon fibers are protected from chemical attack.

In the following sections, data was generated by fabricating standard tensile specimens per ASTM D-3039

3, cured with MBrace Saturant, exposing the specimens to various

conditions for 1,000, 3,000 and 10,000 hours, then testing the specimens to failure. In

addition to tensile data, the apparent interlaminar shear strength (commonly known as the“short beam shear test”) was determined using ASTM D-2344

4. These tests were

performed without a protective finish coat to determine the resiliency of the MBrace

System. For permanent repairs, it is recommended to include a finish coat for added protection and for aesthetic reasons. Protective coating systems should be selected based

on environmental exposure conditions and chemical resistance requirements. Data presented is for the most commonly used carbon fiber, Wabo®

MBrace CF 130.

5.2 Environmental Exposure

The physical properties of polymer materials subjected to hot and moist conditions

eventually degrade because of moisture diffusion. Because moisture diffusion is largelyinfluenced by elevated temperatures, data was generated for specimens exposed to 100%

RH at 100 F per ASTM D-22475 and 20% RH at 140F per ASTM D-3045

6. Results of

this testing are presented in Table 5.1.

The effect of ultraviolet (UV) light and freezing and thawing has also been investigated.

Table 5.1 shows the residual properties of specimens exposed to 100 UV/condensationand 20 freeze/thaw cycles.

The most important concern in FRP repair is maintaining strain compatibility between thefibers and the base concrete. Research has shown that up to 50 saturated freeze/thaw

cycles can be tolerated with no noticeable degradation to the adhesive/concrete interface

or significant change in overall flexural performance7. Appropriate safety factors will

ensure long term performance.




05/30/02 5-3

Table 5.1 – Environmental Exposure, Wabo® MBrace CF 130

Exposure Type

Ultimate

Tensile

Strength (ksi)

Tensile

Modulus

(ksi)

Failure Strain

(%)

Interlaminar

Shear

Strength (ksi)

Control 639 27 32,200 1,600 1.78 0.06 7.7 0.3

100% RH/100 F

1,000 h 591 25 34,000 1,400 1.59 0.08 7.6 0.1 3,000 h 540 17 33,200 400 1.51 0.06 7.2 0.1 10,000 h Due 2/99 Due 2/99 Due 2/99 Due 2/99

20% RH/140 F

1,000 h 637 23 33,400 1,200 1.73 0.08 9.5 0.2 3,000 h 582 12 32,600 900 1.67 0.05 8.6 0.4 10,000 h Due 2/99 Due 2/99 Due 2/99 Due 2/99UV/Condensation

100 Cycles 644 37 33,600 1.2 1.76 0.09 8.4 0.3

Freeze/Thaw20 Cycles 561 29 33,300 1,700 1.57 0.06 7.5 0.1

5.3 Chemical Exposure

The Wabo®

MBrace System is tolerant of mild chemical exposure such as salt-water

immersion per ASTM D-11418 and alkali immersion (pH 9.5 at 73 F) per ASTM C-

5819. Results of this testing is presented in Table 5.2.

Table 5.2 – Chemical Exposure, Wabo® MBrace CF 130

Exposure TypeUltimate

Tensile Strength

(ksi)

TensileModulus

(ksi)

Failure Strain

(%)

Interlaminar Shear Strength

(ksi)

Control 639 27 32,200 1,600 1.78 0.06 7.7 0.3

Salt Water

1,000 h 619 25 33,600 500 1.70 0.05 7.5 0.2

3,000 h 623 23 33,900 1,100 1.74 0.07 7.6 0.4

10,000 h Due 2/99 Due 2/99 Due 2/99 Due 2/99

pH 9.5

1,000 h 597 27 32,900 1,300 1.70 0.11 7.6 0.1

3,000 h 585 35 31,800 800 1.70 0.09 7.2 0.6

10,000 h Due 2/99 Due 2/99 Due 2/99 Due 2/99

Diesel Fuel 4 h 589 9 34,100 1.5 1.61 0.08 8.2 0.1

5.4 Fire

Investigating two related issues can satisfactorily treat the issue of fire durability. The

first issue is that of surface flammability and the second is that of structural integrity.




05/30/025-4

5.4.1 Surface Flammability

Surface finishes such as paints and wall coverings are classified by ASTM E-8410

bydetermining the flame spread and smoke generation of the material when exposed to a

controlled heat source and ignition point. The goal of this testing is to determine how fast

a flame spreads over a given area and to determine the density of the resulting smoke.

The amount of smoke generated is of concern to fire code authorities because in mostcases the loss of life is caused by smoke inhalation and not because of collapsing

structures.

Laboratory tests indicate that because of the heat sink behavior contributed by theconcrete substrate, flame spread on the Wabo

®MBrace System is suppressed. Current

research indicates that the Wabo®MBrace System applied on concrete without a finish

coat can be classified by ASTM E84 with “Class III” fire rating.

Independent testing by Omega Point Research in San Antonio, Texas has determined thatthe Wabo

®MBrace Carbon Fiber system coated with Wabo

®MBrace Topcoat FRL meets

the requirements of ASTM E84 “Class I”. Two coats at 160 ft2/gallon/coat of

Wabo

®

MBrace Topcoat FRL on the Wabo

®

MBrace Carbon Fiber system is recognized by model building codes for unrestricted use in buildings subject to flame spread and

smoke generation limits.

5.4.2 Structural Fire Ratings

In order to prevent structural collapse, the design philosophy of the Wabo®

MBrace

System is to treat the repair as supplemental reinforcement. Because of the supplemental

strength contribution to the overall structure, the new service loads are less than theoriginal ultimate load of the structure (see Chapter 6). This same situation exists with

steel plate bonding, but has traditionally been ignored.

Currently, there are no accepted standards or failure criteria for structures that are either completely built of or repaired with FRP materials. There exists a need for all interested

parties to establish rational guidelines and standards. Until that time, the concept of

supplemental reinforcement for repair must suffice.

5.5 References

1 Judd, N.C.W., “The Chemical Resistance of Carbon Fibers and a Carbon

Fiber/Polyester Composite”, Proceedings of the First International Conference on

Carbon Fibers, Plastics Institute, 1971, p. 258.

2

McKee, D.W. and Mimeault, V.J., “Surface Properties of Carbon Fibers”, Chemistryand Physics of Carbon, Vol. 8, Marcel Dekker, 1973, p. 235.

3 ASTM D-3039, Test Method for Tensile Properties of Polymer Matrix Composite

Materials, Vol. 15.03.

4 ASTM D-2344, Test Method for Apparent Interlaminar Shear Strength of Parallel Fiber

Composites by Short-Beam Method, Vol. 15.03.




05/30/02 5-5

5 ASTM D-2247, Practice for Testing Water Resistance of Coatings in 100% Relative

Humidity, Vol. 06.01.

6 ASTM D-3045, Practice for Heat Aging of Plastics Without Load, Vol. 08.02.

7

Tysl, S.R., Imbrogno, M. and Miller, B.D., “Effect of Surface Delamination on theFreeze/Thaw Durability of CFRP-Reinforced Concrete Beams”, Durability of Fibre

Reinforced Polymer Composites for Construction, Benmokrane. B., and Rahman, H.,Editors, Sherbrooke, Quebec, Canada, 1998, pp. 317-324.

8 ASTM D-1141, Specification for Substitute Ocean Water, Vol. 11.02.

9 ASTM C-581, Practice for Determining Chemical Resistance of Thermosetting Resins

Used in Glass-Fiber-Reinforced Structures Intended for Liquid Service, Vol. 08.04.

10 ASTM E-84, Test Method for Surface Burning Characteristics of Building Materials,

Vol. 04-07.



5/99 6-1

6Flexural Strengthening

6.1 Introduction

6.1.1 Design Approach

6.2 Existing ConditionAssessment

6.2.1 Initial Strains inCracked Concrete

6.2.2 Initial Strains inUncracked Concrete

6.3 Preliminary Design

6.3.1 Existing Shear Strength

6.3.2 Existing Stiffness

6.3.3 Controlling WorkingStress

6.4 Ultimate StrengthAnalysis

6.4.1 Reinforced Concrete

6.4.2 PrestressedConcrete

6.4.3 Summary of Strength

Equations6.5 Ductility

6.5.1 UnreinforcedConcrete


6.5.3 PrestressedConcrete

6.6 ServiceabilityRequirements

6.6.1 Working Stress Analysis

6.6.2 Deflections of Strengthened Beams

6.6.3 Crack Widths

6.7 Examples from Practice

6.7.1 Retrofit of anExisting ReinforcedConcrete BridgeSlab

6.8 References

Chapter 6

Flexural Strengthening

6.1 Introduction

It has been well understood that bonding FRP reinforcementto the tension face of a concrete flexural member with fibersoriented along the length of the member will provide anincrease in flexural capacity.

1, 2, 3 Increases in flexural

capacity from 10% to 160% have been documented.However, when taking into account ductility andserviceability limits, increases of 5% to 40% are morereasonable for actual design cases.

In this chapter, the material characteristics presented in Part2 and information about the existing concrete member areused to develop equations and procedures for computing theincrease in flexural capacity that may be achieved with anWabo

®MBrace strengthening system. In addition, criteria

are suggested for maintaining a reasonable level of ductilityin the member as well as ensuring serviceability. Specificguidance on addressing both regularly reinforced andprestressed members is given.

This chapter deals only with the design and analysis of

member cross sections. Complete design of Wabo®MBraceflexural reinforcement requires an investigation of the bondstrength and other aspects covered in Chapter 10.Furthermore, guidance on detailing the system for specificflexural elements, such as slabs, is given in Part 5.



Wabo®MBrace Composite Strengthening System Engineering Guidelines

05/026-2

Symbols and Notation

Ac = Area of gross concrete section (in.2)

Acr = Area of concrete compression zone after cracking (in.2)

Af = Total area of fiber contained in the FRP laminate = n tf wf (in.2)

Ap = Area of prestressing steel (in.2)

As = Area of tension steel (in.2)

A's = Area of compression steel (in.2)

b = Width of the section (in.)

c = Depth to the neutral axis (in.)

cb = Distance from the neutral axis of the gross concrete section to the bonded substrate (in.)

CD = Tensile strength reduction factor for FRP subjected to sustained loading

CE = Tensile strength reduction factor for FRP subjected to environmental conditions

d = Depth to the tension steel reinforcement centroid (in.)

d' = Depth to the compression steel centroid (in.)dp = Depth to the prestressing steel centroid (in.)

e = Eccentricity of the prestressing force with respect to the neutral axis of the gross concretesection. Positive eccentricities cause compression on the bonded substrate. (in.)

Ec = Approximate elastic modulus of concrete in compression (psi)

Ef = Elastic modulus of the FRP fiber material (psi)

Ep = Modulus of elasticity of prestressing tendons (psi)

Es = Elastic modulus of reinforcing steel (psi)

ff = Stress level developed in the FRP (psi)

ffu = Design strength of the FRP material (psi)

fps = Stress level in prestressing tendons (psi)

fpu = Ultimate strength of prestressing tendons (psi)

fpy = Yield strength of prestressing tendons (psi)

fs = Stress level in the tension steel (psi)

fy = Yield strength of mild steel (psi)

f’s = Stress level in the compression steel (psi)

h = Total height of the section and depth to the FRP flexural reinforcement (in.)

Icr = Moment of inertia of the cracked concrete section (in.4)

Ig = Moment of inertia of the gross concrete section (in.4)

k = Ratio of the depth to the elastic neutral axis to the effective depth, d

l1 = The sum of the lengths of loaded spans that are connected with a continuous, unbondedprestressing tendon (in.)

l2 = The length of an unbonded tendon between end anchorages (in.)

ln = Clear span of the beam (in.)



Chapter 6 Flexural Strengthening

6-3 05/02

Symbols and Notation

Mip = Moment due to loads in place at the time of FRP installation (mainly dead loads) not includingmoments caused by eccentric prestressing forces. (lb.-in.)

Mn = Nominal moment capacity of a section (lb.-in.)

Ms = Moment due to service loads (lb.-in.)

Mu = Moment due to factored loads (lb.-in.)

n = Number of fiber plies

Pe = Effective prestress force at the time of FRP installation (lb.)

rg = Radius of gyration of the gross concrete section = gg A/I (in.)

tf = Thickness of one ply of fiber sheet (in.)

Vn = Nominal shear strength (lb.)

Vu = Ultimate shear strength (lb.)

wf = Total width of the FRP laminate (in.)

u = Bond reduction factor for unbonded tendons at the ultimate limit state

1 = Multiplier on c to determine the depth of an equivalent rectangular stress distribution forconcrete

b = Strain level in the concrete substrate developed by a given bending moment. Tension ispositive. (in./in.)

bi = Strain level in the concrete substrate at the time of FRP installation. Tension is positive. (in./in.)

c = Maximum compressive strain level in the concrete (in./in.)

'c = Strain level in the concrete corresponding to the peak value of stress, f'c (in./in.)

cu = Maximum usable compressive strain in the concrete = 0.003 (in./in.)

f = Strain level in the FRP developed by a given bending moment (in./in.)

fu = Ultimate strain (elongation) of the FRP material (in./in.)

p = Total strain level in prestressing tendons (in./in.)

pu = Ultimate elongation of prestressing tendons (in./in.)

s = Strain level in the tension steel (in./in.)

’s = Strain level in the compression steel (in./in.)

sy = Strain level in the tension steel at its yield point = fy/Es (in./in.)

= Strength reduction factor for flexure

= Multiplier on f'c to determine the intensity of an equivalent rectangular stress distribution forconcrete




05/026-4

6.1.1 Design Approach

The design of bonded FRP reinforcement for flexural members is based on limit statesprinciples. Strength, ductility and serviceability requirements should all be investigated.

The design process requires investigating several possible failure modes and limit states.The recommended design procedure outlined in this chapter is to obtain a preliminary

area of FRP and modify this area based on a comprehensive analysis of the section for strength, ductility, and serviceability. Analysis calculations are necessarily iterative, andimplementation of computer programs to automate the iteration process is highlyrecommended.

This chapter addresses the analysis and design of sections only. After the area of FRP isdetermined for critical sections, the reinforcement should be appropriately detailed for thestructure being considered. Proper detailing of reinforcement is presented in Chapter 10and Part 5.

The following assumptions apply to this chapter:

1) There no slip between the FRP and the bonded substrate*

2) Plane sections remain plane (Bernoulli’s principle)

3) Loads in place at the time of FRP installation are within the structure’s

elastic range

4) The existing conditions have been competently evaluated (including steelareas and properties, concrete strengths, effective prestressing forces, etc.)

The procedures outlined in this chapter use the load factors and strength reduction factorsstipulated in ACI 318

4. Engineers may wish to incorporate additional safety factors

according to uncertainties with the existing structure or degradation of the bondedconcrete substrate.

6.2 Existing Condition Assessment

Externally bonded reinforcement is typically installed unstressed. However, the surface towhich it is bonded is typically under stresses due to the structure’s self weight,prestressing forces, or any other loads present at the time of installation. The strain in the

FRP will, therefore, be different than the strain in the concrete substrate. In order to applystrain compatibility, the existing state of strain on the surface of the concrete substratemust be assessed. This initial strain level may then be subtracted from the strain level inthe concrete substrate (determined by strain compatibility) to find the strain level in theFRP as shown in Equation (6-1).

fu bi bf (6-1)

6.2.1 Initial Strains in Cracked Concrete

Typically a reinforced concrete structure, at some point in its history, will experience abending moment greater than its cracking moment. Initial strains may be determinedusing cracked section properties of the unstrengthened section. Under the assumptionthat the moment in place at the time of FRP installation is within the elastic range of thesection, the initial strain in the concrete substrate may be determined from Equation (6-2).

ccr

ip bi

EI

)kdh(M (6-2)

* This assumption is valid only if the there is perfect bond between the FRP and the substrate. It isrecognized that perfect bond does not exist and that there is some shear deformation of the adhesiveresulting in some relative slip between the FRP and the substrate. However, the relative magnitudeof the strain differential between the FRP and the substrate is such that it may be neglected in design.




6-5 05/02

6.2.2 Initial Strains in Uncracked Concrete

There are situations where the section remains uncracked at the time of FRP installation(particularly in the case of prestressed concrete). If this is true, the concrete is stilleffective in tension and the initial state of strain may be determined from a simplehomogeneous, elastic section analysis (Equation 6-3).

2g

b

cc

e

cg

bip bi

r

ec

1EA

P

EI

cM

(6-3)

6.3 Preliminary Design

Before proceeding with a comprehensive analysis and design of the strengtheningsystem, some initial computations should be performed to determine whether it is possibleto achieve the desired load level. The maximum load level that may be achieved may begoverned by flexural failure, shear failure, deflection limitations, or allowable stresslimitations.

Initial considerations of the following criteria should be made. Each of the criteria listedshould be checked with the structural geometry and material properties of the existing structure and the load conditions required for the strengthened structure.

6.3.1 Existing Shear Strength

The load level that can be achieved may be controlled by the existing structure’s shear strength. Therefore, after the repair, the nominal shear strength of the beam should begreater than the shear force caused by increased loads from strengthening. Thisrequirement is defined by Equation (6-4).

edstrengthen,uexisting,n VV (6-4)

For concrete beams, it may be possible to provide additional shear strength with FRPshear reinforcement bonded to the sides of the beam (see Chapter 7).

6.3.2 Existing Stiffness

Bonded FRP does not significantly change the stiffness of a flexural member. Althoughsome additional stiffness may be achieved, the increase is typically not great. Deflectioncomputations using the existing section properties and the loads on the strengthenedstructure will provide a reasonable estimate of service deflections.

6.3.3 Controlling Working Stress

The use of FRP for flexural strengthening is most useful in tension controlled sections.Bonded FRP will not be as effective if the section is compression controlled. Therefore,an initial check of the working stress in the concrete using the existing section propertiesand the existing load condition should be performed. If the working stress in the concreteexceeds the allowable value, the effectiveness of FRP reinforcement will be limited.




05/026-6

6.4 Ultimate Strength Analysis

The ultimate limit state analysis is used to calculate the capacity of the section bycombining stress equilibrium, strain compatibility, and the constitutive laws of the materialsat failure. The stress and strain distributions at ultimate are shown in Figure 6.1. The

non-linear stress strain behavior of concrete may be replaced, for computational ease, by

a rectangular stress block with dimensions f'c x 1c. Note that the Whitney stress block

employed by ACI 3184 is not always valid. See discussion in Section 6.4.1.2.

The ultimate strength of a flexural member strengthened with FRP is generally controlledby either failure of the concrete by compression crushing or failure of the FRP by tensilefracture. In order to assess the nominal moment capacity of the beam, it is important todetermine if these failures occur before or after yielding of the existing steel. As a result,the overall behavior of the member will be dramatically affected by limiting failure mode.The following list summarizes the possible flexural failure modes. For any given section, itis necessary to determine which failure mode will control.

1) Concrete crushing before steel yielding

2) FRP rupture before steel yielding

3) Steel yielding followed by concrete crushing

4) Steel yielding followed by FRP rupture

In addition to these flexural failure modes, other localized premature failures at theconcrete / FRP interface are possible

5, 6. However, these failure modes can be avoided

through proper detailing of the FRP reinforcement. Guidelines for detailing FRPreinforcement are given in Chapter 10.


The general equation for the nominal moment capacity of a reinforced concrete sectionstrengthened with FRP flexural reinforcement is given in Equation (6-5).

2

c

hf A85.0d2

c

f A2

c

df AM

1

f f

1

ss

1

ssn (6-5)

The term f s indicates that the reinforcing steel is not necessarily at its yield stress. Additionof FRP to the beam may result in over-reinforcement for moment capacity thus the steelwill not yield. The 0.85 factor applied to the moment contribution of the FRP reinforcementis additional to the three standard deviation reduction of the strength of the FRP. Theadditional 0.85 reduction term is to be used at the discretion of the engineer.

f'c

d

d'

h

c 1c

f s

f's

f f

f s

f's

f f

c

's

s

f bi

b

Figure 6.1 – Strain and stress distribution in a RC section at ultimate




6-7 05/02

The stresses in each of the materials will depend on the strain distribution and thegoverning failure mode. Because of the number of variables involved, there is no directprocedure for determining the strain distribution and failure mode. Instead, a trial anderror procedure is necessary. This procedure involves first estimating the depth to theneutral axis, c, and determining the failure mode based on this estimate. The estimateddepth to the neutral axis may be confirmed or modified based on strain compatibility, theconstitutive laws of the materials, and internal force equilibrium. In most situations, a first

estimate of c = 0.15d is reasonable.With the estimate of c, the failure mode may be checked by the following criteria:

If

c

chcu bifu , failure is controlled by concrete crushing.

If

c

chcu bifu , failure is controlled by FRP rupture.

6.4.1.1 Failure by Concrete Crushing

When failure is governed by concrete crushing, the strain in the concrete at failure will be

at its maximum usable strain, cu.

cuc (6-6)

Strain levels in the tension steel and compression steel may be determined based on thisknown strain level in the concrete and the assumed neutral axis position.

c

cdcus (6-7)

c

dccus (6-8)

The strain in the FRP may be determined by finding the strain in the concrete substrate atultimate and subtracting the strain in the concrete substrate at the time of FRP installation.

bicuf c

ch

(6-9)

Because the concrete is at its maximum usable strain level, the rectangular stress blockspecified in ACI 318 may be used to approximate the actual non-linear stress distribution

in the concrete (i.e. = 0.85, 1 from ACI 318 Chapter 10.2.7.3)4. Stresses in the steel may

be considered proportional to strains below the yield point and should be taken as theyield stress for strains beyond the yield point (use an elastic-plastic assumption).

ysss f Ef (6-10)

ysss f Ef (6-11)

The FRP sheet may be taken as linear-elastic to failure.

f f f Ef (6-12)

The estimated value of c may then be checked against the value obtained from Equation(6-13), to satisfy equilibrium of the internal stress resultants.

bf 85.0

f Af Af Ac

1c

f f ssss

(6-13)




05/026-8

6.4.1.2 Failure by FRP Rupture

The calculation procedure used to compute the nominal moment capacity of a sectionwhen failure is governed by FRP rupture is similar. In this case, the known value of strainin the FRP may be used in conjunction with the estimated neutral axis location todetermine the strain level in each of the materials.

bi bfuf (6-24)

ch

c bifuc (6-15)

ch

cd bifus (6-16)

ch

dc bifus (6-17)

Stresses in the steel can again be determined by Equations (6-10) and (6-11), and thestress in the FRP, f f , may be taken as the ultimate tensile strength, f fu. Because theconcrete does not reach its ultimate strain in compression, the Whitney stress block (used

by ACI 3184

) is not appropriate. The stress resultant for concrete should be determinedfrom an appropriate non-linear stress-strain relationship or by a rectangular stress blocksuitable for the particular level of strain in the concrete. Parameters for such a stressblock are given in Equations (6-18) and (6-19)

7. These values may also be determined

from Figures A.1 and A.2 in Appendix A.

2c

2ccc

cc1

cc1

1ln

tan42

(6-18)

cc1

2c

2c1ln90.0

(6-19)

wherec

cc

E

f 71.1 , and

c

c1

'

tan is computed in radians.

Using the equivalent stress block method, the internal force equilibrium equation is givenin Equation (6-20). This equation is again used to check the estimated depth to theneutral axis.

bf

f Af Af Ac

1c

fuf ssss

(6-20)

6.4.2 Prestressed Concrete

The analysis of a prestressed concrete section strengthened with FRP flexuralreinforcement is analogous to that of a partially prestressed beam. The nominal momentcapacity of a prestressed concrete section may be determined from Equation (6-23).

2

chf A85.0

2

cdf AM 1

f f 1

p ps pn (6-23)




6-9 05/02

A similar approach involving estimating the depth to the neutral axis is required todetermine the stress levels in each of the materials. The estimate on the neutral axisdepth must be checked by finding the strain and stress levels in all of the materials andsubstituting them into Equation (6-42).

bf

f Af Ac

1c

fuf ps p

(6-42)

If failure is governed by concrete crushing, Equations (6-6) to (6-12) may be used todetermine the strain and stress levels in the FRP and mild reinforcing steel. If failure isgoverned by FRP rupture, Equations (6-24) to (6-19) apply.

The total strain in the prestressing tendons is due to strains at three load stages as shownin Figure 6.2.

1

23

Prestressing Steel

Centroid

p1 p3 p2

p

Load Stage 1: Prestress Alone

(Effective)

Load Stage 2: Decompression of

Prestressing Steel

Load Stage 3: Ultimate Load

Figure 6.2 – Strain distribution in a PC section at various stages of loading

First, the strain in the tendons due to the initial application of the prestress force and any

subsequent losses may be determined from Equation (6-25).

p p

e1 p

EA

P (6-25)

The second load stage is at decompression of the concrete at the level of the tendons.

2

2

cc

e2 p

r

e1

EA

P(6-26)

After decompression, the strain in the tendons may be determined by strain compatibility if the tendons are bonded to the concrete. The strain level in the tendons at the third loadstage may be determined from Equation (6-27) for concrete crushing or Equation (6-28)

for FRP rupture.

c

cd pcu3 p for concrete crushing (6-27)

ch

cd p bifu3 p for FRP rupture (6-28)




05/026-10

The total strain in the tendons is then the sum of the strains at each load stage as inEquation (6-29).

3 p2 p1 p p (6-29)

The stress in the tendons should be determined from an appropriate equation for thestress-strain relationship of the particular prestressing steel. The PCI Handbook gives the

following equations for Grade 250 and 270 tendons

8

.

008.0for 2000

0065.0

75f

008.0for E

f p

p pu

p p p

ps for Grade 270 steel (6-210)

008.0for 2000

006.0

58f

008.0for E

f p

p pu

p p p

ps for Grade 250 steel (6-211)

In some rare cases, the strain levels in the tendons may be high enough to cause tensilefracture of the prestressing steel. For this reason, the strain in the prestressing steelshould be limited to a value below 0.03.

6.4.2.1 Special Consideration for Unbonded Tendons

When the tendons are bonded to the surrounding concrete as in the case of pre-tensionedtendons or post-tensioned tendons in grouted ducts, it is reasonable to assume that thestrain in the tendons due to loading stage 3 is the same as that in the surroundingconcrete. If the tendons are unbonded as in the case of post-tensioned tendons ingreased ducts, the tendons are free to slip relative to the surrounding concrete. The strainin the tendon does not, therefore, correspond to the strain level in the surroundingconcrete, and strain compatibility does not exist. ACI addresses this by providingseparate equations for the stress in unbonded tendons at ultimate. However, theseequations are only applicable for the traditional concrete crushing failure mode. In thecase of an FRP strengthened section, failure may be controlled by FRP rupture. Thus, adifferent approach is needed.

One of the most convenient methods of dealing with unbonded tendons is to proceed as if the strains were compatible and then apply a bond reduction factor to account for thetendon slip. An accepted formulation for the bond reduction factor is available in theliterature

9 and is given in Equation (6-30). This bond reduction coefficient is valid for a

continuous beam loaded with a uniformly distributed load. Reduction factors for other conditions are also available.

2

1

pnu

l

l

dl

0.3 (6-30)

In this equation l 1 is the length of all the loaded spans that a continuous tendon coversand l2 is the length of the tendon between end anchorages. With this reduction factor, the

total strain in the unbonded tendons may be found by Equation (6-31) where the strains atthe various load levels are those given in Equations (6-25) through (6-28).

3 pu2 p1 p p (6-31)

It has been further recognized that unbonded tendons will rupture at an average stresswell below the ultimate strength of the prestressing steel. It is suggested that the stress inthe tendons at ultimate be limited to below the yield stress for unbonded tendons. Thestress will therefore be proportional to the strain and may be expressed as Equation

(6-32).

py p p ps f 94.0Ef (6-32)




6-11 05/02

6.4.3 Summary of Strength Equations

The ultimate strength of any section may be computed by assuming a strain distribution(estimating the depth to the neutral axis), determining the governing mode of failure, andchecking or revising the assumption based on stress equilibrium. Once the actual strainand stress distribution is found through trial and error, the nominal moment capacity maybe determined by computing the moment of resistance of the stress resultants.

6.5 Ductility

The use of FRP as a means of flexural strengthening will compromise the ductility of theoriginal system. Figure 6.3 shows the idealized moment curvature relationships of abonded FRP strengthened beam. Significant increases in moment capacity with FRPsheets are afforded at the sake of ductility. In many cases, the loss of ductility isnegligible. However, sections that experience a significant loss in ductility must beaddressed. The approach taken by this manual follows the philosophy of ACI 318 Appendix B, where a section with low ductility must compensate with a higher strengthreserve

4. The higher reserve of strength is achieved by applying a strength reduction

factor of 0.70 to brittle sections as opposed to 0.90 for ductile sections.

Curvature

M o m e n t

Unstrengthened

Strengthened with 1 ply

Strengthened with 2 plies

Strengthened with 3 plies

Figure 6.3 – Typical idealized moment curvature relationship for various degrees of strengthening (RC beams)

Concrete crushing or FRP rupture before yielding of the steel is both brittle failure modes.Steel yielding followed by concrete crushing provides some level of ductility depending onhow far the steel is strained over the yield strain. Steel yielding followed by FRP rupture istypically ductile because the level of strain needed to rupture FRP is significantly higher than the strain level needed to yield the steel. Additionally, the tension steel and FRPsheet are at a similar distance from the neutral axis.

In addition to failure modes at the ultimate limit state, ductility is also affected by theservice condition. If the tension steel yields at service load levels, both ductility andresidual stresses become of concern. Working stress limits presented in Section 6.6 willguard against such circumstances.




05/026-12

6.5.1 Unreinforced Concrete

Although using externally bonded FRP as primary reinforcement may not berecommended, the designer may want to ignore the contribution of steel reinforcementdue to degradation problems. If no steel is considered in the design of the strengtheningsystem, then the failure should be considered to be brittle. Thus, the strength reduction

factor used should be = 0.70 to ensure an adequate reserve of strength.


The only brittle failure mode a reinforced concrete section could experience is concretecrushing. Lower ductility is also a concern in sections that, at ultimate, only strain thesteel to levels between the yield strain and twice the yield strain. These sections intraditional reinforced concrete design have reinforcement ratios roughly between thebalanced reinforcement ratio and 75% of the balanced reinforcement ratio. Thesesections must also have a higher reserve of strength than more ductile sections.

It is, therefore, recommended to use a strength reduction factor given by Equation (6-33),where s is the strain in the steel at the ultimate limit state determined from Equation (6-7).

sys

syssysys

sys

for 70.0

2for 20.050.0

2for 90.0

(6-33)

This equation sets the reduction factor at 0.90 for ductile sections where the steel isstrained over twice its yield strain, 0.70 for brittle sections where the steel does not yield,and provides a linear transition for the reduction factor between these two extremes. Thisis presented graphically in Figure 6.4.

0.90

0.70

Steel Strain at

Ultimate

2sysy

Figure 6.4 – Graph representing the strength reduction factor as a function of the ductility

6.5.3 Prestressed Concrete

The addition of FRP reinforcement to a prestressed flexural element does not dramaticallyaffect its ductility. It is recommended that the strength reduction factor of 0.90 bemaintained for all prestressed concrete sections.




6-13 05/02

6.6 Serviceability Requirements

Serviceability limit states are crucial to obtaining a well-designed strengthening system.The significant increases in the ultimate capacity of a section afforded by FRPreinforcement are not achieved by substantial increases in stiffness (though someadditional stiffness is obtained). When the demand on a flexural element is increased, it isimportant, therefore, to determine the effects the increase will have on the service loadstresses and deflections.

6.6.1 Working Stress Analysis

Insuring that the working stresses of an FRP reinforced section fall within allowableranges is important in maintaining safe levels of ductility and performance under cyclicloading. Care must be taken to avoid yielding the steel at service load levels. Unliketraditional reinforced concrete design, it is necessary to check allowable stresses inaddition to the ultimate limit state.

6.6.1.1 Allowable Stresses

The allowable stresses for each of the various materials are listed in Table 6.1. Theallowable stress in the concrete and mild compression steel are taken directly from coderequirements

4. For mild tension steel, a higher allowable stress is suggested due to the

presence of an additional material capable of carrying tensile stress (i.e. the FRP). Theallowable stresses in the FRP materials are suggested to maintain their long-termperformance

10. Further reductions to the allowable stress may be prescribed by using the

duration and environmental factors, CD and C E. Subjected to sustained load greater than30% of ultimate for glass fibers and 95% of ultimate for carbon fibers, the fibers may faildue to creep rupture. The duration factor reflects this behavior. The environmental factor is determined from long term coupon testing in harsh conditions without protectivecoatings (see Chapter 5 – Durability). The environmental factor reflects degradationunder extreme conditions. Using these allowable stresses, performance of thesematerials under sustained loading or environmental exposure will not be compromised.

Table 6.1 – Allowable stresses in materials

Material Allowable Stress

Concrete (Compression) 0.45f'c

Mild Tension Steel 0.80fy

Mild Compression Steel 0.40fy

Prestressing Steel 0.74fpu < 0.82fpy

Carbon FRP (tension) 0.33CDCEffu

Glass FRP (tension) 0.33CDCEffu

Table 6.1.1 – FRP Adjustment FactorsFRP Material Duration Factor, CD Environmental Factor, CE

Carbon Fiber 1.00 0.65 – 1.00

Glass Fiber 0.30 0.60 – 1.00




05/026-14

6.6.1.2 Working Stresses in Reinforced Concrete

The computation of working stresses in reinforced concrete involves determining thedepth of the cracked neutral axis (assuming linear-elastic behavior of all materials) andcomputing the stresses in each material based on the service moment. The stress and

strain distribution for working stress analysis is shown in Figure 6.5. Similar toconventional reinforced concrete, the depth to the neutral axis at service may becomputed by taking the first moment of the areas of the transformed section. Thetransformed area of the FRP may be obtained by multiplying the area of FRP by themodular ratio of FRP to concrete. Although this method ignores the difference in the initialstrain level of the FRP, the initial strain level does not greatly influence the depth to theelastic neutral axis.

d

d'

h

b

kd

f s

f f

f's

c

's

s

f bi

b

f c

Figure 6.5: Strain and stress distribution for a working stress analysis

The stresses in each of the materials may be determined by Equations (6-34) to (6-37).

h3

kdhEAdkdd3

kdEAkdd3

kddEA

Ekdd3

kdhEAMf

f f ssss

sf f bis

s

(6-34)

kdd

kd

E

Ef f

s

csc

(6-35)

kdd

dkdf f ss

(6-126)

f bis

f sf E

kdd

kdh

E

Ef f

(6-37)




6-15 05/02

6.6.2 Deflections of Strengthened Beams

The cracked section properties of the strengthened section may be determined by using atransformed area of FRP according to its modular ratio, and the effective moment of inertia may be found by the traditional fashion (ACI 318-95 Equation 9-7). In computingthe effective moment of inertia, the maximum moment at the time deflections are

computed, Ma, should be taken equal to the full service moment. However, immediate

deflections should only be computed for moments applied after the strengthening is

completed, (Ms – Mip).11, 12, 13

6.6.3 Crack Widths

The crack width at service should be investigated using the Gergely-Lutz equation used inconventional reinforced concrete design

4. The effect of the FRP may be neglected in this

calculation. Available research has shown the presence of FRP to reduce the crack sizeand spacing, however its effect cannot be quantified at this time. Ignoring the contributionof the FRP will be conservative.

6.7 Examples from Practice

6.7.1 Retrofit of an Existing Reinforced Concrete Bridge Slab14

The 70-year-old, solid-slab,concrete bridge requiredstrengthening in order toaccommodate current trafficloads. Based on analysis,the new service loads willproduce a maximum positivebending moment of M s = 42

kip ft/ft, and the total factored

loads result in a design

moment of M u = 66 ki ft/ft. An assessment of theexisting bridge conditionyields the section information

given in 6.6. Testing andresearch into the material properties result in a nominal concrete strength f’c = 3000 psi and

a yield strength for the mild steel of f y = 30,000 psi. Upon inspection, the concrete is in

good condition and no signs of activecorrosion are present.

As a means of strengthening this structureto accommodate the larger loads, theWabo

®MBrace Composite Strengthening

System was employed. The followingoutlines the design procedure used todetermine the amount of Wabo

®MBrace

reinforcement required.

Determine the existing flexural capacity and whetherstrengthening is required

d =

1 6

. 5 ”

h =

1 8

. 5 ”

b = 12”

As = 1.5 in2/ft

Af = ?

Figure 6.6 – Geometry of unit strip for Example 6.7.1




05/026-16

in47.1)in12)( psi3000(85.0

) psi000,30)(in5.1(

bf 85.0

f Aa

2

c

ys

lbsin500,6382

in47.1in5.16) psi000,30)(in5.1(90.0

2

adf AM

2ysn

d'reqingStrengthenftkip66Mftkip2.53lbsin500,638M un

The existing capacity is 25% below the design moment capacity. It is reasonable that theWabo

®MBrace System will be capable of correcting this deficiency. Wabo

®MBrace CF

130 is selected for its high strength and excellent performance under sustained and cyclicloading.

Estimate the amount of CF 130 required.

It is recommended to design the area of FRP by making a rough estimate of the requiredarea based on the additional tensile force, T, required to equilibrate the momentdeficiency. Do note, however, that this is a rough estimate and should be modified basedon a full analysis.

kips34.10

)in5.16(90.0

ftin12)ftkip2.53ftkip66(

d90.0

MMT nu

2

fuest,f in0246.0

ksi55085.090.0

kips34.10

f 85.0

TA

Based on this area, the width of FRP may be computed. For a slab, a series of evenlyspaced FRP strips is typically used. Thus, the estimated width becomes:

in8.3)in0065.0(1

in0246.0

tn

Aw

2

f

f f

Try 1 ply, 4 in. wide Af = 0.026 in2

The actual flexural capacity must now be computed.

Find the existing state of strain on the soffit

Based on an existing condition assessment, the total moment in place at the time that theFRP will be installed is Mip = 20 kipft. The existing state of strain may be computed for

this moment assuming that the section is cracked.

ccr

ip bi

EI

)kdh(M from Equation (6-2).

The multiplier on the beam depth, d, to find the cracked neutral axis position is k = 0.326.Further, the cracked moment of inertia is Icr = 2570 in4. The strain level on the soffit at the

time of FRP installation, thus becomes:

430)ksi2850)(in2570(

)in5.16326.0in5.18)(ft/in12ftkip20(

4 bi

Estimate c, and adjust by trial and error

A first estimate of c = 0.15d is used. Thus, c = 0.15(16.5 in) = 2.475 in is the first estimate.




6-17 05/02

Find the mode of failure for the estimated c

RuptureFRP01942.001743.0

475.2

475.25.18003.0?000430.0017.0

c

ch? cu bifu

Find the strain level in each of the materials

017.0fuf

00263.0475.25.18

475.201743.0

ch

c bifuc

0149.0475.25.18

475.25.1601743.0

ch

cd bifus

Find the stress level in the FRP and steel

ff = ffu = 550 ksi

fs = fsy = 30 ksi since s >> sy

Find the parameters to define an equivalent concrete stress block

0015.0 psi000,850,2

) psi2500(71.1

E

f 71.1

c

cc

635.10015.0

00263.0

c

c

847.0

)635.1(1ln635.1

635.1tana635.142

1ln

tana42

22c

2ccc

cccc1

845.0635.1847.0

)635.1(1ln90.01ln90.0 2

cc1

2c

2c

Check the estimate on c

in300.2)in12(847.0) psi2500(845.0

) psi000,550)(in026.0(0) psi000,30(in5.1

bf

f Af Af Ac

22

1c

f f ssss

2.300 in 2.475 in A revision is required by iterating values of c.

A summary of the trial and error procedure is given in Table 6.2.

Table 6.2 – Summary of trial and error calculations to obtain c

cest

(in)FailureMode

fff

(ksi) s

fs

(ksi) c 1 ccalc

(in)

2.475 FRP 0.017 550 0.0152 30 0.00269 0.847 0.845 2.300

2.400 FRP 0.017 550 0.0152 30 0.00259 0.840 0.849 2.311

2.330 FRP 0.017 550 0.0152 30 0.00251 0.833 0.851 2.323

Thus, the value of c is taken as 2.33 in.




05/026-18

Compute the nominal moment capacity

ftkip76inkip912M

2

)33.2(833.05.18)550)(026.0(85.00

2

)33.2(833.05.16)30(5.1

2

chf A85.0d

2

cf A

2

cdf AM

n

1f f

1ss

1ssn

Compute the design moment capacity

Because the strain in the steel at ultimate is much greater than twice its yield strain, the

section retains sufficient ductility. The factor is therefore taken as 0.90.

ftkip66Mftkip4.68)ftkip76(90.0M un O.K.

Check serviceability by checking working stresses

Compute the elastic depth to the cracked neutral axis, kd.

By taking the first moments of the areas of concrete, steel (transformed to concrete), andFRP (transformed to concrete), the following expression is obtained:

0)kdin5.18)(in026.0(ksi2771

ksi33000)kdin5.16)(in5.1(

ksi2771

ksi29000

2

in12)kd(

0kdhAnkddAn2

b)kd(

222

f f ss

2

Solving this quadratic, the depth to the neutral axis is kd = 5.185 inches (k = 0.314).




6-19 05/02

Compute the stress in the steel at a service moment of Ms = 42 kip-ft = 504 kip-in.

kdh3

kdhEAdkdd3

kdEAkdd3

kddEA

Ekdd3

kdhEAMf

f f ssss

sf f bis

s

)185.55.18(3

185.55.18)33000)(026.0(0)185.55.16(

3

185.55.16)29000(5.1

)29000)(185.55.16(3

185.5

5.18)33000)(026.0(00039.0504

ksi24f 80.0ksi41.22f ys O.K.

Compute the maximum compressive stress in the concrete at service

ksi106.1185.55.16

185.5

29000

2771ksi57.22

kdd

kd

E

Ef f

s

csc

psi1350f 45.0 psi1106f cc O.K.

Compute the stress in the FRP at service

ksi76.15)ksi33000(00044.045.55.16

45.55.18

29

33ksi53.22E

kdd

kdh

E

Ef f f bi

s

f sf

ksiksi f C C ksi f fu E D f 112550650950330330916 ). )( .( ... O.K.

Conclusions

Based on the analysis, one ply of FRP with a width of 4” per 12” width of beam will be sufficient tostrengthen the bridge. The final design could call for a 10” wide one-ply strip spaced at 30” on center for constructability and material economy. Because the Wabo

®MBrace CF 130 sheets come in 20” wide rolls,

these strips are easily field cut.

As evidence of the validity of this design example, a full size mock-up of a unit strip of this

bridge slab was tested to failure. The experimental beam was constructed using similar materials and the exact section and span dimensions. Figure 6.7 shows the experimentalload deflection curve as compared to the theoretical curve that is based on the principlespresented in this chapter. These curves show reasonable correlation. In addition, thepredicted failure mode, FRP rupture, was the mode of failure observed during testing.




05/026-20

Concrete

Crushing

Concrete

Crushing

FRP RuptureFRP Rupture

0

10000

20000

30000

40000

50000

60000

0 1 2 3 4 5 6 7 8

Deflection (in)

L o a d ( l b s )

Theoretical (Before Strengthening)

Experimental (Before Strengthening)

Theoretical (After Strengthening)

Experimental (After Strengthening)

Figure 6.7 – Experimental validation of Example 6.7.1

6.8 References

2 Kobayashi, A., Endoh, M., Kuroda, H., and Kliger, H., (1995). “Use of Carbon Fiber Tow Sheet

Reinforcement for Improved Bridge Capacity Ratings in Japan,” Proceedings of the International SAMPE Symposium and Exhibition, Anaheim, California, May 8-11.

3 Nanni, A., (1995). "Concrete Repair with Externally Bonded FRP Reinforcement: Examples from Japan,"

Concrete International , v. 17, no. 6, June, pp. 22-26.

4 ACI-318, (1995). "Building Code Requirements for Reinforced Concrete." American Concrete Institute.

5 Triantafillou, T. C. and Plevris, N., (1992). "Strengthening of RC Beams with Epoxy-Bonded Fibre-

Composite Materials," Materials and Structures, Vol. 25, pp. 201-211.

6 Oehlers, D. J., (1992). “Reinforced Concrete Beams with Plates Glued to Their Soffits,” Journal of Structural Engineering , Vol. 118, No. 8, August, pp. 2023-2038.

7 Todeschini, C., Bianchini, A, and Kesler, C. (1982) "Behavior of Concrete Columns Reinforced with High

Strength Steels." ACI Journal, Proceedings, Vol. 61, No. 6, pp 701-716, November-December

8 PCI Design Handbook Edition 3 (1985), Precast Concrete Institute

9 Namaan, A. and Alkhairi, F. (1991) "Stress at Ultimate in Unbonded Post-Tensioning Tendons: Part 2 --

Proposed Methodology." ACI Structural Journal , Vol. 88, No. 6, November-December, pp 683-692.




6-21 05/02

10 ACI Committee 440 (1996), “State-of-the-Art Report on FRP for Concrete Structures,” ACI440R-96,

American Concrete Institute, Farmington Hills, MI, 68 pgs.

11 Arduini, M. and Nanni, A., (1997). "Behavior of Pre-Cracked RC Beams Strengthened with Carbon FRP

Sheets," ASCE, Journal of Composites in Construction, Vol. 1, No. 2, May, pp. 63-70.

12 Sharif, A., Al-Sulaimani, G., Basunbul, A., Baluch, M., and Ghaleb, B., (1994). "Strengthening of Initially

Loaded Reinforced Concrete Beams Using FRP Plates," ACI Structural Journal , Vol. 91, No. 2, pp160-168.

13 Nanni, A., Focacci, F., and Cobb, C.A., “Proposed Procedure for the Design of RC Flexural Members

Strengthened with FRP Sheets,” Proceedings, ICCI-98, Tucson, AZ, Jan 5-7, 1998, Vol. 1, pp. 187-201.

14 Mayo, R.L., Nanni. A,. Gold, W., and Barker, M., “Strengthening of Bridge G270 with Externally Bonded

CFRP Reinforcement,” FRPRCS-4, Baltimore, MD, 1999 (submitted).



Chapter 7 Shear Strengthening

7.1 GENERAL 7-2

7.1.1 Notation 7-2

7.2 SHEAR STRENGTHENING OPTIONS 7-3

7.2.1 Bonded Surface Configuration 7-3

7.2.2 Shear Reinforcement Distribution 7-4

7.2.3 Fiber Orientation 7-4

7.2.4 Bi-axial Reinforcement 7-5

7.3 STRENGTH DESIGN 7-5 7.3.1 Shear Capacity of a FRP Strengthened Section 7-5

7.3.2 Contribution of FRP Reinforcement to the Shear Capacity 7-5

7.3.3 General Application of the Equations to Shear Problems 7-9

7.3.4 Design Recommendations 7-9

7.4 EXAMPLE PROBLEM 7-11

7.4.1 Correcting the Omission of Steel Stirrups 7-11

7.4.2 Accomodating a New Load Pattern 7-16

7.5 REFERENCES 7-19




05/30/027-2


7.1 General

This chapter addresses the design of bonded FRP reinforcement as a means of increasing the shear capacity of a concrete beam. Partial or complete beam

wrapping with transversely oriented FRP has been shown to improve the shear strength of beams

1, 2, 3. The amount of additional strength that may be achieved

is dependent on several factors including the wrapping scheme, the amount andtype of FRP, the existing concrete strength, and the nature of the loads andsupport conditions. It is also important to realize that because the overall beamshear strength is significantly dependent on the interfacial bond between the FRPand concrete (especially in the case of partially wrapped beams); the additionalshear strength is not necessarily proportional to the amount of FRP used. Thisphenomenon will become evident in the design procedure.

7.1.1 Notation

Afv = Total area of one strip of transverse FRP reinforcement = 2 n tf wf (in2)

bw = Width of the web of the cross section (average width for tapered sections) (in.)

d = Depth to the tension steel reinforcement centroid (prestressed and/or mild) (in.)

df = Depth of the FRP shear reinforcement (typically d – hs) (in.)

dfe = Effective depth of the FRP shear reinforcement considering only sufficiently bondedareas (in.)

Ef = Elastic modulus of FRP (psi)

f'c = Nominal compressive concrete strength (psi)

ffe = Stress level in the FRP shear reinforcement at failure (psi)

ffu = Ultimate (rupture) strength of FRP (psi)hs = Thickness of the monolithic slab or flange, if present (in.)

k1 = Multiplier on the effective bond length to account for the concrete strength

k2 = Multiplier on the effective bond length to account for the wrapping scheme

Le = Effective bond length of the FRP strip (in.)

Lo = Effective bond length of one ply of FRP (in.)

n = Number of plies of FRP shear reinforcement with fibers oriented in the primary ()direction

R = Reduction factor on the ultimate strength of the FRP to find the stress level in the FRP

at failuresf = Spacing of the strips of FRP shear reinforcement. If continuous reinforcement is used,

the spacing of the strips should be set equal to the width of the strip, wf. (in.)

tf = Thickness of one ply of fiber reinforcement (in.)

Vc = Shear strength of the concrete in a given section (lb.)

Vf = Shear strength of the transverse FRP reinforcement in a given section (lb.)




05/30/02 7-3

Vn = Nominal shear strength of a given section (lb.)

Vs = Shear strength of the transverse mild steel reinforcement in a given section (lb.)

wf = Width of one strip of FRP shear reinforcement (in.)

= Orientation of the primary fibers with respect to the longitudinal beam axis (degrees).

fu = Ultimate strain (elongation) of the FRP material (in./in.)

= Strength reduction factor for shear

7.2 Shear Strengthening Options

The Wabo®MBrace Composite Strengthening System offers the designer several

options for shear strengthening. The system is used to wrap a concrete sectionwith the fibers in the transverse direction in order to reinforce diagonal tensioncracks in much the same way as steel stirrups. From this general approach,several configurations of FRP shear reinforcement have been devised andinvestigated

4. The goal of this section is to describe several alternatives that are

available to the designer. The figures in this section all reference a simplysupported T-beam for clarity.

7.2.1 Bonded Shear Strengthening Configurations

The most effective method of shear strengthening with FRP sheets is to wrap theentire cross section of the beam with FRP as shown in Figure 7.1(a). Typically,this is not practical from a constructability standpoint. The presence of monolithicslabs or other supported elements often prevents wrapping the sheet around thetop of the section. One option might be to drill holes through the slab and wrapstrips or bands of FRP around the section. However, this method is often toocomplicated and costly.

(a) (b) (c)

Figure 7.1 – Various schemes for wrapping transverse FRP reinforcement. (a) FRPwrapped entirely around the beam. (b) FRP “U” wrap. (c) FRP bonded to the two sidesof the beam.

The most common method of shear strengthening is to wrap the sides andbottom of the section. This method referred to as a “U” wrap and shown in

Figure 7.1(b). The “U” wrap is practical and is effective in increasing thesection’s shear strength. The use of the “U” wrap is, however, only highlyeffective in positive moment regions. In negative moment regions, shear cracking initiates from the top of the section near the slab. Due to its locationbelow the slab, the FRP may not be able to control the initiation of these cracks.Once these cracks open, there is the potential for the crack to drive throughsection without any reinforcing effect from the FRP.




05/30/027-4

In some situations, it may not be possible to wrap the top or bottom of thesection. Shear strengthening is still possible by placing the reinforcement onboth sides of the section as shown in Figure 7.1(c). However, the effectivenessof this configuration is limited due to possible anchorage confines of the FRPsheet.

7.2.2 Shear Reinforcement Spacing

(a) (b)

Figure 7.2 – Various reinforcement distributions. (a) Continuous reinforcement. (b)Reinforcement placed in strips.

The transverse FRP reinforcement may be in the form of a continuous jacket or as spaced strips as shown in Figure 7.2. The use of strips may be effective inoptimizing the amount of material used. Furthermore, if the entire length of thebeam is to be wrapped, the use of strips may allow for better moisture migrationthrough the concrete.

7.2.3 Fiber Orientation

Because FRP is an anisotropic material with high strength in the direction of thefibers, the fibers may be oriented in such a way to best reinforce diagonal tensioncracks. This is achieved by the use of inclined strips, Figure 7.3(a). However,vertically oriented plies are easier to install and may reduce the total length of thewrap, Figure 7.3(b).

(a) (b)

Figure 7.3 – Sheets with their fibers oriented in various primary directions. (a) 45 wrap. (b) 90 wrap.




05/30/02 7-5

7.2.4 Bi-axial Reinforcement

It has been found that the use of bi-axial FRP reinforcement increases the overallperformance of the system

5. Bi-axial FRP reinforcement is achieved by placing

two unidirectional FRP plies in mutually perpendicular directions, Figure 7.4. Theply in the primary direction acts to provide most of the reinforcement. While theply in the secondary direction limits shear crack openings and provides

anchorage for the ply in the primary direction.

(a) (b)

Figure 7.4 – Beams with bi-axial FRP shear reinforcement. (a) 0 /90 wrap. (b) 45 wrap.

7.3 Strength Design

At the ultimate limit state, it is not possible to attain the full strength of the FRP ina shear strengthening situation. Failure is governed by either rupture of thesheet at average stress levels well below ultimate due to stress concentrations,debonding of the FRP sheet from the concrete surface, or a significant decreasein the post-cracking concrete shear strength from a loss of aggregate interlock.The strength design procedure takes all of these failure modes intoconsideration.

7.3.1 Shear Capacity of a FRP Strengthened Section

The nominal shear strength of a reinforced concrete section, per ACI 318-95, isthe sum of the shear strength of the concrete and the strength of the steel shear

reinforcement6. For beams strengthened with FRP shear reinforcement, thenominal shear strength may be computed by the addition of a third term toaccount for the contribution of the FRP sheet. The nominal shear strength isexpressed in Equation (7-1). A factor of 0.85 is applied to the contribution of FRP to the shear capacity because of the novelty of this repair technique.

*

f scn V85.0VVV (7-1)

The design shear strength, Vn, is obtained by multiplying the nominal shear

strength by a strength reduction factor for shear, . It is suggested that the

reduction factor of = 0.85 for shear given in ACI 318-956 be maintained. The

designer may wish to incorporate a more conservative factor if there areuncertainties about the condition of the existing structure.

7.3.2 Contribution of FRP Reinforcement to the Shear Capacity

The general expression for the additional capacity afforded by FRP shear reinforcement is given in Equation (7-2). The determination of the capacity of FRP shear reinforcement is similar to that for the shear contribution of transversesteel reinforcement

7, and the equation is consistent with the ACI format. As in

* As with the factor used for flexural FRP reinforcement, there is no theoretical reliability basis for this factor at this time.




05/30/027-6

the ACI equation, the shear contribution is computed by assuming a shear crackangle of 45 degrees, computing the area of reinforcement that crosses thispotential crack, and multiplying the area by the strength of the material.

6

d bf 4

s

dcossinf AV wc

f

f fefvf

A reasonable limit on the maximum amount of additional shear strength that maybe achieved is placed in terms of the shear strength of the concrete. This limit isimposed primarily to establish a basis for judging when the use of FRP is notsuitable for shear reinforcement. Furthermore, this limit maintains the use of FRP as supplemental reinforcement.

In order to determine the area of FRP reinforcement that crosses a potential 45-

degree shear crack, the terms Afv, df , sf , and are required. Afv is the area of onestrip of transverse FRP reinforcement covering two sides of the beam. This areamay be expressed by Equation (7-3), where n is the number of plies, tf is thethickness of one ply, and wf is the width of the strip.

f f fv wnt2A

In a positive moment region, the depth of the strip, df , is the horizontal projection

of the shear crack (assumed to be 45) minus the distance from the top of thecrack to the top of the sheet. Because shear cracks typically initiate as verticalcracks until they reach the depth the longitudinal steel reinforcement, theeffective depth of the FRP strip should be measured from the centroid of thesteel at the bottom of the section. Typically, strips extend only to the soffit of theslab at the top of the beam. Therefore, the effective depth of the FRP strip maybe computed by subtracting the slab depth, hs, from the depth to the steel, d.

df

wf

sf wf sf

(a) (b)

Figure 7.5 – Dimensions used to define the area of FRP for shear.(a) Vertically oriented FRP strips. (b) Inclined strips.




05/30/02 7-7

The spacing between the strips, sf , is defined as the distance from the centerlineof one strip to the centerline of an adjacent strip. Note that for continuous shear reinforcement, as shown in Figure 7.5(b), the spacing of the strip, sf , and thewidth of the strip, wf , are equal.

The angle defines the orientation of the primary fibers with respect to thelongitudinal axis of the beam. The primary fibers are most effective when

oriented perpendicular to the potential crack. Figure 7.5 summarizes thedefinition of the variables used to define the area of FRP that crosses a potentialshear crack.

The final variable in Equation (7-2) that is required to compute the shear capacityof the FRP sheet is the effective stress in the sheet at failure. As stated earlier,the ultimate strength of the sheet cannot be attained in a shear strengtheningsituation. The effective stress is therefore computed by applying a reductionfactor, R, on the ultimate strength as shown in Equation (7-4).

fufe Rf f

The reduction factor is determined by the governing mode of failure. For sheetswhich do not entirely wrap the beam cross section, the primary mode of failure isdebonding of the sheet from the concrete. By wrapping the section entirely,adequate anchorage is provided, and bond is less critical.

The other failure mode of interest is the loss of aggregate interlock in theconcrete. If the shear crack width becomes too large, aggregate interlock is lostalong with the majority of the shear strength of the concrete, Vc. In order tocontrol the shear crack width, the strain (and thus the stress) of the FRP sheet

must be limited. This limiting factor applies mainly to beams that are wrappedentirely, however it must be considered a general limiting factor for all wrappingschemes.

Consideration of these two failure modes was made in the development of Equation (7-5).

fufu

e21 005.0

468

Lk k R

The first part of this equation addresses debonding of the FRP sheet. Thisequation was developed from a combination of empirical and experimental workinvolving a determination of the bond strength of FRP, loaded in tension, toconcrete.

8This bond test arrangement is particularly well suited to a shear

strengthening situation because the method of force transfer is similar *.

* Note that for flexural FRP reinforcement, this bond mechanism is less applicable because flexural curvature tends tostabilize the progressive debonding of FRP from the concrete. See reference 11.




05/30/027-8

The limit of 0.005/fu on the equation addresses the loss of aggregate interlock.

Aggregate interlock is maintained by limiting the shear crack opening. It hasbeen suggested that this may be achieved by limiting the strain in the FRP tovalues on the order of 0.004 to 0.005 in/in.9 The limit used in this manual, 0.005,

is not on the conservative end of this range. However, this value has beenselected in recognition of additional safety factors in place for the calculation of

the design capacity (strength reduction factors and the factor of 0.85 applied tothe contribution of FRP).

The other possible failure mode, FRP rupture, has not been considered.However, this failure mode typically occurs at strains above 0.005 in/in.Therefore, this failure will only occur after loss of aggregate interlock.

In determining the limiting factor for bond, the effective bond length, Le, must bedetermined. According to experimental observations, the ultimate tensile forcethat the CFRP strip carries is not dependent on its total bonded length. Thereason for this is that load is sustained by bond only in a concentrated area of active bonding. Bond stresses in the remaining portion of the sheet are relativelysmall. If delamination occurs in this vicinity, the area of active bonding is shiftedto a new area. This action is repeated until delamination propagates completelythrough the length of the CFRP. Therefore, the maximum force that can becarried by bond stresses in the active bonding area governs the highest tensileforce that the sheet can carry. The effective bond length times the width of thestrip defines this active bonded area.

The effective bond length decreases with increasing stiffness of the sheet (moreplies). Physically, this results in the stress in the sheet being transferred to asmaller area of concrete and increasing the stress in the concrete. Thus, theaddition of more plies increases the overall strength, but the efficiency of the FRPsystem decreases. The equation for the effective bond length is given inEquation (7-6).10

oe Ln

1L

In this equation, Lo is the effective bond length for one ply of FRP. The effectivebond length for one ply of each of the Wabo

®MBrace Fiber Reinforcement

Systems has been computed and are given as follows:*

Lo = 2.0 in for CF 130

Lo = 1.5 in for CF 530

Lo = 2.5 in for EG 900†

* In general, the effective bond length of one ply of FRP may be determined by the equation:

58.0

f f

oEt

2500L . Also see

reference 10.

† The experimental base for shear strengthening with glass FRP is not extensive at this time. The designer should takeparticular care in specifying EG 900 for shear strengthening.




05/30/02 7-9

The effective bond length is further effected by the concrete strength and thebonded configuration (Figure 7.1). Thus two additional factors are applied tocompensate for these effects. The factor, k1, given in Equation (7-7) accounts for concrete strengths other than 4000 psi.

11

3/2

c1

4000f k

(7-7)

The factor k2 accounts for the type of wrapping scheme used. This factor isgiven in Equation (7-8).

f

fe2

d

dk

(7-8)

After a shear crack develops only that portion of FRP extending past the crack bythe effective bonded length will be capable of carrying shear. The depth of the

FRP reinforcement will, therefore, be reduced unless the FRP is anchored bywrapping it around the section. The effective depth may be computed based onthe wrapping scheme from the criteria given below.

12

ef fe Ldd if the FRP strip is “U” wrapped, Figure 7.1(b)

ef fe L2dd if the FRP strip is bonded only to the two sides of the beam,

Figure 7.1(c)

As stated earlier, bond becomes less of a concern when the sheet is wrappedentirely around the beam cross section. In this case the limiting factor for bondmay be disregarded, and the reduction factor, R, may be taken as the maximumvalue.

fu

005.0R if the beam is wrapped entirely, Figure 7.1(a)

7.3.3 General Application of the Equations to Shear Problems

The procedure given in Section 7.3.2 applies directly to FRP used to reinforceflexure-shear cracking in beams. This is only one of a wide variety of shear problems that may exist in a concrete structure. The procedure in Section 7.3.2can be extended to apply to other shear problems by modifying the term df .Instead of taking this variable as the depth to the steel minus the slab thickness,this variable may be set to the horizontal projection of a potential shear crack.

7.3.4 Design RecommendationsIn addition to strength considerations, there are several detailing issues that areof importance in design of FRP shear reinforcement. The details that applyspecifically to shear strengthening are addressed in this section.

7.3.4.1 Bi-axial FRP Reinforcement

The design equations presented do not address the use of bi-axial FRPreinforcement where the fibers are oriented in two perpendicular directions. Although the effect of this reinforcement is not quantifiable at this time, its use is




05/30/027-10

highly recommended. When shear cracks form, it is typically assumed that thedisplacement is in the vertical direction and the vertical component of theresistive force supplied by reinforcement is effective. However, in reality thedisplacement has a horizontal component as well resulting from rigid body

rotation about the shear crack tip. If only vertical plies of FRP are used ( = 90),there is nothing to resist this horizontal strain component. (In the case of steel

stirrups, this component is resisted by dowel action of the stirrup.) It is, therefore,recommended to use an additional horizontal ply ( = 0) to resist this movement

and further limit shear crack opening.

The horizontal ply also acts to arrest the vertical crack that starts at the bottom of the section (for positive bending) below the longitudinal steel centroid. Due tothis crack control mechanism, the horizontal ply should always be located asclose as possible to the bottom of the section for positive bending and as closeas possible to the top of the section for negative bending as possible.

Without a quantifiable method for determining the amount of secondaryreinforcement to use, a general approach will suffice. In general, one secondaryply should be used when one primary ply is used, and another secondary plyshould be used for every two additional primary plies. For example, a designusing 3 primary plies should include 2 secondary plies. Placement of the pliesshould alternate between primary and secondary with the primary ply placed first.

7.3.4.2 Spacing Requirements

Similar to steel shear reinforcement, the spacing of FRP strips should not be sowide as to allow the full formation of a diagonal crack without intercepting a strip.For this reason the strips should not be spaced by more than the maximum givenin Equation (7-9).

4

dws f max,f

7.3.4.3 Limit on Total Shear Reinforcement

ACI 318-95 Section 11.5.6.7 and 11.5.6.8 set a limit on the total shear strengththat may be provided by more than one type of shear reinforcement.

6 FRP shear

reinforcement should be included in this limit. A modification to ACI 318-95Section 11.5.6.8 is suggested by Equation (7-10).

d bf 8VV wcf s




05/30/02 7-11

7.3.5 Comparison to Experimental Data

The design procedure outlined has been compared to data from variousexperimental programs available in the literature

*. This comparison is shown in

Figure 7.6.

0

10

20

30

40

50

0 10 20 30 40 50

Experimental FRP Shear Contribution (kips)

C a l c u l a t e d

F R P S h e a r C o n t r i b u t i o n

( k i p s )

FRP Bonded to Sides OnlyFRP U-wrap

FRP Wrapped around Beam Entirely

Nominal Datum

Design Datum

Figure 7.6 – Comparison between experimental results and results obtained through the proposeddesign procedure.

In the figure, the line labeled “Nominal Datum” represents a perfect correlationbetween the computed nominal shear strength provided by the FRP, Vf , and theexperimental shear strength provided. The line labeled “Design Datum”represents a perfect correlation between the computed design shear strength

provided by the FRP, (0.85Vf), and the experimental shear strength provided.

Data points falling below the “Design Datum” represent beams with shear strengths that were higher than the computed design value and therefore,represent the design procedure as conservative. From the data, the designprocedure tends to be conservative in nearly all cases.

7.4 Example Problems

7.4.1 Correcting the Omission of Steel Stirrups

The T-beam shown in Figure 7.7 is simply supported on each end by masonrywalls. The beam has a span of ln = 30 ft and supports a uniformly distributed

dead load of wdl = 1.3 k/ft (including its own self-weight) and a uniformly

* The experimental data originate from several sources, however the data is summarized in Reference 8.




05/30/027-12

distributed live load of wll = 1.6 k/ft. The beam was originally designed with #3

stirrups spaced at 12” over mid-span and 6” near the support. However, some of the stirrups near the support were omitted during construction leaving stirrupsspaced at 12” throughout the entire length of the beam. It is desired to correctthe omission by using Wabo

®MBrace CF 130. Other pertinent data from the

construction specifications are as follows: f’c = 4000 psi, f y = 60 ksi, f vy = 40 ksi.

w = 12 in

hs = 6 in

= 36 in

d = 24 in

#3 Stirrups

@ 12” o.c.

Figure 7.7 – T-Beam cross section for Example 7.4.1.

Compute the existing capacity

Based on analysis, the shear capacity of the concrete is V c = 34.6 kips and theshear capacity of the stirrups is V s = 17.6 kips. Thus, the nominal shear capacityof the as-built beam is V n,existing = 54 kips. The factored shear demand at a

distance, d, away from the support is (V u / ) = 71 kips. Shear strengthening will,

therefore, be required. Figure 7.8 shows the shear diagram with the locationswhere shear strengthening is required along the length of the beam.

71 kips

54 kips

Vu /

Vn

d

12 kips

Beam

Centerline

69 in

Capacity to be taken bysupplemental FRP

Reinforcement

Figure 7.8 – Shear diagram showing demand versus existing capacity. The FRP reinforcementmust correct the deficiency shown shaded.




05/30/02 7-13

Find the FRP contribution to shear capacity, Vf

kips0.20

85.0

kips54kips71

85.0

VVV

existing,nu

d'req,f

Assume one ply of CF 130 will be used and compute the effective bonded length

in2Ln

1Loe

Compute the effective depth of the FRP shear reinforcement

The FRP wrap can only extend to the slab soffit. Therefore, the FRP must be inthe form of a “U” wrap. The total depth of the FRP will, therefore, be df = d – h s.

df = d – h s = 24 in – 6 in = 18 in

The effective depth will be:

dfe = d f – L e = 18 in – 2 in = 16 in

Find the reduction factor on the ultimate strength of the FRP

fufu

e21 005.0

468

Lk k R

14000

f k

3/2

c1

889.0in18

in16

d

dk

f

fe2

22300170468

2889001R .

).(

) )( . )( .(

Checking the upper limit on R, 0.005/fu = 0.294, it is found that the computedvalue ofR = 0.223 is acceptable.

Compute the effective stress level in the FRP sheet

ffe = R ffu = 0.223(550 ksi) = 123 ksi

Find the required amount of CF 130

For constructability and to conserve materials, the FRP will be oriented in thevertical

( = 90) direction. The amount of FRP can be found from Equation (7-2).

The spacing and the width of the strips are the two design variables. For convenience it will be helpful to compute the ratio wf / sf . Based on the wf / sf

ratio, the following conclusions can be drawn:

If wf / sf < 1.0, it is acceptable to use one-ply strips with a width to spacing ratio greaterthan or equal to wf / sf.

If wf / sf = 1.0, it is acceptable to use a continuous one-ply sheet (i.e., wf = sf).

If wf / sf > 1.0, one-ply will not be sufficient; more plies will be required.




05/30/027-14

With Afv = 2 n tf wf this ratio may be computed as follows:

6950s

w

s

in18ksi123w0065012kips020V

f

f

f

f f

. ) )( ( ). )( (

.

Thus, it will be permissible to use evenly spaced, one-ply strips.

Design the width and spacing of the FRP strips

Considering Wabo®MBrace CF 130 comes in 20 in wide rolls, material may be

conserved by using strip widths that are divisors of 20 inches (i.e., 4, 5, 10, or 20inch widths). In addition, the placement of the existing steel should beconsidered. It will be most beneficial to place the FRP strips between theexisting steel reinforcement. A configuration that satisfies both of these criteriaplus the strength criteria is to use 10 inch wide strips spaced at 12 inches oncenter. Thus, the wf /s f ratio becomes 0.833 which is greater than the requiredratio.

Check capacity and spacing requirements

The capacity of the FRP as designed is:

kips923in12

in1801ksi123in10in0065012

s

df AV

f

f fefvf .

) )( )( )( . )( ( cossin

This is less than the upper limit of:

kips8.72)in24)(in12( psi40004d bf 4 wc

The 12 inch spacing is less than the maximum of:

in164

in24in10

4

dws f max,f

Checking the total capacity of the entire cross section:

kips923850kips617kips436V850VVV f scn ).( ....

Detailing longitudinal plies

In addition to the vertical strips, strips running in the longitudinal direction willprevent the propagation of shear cracks and anchor the vertical strips. Theselongitudinal strips should be placed on the sides of the web and be located asclose as possible to the top of the vertical strip (for anchorage) and the bottom of the section (for crack control). For this purpose a 5 inch wide strip will be placedlongitudinally in these two locations.

Final design

The final ply sheet dimensions and orientation are shown in Figure 7.9. Thisfigure also shows the shear requirement of the beam and the shear strengthening provided by the Wabo

®MBrace repair.

kips71V

kips374V un

.




05/30/02 7-15

74.3 kips

Vu /

Vn

d

12 kips

10” Vertical Pliesof CF-130 @ 12”

o.c.

72 in

Beam

Centerline

Existing

Stirrups5” Horizontal Plies

of CF-130

Figure 7.9 – Final design and shear diagram for Example 7.4.1.




05/30/027-16

7.4.2 Accommodating a New Load Pattern

The beam shown in Figure 7.10 was originally designed to carry two point loadsfrom mechanical equipment spaced 6 ft apart. New equipment was installed thatresulted in the same load magnitude but with a smaller footprint; the point loadsfrom the new equipment were spaced 3 ft apart. In the original construction,

stirrups were left out of the 6 ft region at mid-span because of the low shear demand. The new load pattern may, therefore, result in a shear deficiency in thisregion. In order to accommodate this new load pattern, Wabo

®MBrace shear

reinforcement may be designed to correct the deficiency. The beam crosssection is shown in Figure 11 and the following material properties have been

determined: f’c = 4000 psi, f y = 60 ksi.

Pu = 27 k

wu = 3.27 k/ft

Original Load Pattern

10 ft

Pu = 27 k Pu = 27 k

wu = 3.27 k/ft

New Load Pattern

11.5 ft

Pu = 27 k

6 ft 10 ft 3 ft 11.5 ft

Figure 7.10 – Beam elevation for Example 7.4.2 showing the change in load pattern.

18”

12”

17”

5”

Figure 7.11 – Cross section of beam at mid-span.

36.81 k

31.9 k

9.81 k

69.51 k

10’

Vu, original

Vu, new

This part of the beam needs

strengthening

1.5’ 1.5’ 1.5’ 1.5’




05/30/02 7-17

Figure 7.12 – Shear requirements.

Assess the current condition

kips3.27lb322,27)in18)(in12( psi000,42d b'f 2V wcc

There are no stirrups in the portions of the beam that require strengthening,because Vu was less than ½(Vc).

kips81.9Vkips6.112

)kips3.27(85.0

2

Vu

c

But in the new condition, Vu became 36.81 kips > ½(Vc), so additional shearreinforcement must be provided.

Determine the shear contribution that must be provided by the FRP

)V85.0kips3.27(85.0kips81.36

)V85.0V(V

f

f cu

kips8.18Vd'reqf

Select materials and geometry

Wabo®MBrace CF 130 reinforcement is chosen for the shear retrofit. Due to

geometric considerations, it is desired to use a 20” wide U-wrap to cover each of the two 1.5 ft lengths of the beam that are deficient in shear. Assuming one ply,the shear contribution may be computed.

Determine the effective bond length

in2Lo for Wabo®MBrace CF 130

in2Ln

1L oe for one ply (n = 1)




05/30/027-18

Determine the reduction factor on the ultimate strength of the sheet

14000

f k

3/2

c1

in13in5in18hdd sf

in11in2in13Ldd ef fe

846.0in13

in11

d

dk

f

fe

2

21300170468

in284601

468

Lk k R

fu

e21 . ).(

) )( .(

Determine the stress level in the fiber at ultimate.

ksi9116ksi5502130Rf f fufe . )( .

Find the shear contribution of the FRP and compare to the required value.

kips654kips932

in18in12 psi00044in12

in1301ksi9116in20in0065012

d bf 4s

df AV wc

f

f fefvf

..

) )( ( , ) )( . )( )( . )( (

cossin

kips818Vkips932V dreqf f .. ' , One ply is sufficient

Final design

The final design is summarized in Figure 7.13.

20”9’-11” 2’-10” 9’-11”20”

One ply of MBrace CF-130 in a “U”-

wrap configuration

Figure 7.13 – Beam elevation showing the location and configuration of the designed FRP shear reinforcement.




05/30/02 7-19

7.4.3 References

1 Chajes, M. J.; Januska, T.F.; Mertz, D.R.; Thomson, T.A.; and Finch, W.W., “Shear

Strengthening of Reinforced Concrete Beams Using Externally Applied Composite Fabrics,” ACI Structural Journal , Vol. 92, No. 3, May - June 1995, pp. 295-303.

2 Umezu, K.; Fujita, M.; Nakai, H.; and Tamaki, K., “Shear Behavior of RC Beams with Aramid

Fiber Sheet,” Non-Metallic (FRP) Reinforcement for Concrete Structures, Proceedings of theThird Symposium, Vol. 1, Japan, Oct 1997, pp. 491-498.

3 Funakawa, I.; Shimono, K.; Watanabe, T.; Asada, S.; and Ushijima, S., “Experimental Study on

Shear Strengthening with Continuous Fiber Reinforcement Sheet and Methyl MethacrylateResin,” Non-Metallic (FRP) Reinforcement for Concrete Structures, Proceedings of the Third Symposium, Vol. 1, Japan, Oct 1997, pp. 475-482.

4 Triantafillou, T.C., “Shear Strengthening of Reinforced Concrete Beams Using Epoxy-Bonded

FRP Composites,” ACI Structural Journal , Vol. 95, No. 2, March-April 1998, pp. 107-115.

5

Rizkalla, S.; Abdelrahman, A.; Hutchinson, R.; and Donald, D. Shear Strengthening of theMaryland Bridge Using CFRP Sheets. Submitted to the City of Winnipeg, July 1997, 23 pgs.

6 ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-95) and

Commentary (ACI 318R-95), American Concrete Institute, Detroit, MI, 1995, 369 pgs.

7 Ohuchi, H; Ohno, S.; Katsumata, H.; Kobatake, Y.; Meta, T.; Yamagata, K; Inokuma, Y.; and

Ogata, N., “Seismic strengthening Design Technique for Existing Bridge Columns withCFRP,” Seismic Design and Retrofitting of Reinforced Concrete Bridges, edited by Park, R.,1994, pp. 495-514.

8 Khalifa, A.; Gold, W.; Nanni, A., and Abel-Aziz M.I. “Contribution of Externally Bonded FRP to

the Shear Capacity of RC Flexural Members.” J. of Composites in Construction, ASCE, Vol.2, No. 4, Nov. 1998.

9

Seible, F. and Innamorato, D. Earthquake Retrofit of Bridge Columns with Continuous CarbonFiber Jackets. Report to Caltrans, Division of Structures, La Jolla, CA, August 1995, 56 pgs.

10 Maeda, T.; Asano, Y.; Sato, Y.; Ueda, T.; and Kakuta, Y., “A Study on Bond Mechanism of

Carbon Fiber Sheet,” Non-Metallic (FRP) Reinforcement for Concrete Structures,Proceedings of the Third Symposium, Vol. 1, Japan, Oct 1997, pp. 279-286.

11 Horiguchi, T.; and Saeki, N., “Effect of Test Methods and Quality of Concrete on Bond Strength

of CFRP Sheet,” Non-Metallic (FRP) Reinforcement for Concrete Structures, Proceedings of the Third Symposium, Vol. 1, Japan, Oct 1997, pp. 265-270.

12 Sato, Y.; Ueda, T.; Kakuta, Y.; and Tanaka, T., “Shear Reinforcing Effect of Carbon Fiber

Sheet Attached to Side of Reinforced Concrete Beams,” Advanced Composite Materials inBridges and Structures, edited by El-Badry, M.M., 1996, pp. 621-627.



Chapter 8 Enhancement of Axial Performance

8.1 GENERAL 8-2

8.1.1 Notation 8-2

8.2 BEHAVIOR OF FRP CONFINED CONCRETE 8-3

8.2.1 Behavior of FRP Confined Concrete in Circular Sections 8-5

8.2.2 Confining Pressure as a Function of Longitudinal Strain 8-7

8.2.3 Modified Consitutive Law for FRP Confined Concrete 8-8

8.3 COMBINED AXIAL AND BENDING FORCES 8-8

8.3.1 Ultimate Strength Analysis 8-8

8.3.2 Serviceability Considerations 8-9

8.4 INCREASE IN SHEAR CAPACITY 8-9

8.5 FURTHER CONSIDERATIONS 8-9

8.5.1 Strengthening Purpose 8-10

8.5.2 Existing Reinforcement 8-10

8.5.3 Size Effect 8-10

8.5.4 Seismic Retrofit 8-10

8.6 DESIGN EXAMPLE 8-11

8.6.1 Increasing the live load capacity of a column 8-11

8.7 REFERENCES 8-12




05/30/028-2


8.1 General

The use of FRP reinforcement to enhance the axial compressive performance of concretemembers is a commonly used FRP retrofit technique. By wrapping a concrete column with anFRP jacket, the shear, moment, and axial capacity are improved. In addition, the ductility of themember may be significantly improved. Wrapping the column with the FRP fibers oriented in thetransverse (hoop) direction forms the FRP jacket. The jacket provides significant confinement tothe concrete, which leads to the mechanical performance improvements.

Both glass and carbon FRP are very effective in enhancing the axial performance of concretecolumns. Creep rupture of glass FRP is not a concern with column wrapping because under normal sustained service loads, the FRP jacket remains virtually stress free. On a weight basis,the strength improvements afforded with glass FRP are lower than those achieved with carbon.

This chapter deals specifically with circular cross sections. The technique has been shown toimprove the performance of rectangular cross sections as well. However, these improvementsare not quantifiable at this time.

8.1.1 NotationEc = Elastic modulus of concrete (psi)


f c = Longitudinal stress level in the concrete (psi)

f'c = Nominal compressive strength of unconfined concrete (psi)

f'cc = Nominal compressive strength of confined concrete (psi)

f cp = Confining pressure provided by the FRP jacket (psi)

f f = Stress state in the FRP fibers (psi)

f fu = Ultimate (rupture) strength of the FRP fibers (psi)

f y = Yield strength of longitudinal mild steel (psi)

h = Height or diameter of the circular column section (in.)

n = Number of plies of FRP reinforcement with fibers oriented in the hoop

direction

R = Reduction factor on the ultimate strength of the FRP to find the stress level in

the FRP at failure


Vc

= Shear strength of the concrete in a given section (lb.)

Vf = Shear strength of the transverse FRP reinforcement in a given section (lb.)

Vn = Nominal shear strength of a given section (lb.)

Vs = Shear strength of the transverse mild steel reinforcement in a given section(lb.)




05/30/02 8-3

c = Concrete strain (confined or unconfined) in the axial (longitudinal) direction

(in./in.)

c,cr = Longitudinal strain corresponding to the onset of transverse cracking in the

concrete (in./in.)

'c= Unconfined concrete strain level corresponding to the peak value of stress, f'

c(in./in.)

'cc = Confined concrete strain level corresponding to the peak value of stress, f'cc

(in./in.)

f = Strain in the FRP jacket in the direction of the fiber orientation (in./in.)

fu = Ultimate strain (elongation) of the FRP fibers (in./in.)

s = Tensile strain in the longitudinal steel (in./in.)

y = Strain corresponding to yield in the longitudinal steel reinforcement (in./in.)

t = Concrete strain (confined or unconfined) in the transverse (hoop) direction

(in./in.)

t,cr = Transverse strain corresponding to the onset of transverse cracking in the

concrete (in./in.)

't = Strain corresponding to the peak value of tensile stress in the concrete (in./in.).

A typical value of 0.0002 is recommended.

= Strength reduction factor

c = Poisson’s ratio for concrete in the elastic range. Typically Poisson’s ratio is

assumed to be equal to 0.19.

f = Volumetric FRP reinforcement ratio; ratio of the volume of fibers to the

volume of the encased concrete.

8.2 Behavior of FRP Confined Concrete

As concrete is uniaxially compressed, Poisson’s effect induces transverse strains that result inradial expansion of the concrete. At low levels of longitudinal strain, the concrete behaveselastically and the transverse strain is related proportionally by Poisson’s ratio to the longitudinalstrain. At a critical value of longitudinal stress (typically 75% to 80% of f'c), cracks forming in theconcrete paste between the aggregate result in large increases in transverse strain with relativelysmall increases in longitudinal stress. This rapid increase in transverse strain results in anequally rapid volumetric expansion. This behavior is best summarized in Figure 8.1.

1




05/30/028-4

TensionStrain

Stress

c,cr

f'c

Compresssion'c

c

~0.70f'cf c

t

Unconfined Concretet

t,cr

Figure 8.1 – Typical relationship for uniaxially loaded unconfined

concrete showing stress versus longitudinal, transverse, and volumetric strain

By wrapping the concrete with a continuous FRP jacket, the fibers resist the transverseexpansion of the concrete. This resistance provides a confining pressure to the concrete. At lowlevels of longitudinal stress, the transverse strains are so low that the FRP jacket induces littleconfinement. However, at longitudinal stress levels above the critical stress, the dramaticincrease in transverse strains engages the FRP jacket and the confining pressure becomessignificant. The effect of the confining pressure is to induce a triaxial state of stress in theconcrete. It is well understood that concrete under triaxial compressive stress exhibits superior behavior in both strength and ductility than concrete in uniaxial compression.

1

FRP Jacket

Fiber Direction

for Confinement

Figure 8.2 – Schematic of an FRP wrapped column showing fiber orientation

The improvement to the behavior of concrete is quantified based on the observation that concreteencased by an FRP jacket exhibits a bilinear stress-strain response.

2 Initially the stress strain

behavior is unchanged from that of unconfined concrete. However, beyond the peak stress for unconfined concrete, the stress level in confined concrete continues to increase with increasingstrain. The rate of increase is roughly proportional to the stiffness of the confining jacket.

3




05/30/02 8-5

Because the FRP jacket acts to contain damaged sections of concrete; the maximum usablestrain level in the concrete is only limited by the ultimate strain obtainable in the FRP jacket. Thegeneralized stress-strain behavior of concrete confined with an FRP jacket is shown in Figure 8.3.

Strain

S t r e s s

Figure 8.3 – Generalized stress-strain relationship for concrete confined by an FRP jacket

As shown in Figure 8.4, the improvements to the behavior of the concrete are proportional to thedegree of confinement provided.

Strain

S t r e s s

Unconfined I n c r e a s i n g

C o n

f i n e m e n

t

Figure 8.4 – Stress-strain curves for concrete under various levels of confinement

8.2.1 Behavior of FRP Confined Concrete in Circular Sections

To quantify the behavior of concrete encased by an FRP jacket, it is necessary to determine theamount of confining pressure the FRP jacket supplies. The confining pressure is a function of thestiffness of the jacket and the transverse expansion of the concrete.




05/30/028-6

f f f f

f cp = 2 t j f f / h

f cp

f cp

FRP Jacket

(Thickness = t j = n tf )

Concrete Column

(Diameter = h)

Figure 8.5 – Free body diagram showing the internal and external forceson the FRP jacket and concrete column

By strain compatibility, the strain in the jacket is equal to the transverse strain in the concrete asexpressed in Equation (8-1). The confining pressure may then be found by analyzing the staticsof a thin-walled cylindrical cylinder (Figure 8.5). This analysis yields the confining pressure givenby Equation (8-2).

tf (8-1)

2

E85.0f f tf

cp

(8-2)

where,h

nt4 f f

In the expression for the confining pressure, the 0.85 factor is intended to account for anylocalized debonding that may result in incompatibility between the strains in the concrete and the jacket and as a general reduction factor to account for the novelty of this repair technique. Thereis no theoretical reliability basis for this factor at this time.

The apparent increase in the compressive strength of concrete under the confining pressuresupplied by the jacket may be quantified by Equation (8-3) and the strain corresponding to thispeak value of stress is given by Equation (8-4)

4

25.1

f f 2

f f 9.7125.2f f

c

cp

c

cpccc (8-3)

5

f

f 6

c

ccccc (8-4)




05/30/02 8-7

In the above expressions, f'c and ' c are properties of unconfined concrete. The term ' c is thestrain corresponding to the peak value of unconfined compressive stress and can be found fromEquation (8-5).

c

c

c E

f 71.1

(8-5)

8.2.2 Confining Pressure as a Function of Longitudinal Strain

The strain in the FRP (and therefore the confining pressure it supplies) is equal to the transversestrain in the concrete. The transverse expansion of the concrete, in turn, is dependent on thelongitudinal strain in the concrete. Thus, as the axial strain is increased, the transverse strainincreases, and the confining pressure will increase. It is necessary to define a relationshipbetween the transverse strain in the concrete and the longitudinal strain. Such a relationship hasbeen developed based on research of concrete under a triaxial state of stress

5. For a variable

confining pressure depending on the properties of the FRP jacket, the relationship for the axial

strain, c, in terms of the transverse strain, t, may be expressed as Equation (8-6).

c

cr ,ttt

cc

cr ,ccc

c

cr ,cccc

cr ,c

cr ,tt

cc

cpc

c

t

for )(g21

for E

f 21

(8-6)

where,

1

21

12

211)(g

c

cr ,cc

cr ,cctcr ,t

cc

2

c

ct

This expression states that the transverse strain and longitudinal strain are initially related byPoisson’s ratio. After the onset of transverse cracking in the concrete, the transverse strainincreases rapidly. The transverse strain at which cracking initiates is given by Equation (8-7).The corresponding longitudinal strain is given by Equation (8-8).

c

ccp

tcr ,tE

21f (8-7)

c

cr ,t

cr ,c

(8-8)




05/30/028-8

8.2.3 Modified Consitutive Law for FRP Confined Concrete

The stress corresponding to any value of longitudinal strain may be computed by Equation (8-9).

2

cc

c

cc

c

cc

c

1

f 8.1

f

(8-9)

The complete stress-strain behavior of FRP confined concrete may be developed by selecting astrain in the FRP (or transverse strain in the concrete), computing the confining pressuresupplied, computing the peak value of stress for this confining pressure, finding the longitudinalstrain corresponding to the transverse strain, and finally calculating the stress corresponding tothis value of longitudinal strain. This procedure is valid for all values of strain in the FRP fromzero up to the ultimate elongation of the FRP fiber material ( fu).

8.3 Combined Axial and Bending ForcesThe axial and moment strength interaction of the FRP confined column may be computed byapplying strain compatibility, the constitutive laws of the materials, and equilibrium of stressresultants in the traditional fashion. The FRP jacket only has the effect of modifying theconstitutive law for concrete as described in Section 8.2. This constitutive law may be used for any distribution of stress in the section assuming that the confinement remains active in partiallycracked conditions or if the column is subjected to cyclic loading.

8.3.1 Ultimate Strength Analysis

Theoretically, the ultimate longitudinal strain that is achievable in the concrete is only limited bythe strain corresponding to the strain in the FRP material at rupture. However, the transversestrain in the concrete should be limited to 0.005 in./in. to maintain the shear integrity of theconcrete

6.

In the process of determining stress resultants, it is necessary to integrate the stress-strainrelationship given in Equation (8-9) over a circular concrete cross section to find the magnitudeand location of the concrete stress resultant. The computational effort involved can become quitecomplex, and the use of computer programs to automate the process is highly recommended. Alternately, dimensionless interaction diagrams for several concrete strengths and configurationsof longitudinal steel reinforcement are given in Appendix A.

The interaction diagrams in Appendix A use the same factors given in ACI 318-957 for columns

with spiral reinforcement*. If the purpose of the FRP confinement is to replace deficient spiral

reinforcement, it is recommended to use more conservative factors. In particular, the factors

associated with tied columns would be appropriate†.

* = 0.75 for compression controlled sections with a maximum axial force of 0.85Pn. Additionally, the factors are adjusted in the tension controlled region per ACI Section B.9.9.3.2 ( = 0.90 if s,max > 0.005, = 0.65 – 50 s,max if y < s,max < 0.005)

† = 0.70 for compression controlled sections with a maximum axial force of 0.80Pn. The adjustment in

the tension controlled region per ACI Section B.9.3.2 is = 0.90 if s,max > 0.005, = 0.56 – 58 s,max if y <

s,max < 0.005.




05/30/02 8-9

8.3.2 Serviceability Considerations

At load levels near ultimate, the designer should be aware that damage to the concrete in theform of significant cracking in the radial direction might occur. The FRP jacket contains thedamage and maintains the structural integrity of the column. However, at service load levels, thistype of damage should be avoided. In this way, the FRP jacket will only act during overloads thatare temporal in nature.

To insure that radial cracking will not occur under service loads, the strain in the concrete shouldremain below cr at service load levels. This corresponds to limiting the stress in the concrete to0.65f’c. In addition, the stress in the steel should remain below 0.60f y to avoid plastic deformationunder sustained or cyclic loads. By maintaining the specified stress in the concrete at service,the stress in the FRP jacket will be virtually zero. The jacket is only stressed when the concreteis strained above cr the rate of the transverse expansion becomes large.

*

8.4 Increase in Shear Capacity

Because the FRP jacket provides additional strength in the transverse direction, the shear strength is improved as well. Similar to the shear strength of beams wrapped with transverseFRP reinforcement, the shear capacity of a FRP wrapped column may be determined fromEquation (8-10). The 85% multiplier is the same as that used for computing the shear capacity of

a beam section (see Chapter 7) and is intended to account for the novelty of this strengtheningtechnique.

f scn V85.0VVV (8-10)

The contribution of the FRP jacket to the shear capacity may be determined from Equation (8-11).

8

hRf nt2

V fuf f

(8-11)

Because the FRP jacket completely encases the column, the reduction factor, R, can becomputed from Equation (8-12).

fu

005.0R

(8-12)

This factor is the same as that given for a beam wrapped entirely with transverse FRPreinforcement (see Chapter 7). This factor also remains consistent for the limit imposed on the jacket acting as confinement. As stated previously, the value of this factor is chosen to limit thetransverse strain in the concrete so that aggregate interlock is maintained.

8.5 Further Considerations

The following observations are presented to help the designer make an educated judgement asto the applicability of FRP confinement to a specific project.

* The stress levels indicated are not intended to be “Allowable” stresses. These values are only to insure

that damage to the column under service loads is avoided.




05/30/028-10

8.5.1 Strengthening

Columns may require retrofit due to a number of circumstances such as changes in loadrequirements, design/construction deficiencies, physical damage, corrosion or other durabilityproblems, etc. Depending on the circumstance, the condition of the existing concrete may rangefrom excellent to very poor. The following considerations should be made depending on thecondition of the existing concrete and the reason for the retrofit.

1) If the existing concrete is damaged then subsequently repaired (by epoxy injection for instance), the designer may consider reducing the nominal compressive strength of the concrete,f’c depending on the extent of the damage. This reduced compressive strength may beincorporated into the design methods presented in this chapter.

2) If there is an active corrosion problem, the source of the corrosion must beinvestigated and the problem corrected before any strengthening work is commissioned. This isespecially critical considering that the FRP jacket will hide visual signs of corrosion.

3) Similarly, other durability related concerns such as the presence of efflorescence or exudation, any form of chemical attack, and non-structural cracking should be addressed andcorrected prior to strengthening.

8.5.2 Existing ReinforcementFor columns with high, existing steel reinforcement ratios, the effect of the confining jacket maybe limited due to decreased volumetric expansion of the concrete in the column. In the absenceof further study, it is suggested to use FRP confinement only in columns with reinforcement ratios

lower than g = 0.03.

Similarly, the presence of existing spirals or ties may effect the volumetric expansion of thecolumn. Further research into this topic is required for an adequate assessment of the effect of the presence of spirals or ties.

8.5.3 Size Effect

The procedures outlined in this chapter do not imply a restriction on the column diameter (although the reinforcement ratios for large columns may result in excessive jacket thickness that

may become economically restrictive). However, the effect of the confining jacket may bereduced or may be non-existent in very large diameter columns. Until further research isavailable, it is suggested to use the methods provided in this chapter only for columns with adiameter smaller than 72 inches.

8.5.4 Seismic Retrofit

Future editions of this manual will contain specific guidelines on the use of FRP jacketing for seismic retrofits. Topics that remain to be addressed are the effect of cyclic loading, theformation of plastic hinges, and a quantitative assessment of the ductility improvements affordedby the FRP jacket.

8.6 Example Problem

8.6.1 Increasing the ultimate load capacity of a column

A 16” diameter circular column with 10-#7 bars was originally designed to carry a factored axialload of 570 kips and a factored moment of 134 kip-ft. The column has 1.5” of clear cover and #3spiral transverse reinforcement. Design the number of plies of CF 130 needed to be able tosupport a 20% increase in factored loads. The concrete and steel properties are f’ c = 5000 psi, f y= 60,000 psi.




05/30/02 8-11

Compute the factored axial force and bending moment for the 20% live load increase

k 684kips57021Pu )( .

ftk 162ftk 13521M u )( .

To use the non-dimensional interaction diagrams given in Appendix A, the following values mustbe calculated:

Compute the existing steel reinforcement ratio

030in201

in06

A

A2

2

g

sg

..

Compute the diameter of the circle defining the reinforcement centroid

in875.10)in8/11()in8/3(2)in5.1(2in16h

68.0in16

in875.10

h

h

Find the factored unit axial force and bending moment

ksi403in201

kips684

A

P2

g

u .

ksi600in16in201

ft

in12ftk 162

hA

M2

g

u .

With these values, the required FRP reinforcement ratio may be determined from the non-dimensional interaction diagrams given in Appendix A.

From Figure A.8 ( g = 0.03 f = 0.003

From Figure A.10 ( g = 0.03 f = 0.0015

From linear interpolation, if = 0.68 then f = 0.0026

Compute the required jacket thickness

in01004

in1600260

4

hnt f

f .

.

Compute the required number of plies

plies2Use plies61

plyin00650

in0100n .

.

.

Thus, 2 plies of CF 130 will be adequate to allow a 20% increase in factored loads.




05/30/028-12

8.7 References

1 MacGregor, J.G. (1997) Reinforced Concrete Mechanics and Design 3

rd Ed., Prentice Hall,

Upper Saddle River, NJ, 939 pg.

2 Nanni, A. and Bradford, N. (1995), “FRP Jacketed Concrete Under Uniaxial Compression,”

Construction and Building Materials, Vol. 9, No. 2, pp. 115-1243 Samaan, M.; Mirmiran, A.; and Shahway, M., “Modeling of Concrete Confined by Fiber

Composites,” submitted

4 Mander, J.B.; Priestley, M.J.N.; and Park, R. (1988), “Theoretical Stress-Strain Model for

Confined Concrete,” Journal of Structural Engineering , ASCE, Vol. 114, No. 8, pp. 1804-1826.

5 Imran, I., and Pantazopoulou, S.J. (1996), “Experimenal Study of Plain Concrete Under Triaxial

Stress,” Materials Journal , American Concrete Institute, Vol. 93, No. 6, pp. 589-601.

6 ACI Committee 440 (1996), “State-of-the-Art Report on FRP for Concrete Structures,” ACI440R-

96, Manual of Concrete Practice, American Concrete Institute, Farmington Hills, MI, 68 pg.

7 ACI 318 (1995), “Building Codes and Requirements for Reinforced Concrete,” American

Concrete Institute, Farmington Hills, MI 369 pg.

8 Seible, F. and Innamorato, D. (1995), Earthquake Retrofit of Bridge Columns with Continuous

Carbon Fiber Jackets, Report to Caltrans, Division of Structures, La Jolla, CA, 56 pg.



Chapter 9 Other Applications

9.1 CLAMPING THE DEVELOPMENT LENGTH OF EXISTINGREINFORCEMENT 9-2

9.1.1 Notation 9-2

9.1.2 Basic Theory 9-2

9.1.3 Quantifying the Reduction in Development Length 9-3

9.2 REFERENCES 9-4




05/30/029-2


9.1 Clamping the Development Length of Existing Reinforcement

The MBrace System can be used to clamp the concrete along the development length of existingsteel reinforcement in tension to reduce the development length of this reinforcement.

1 This is

particularly useful in retrofitting existing columns in which inadequate lap splices were used in theoriginal construction. The analysis of the MBrace System used for this purpose is similar toutilizing the area of transverse steel reinforcement to reduce the development length of bars intension.

9.1.1 Notation

f'c = Nominal compressive concrete strength of unconfined concrete (psi)

f fe = Effective stress in the FRP fibers (psi)


k 1 = Multiplier on the reduction factor, R, to account for various concrete strengths

K tr = Transverse reinforcement factor (modified to reflect contribution of FRP)

K tr,f = Transverse reinforcement factor due to transverse FRP reinforcement

K tr,s = Traditional transverse reinforcement factor due to transverse steelreinforcement

Le = Effective bonded length of the FRP transverse strip (in.)

n = Number of plies of FRP reinforcement with fibers oriented in the transverse

direction that intersect a potential splitting failure plane

n b = Number of existing longitudinal bars being developed

R = Reduction factor on the ultimate strength of FRP based on the bondmechanism

sf = Spacing of transverse FRP strips (in.)


wf = Width of one strip of transverse FRP reinforcement (in.)

fu = Ultimate elongation (strain) of the FRP fibers (in./in.)

9.1.2 Basic Theory

As steel reinforcement embedded in concrete is pulled in tension, the deformations on the steelbar produce an outward radial pressure on the surrounding concrete. This pressure may produce

splitting cracks in the concrete if sufficient development length is not provided.

FRP reinforcement may be used to wrap the concrete section transversely and thus reinforcethese splitting cracks. It is recommended to wrap the section entirely where possible, particularlyfor columns. However a “U” wrap may also be used to clamp a beam section.




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Potential

Splitting

Failure

FRP “U” Wrap

Reinforcement

Potential

Splitting

Failure

Full FRP Wrap

(a) (b)

Figure 9.1 – FRP reinforcement used to clamp the development length of longitudinal bars. (a) A “U” wrap used for a beam section (b) A full

wrap used for a column section.

9.1.3 Quantifying the Reduction in Development Length

The development length of bars in tension reinforced with transverse FRP wraps may bedetermined in the traditional fashion presented in ACI 318 Section 9.3.3

2. The effect of the FRP

reinforcement may be accounted for by introducing a new transverse reinforcement index, Ktr .

f ,tr s,tr tr K 85.0K K (9-1)

The first term, Ktr,s, is the traditional transverse reinforcement factor given in ACI 318 Section12.2.4 for transverse steel reinforcement. The second term is a new transverse reinforcementfactor for transverse FRP reinforcement. The 85% reduction factor is meant to account for thenovelty of this strengthening technique.

The transverse FRP reinforcement factor may be computed based on the general principlespresented in Chapter 7. The expression for this factor is similar to that for steel and is given byEquation (9-2).

bf

fetf f ,tr

ns1500

f AK

(9-2)

Where the area of transverse FRP reinforcement may be computed by the following expression.

f f tf wntA (9-3)

In this expression, “n” is the total number of plies which cross a potential plane of splitting alongthe longitudinal steel being developed and wf is the width of the FRP strip. Note that, similar toshear strengthening, the width of the strip and the spacing of the strips, s f , should be equal for acontinuous FRP wrap.




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The effective stress in the sheet, f fe, is dependent on the bond mechanism of the FRP to theconcrete. This variable is quantified similarly to the effective stress for shear strengthening givenin Chapter 7.

fufe Rf f (9-4)

wrapsFullfor 005.0

wraps"U"for 005.0

468

Lk

R

fu

fufu

e1

(9-5)

Where,

3/2

c1

4000

f k

(9-6)

Effective lengths, Le, are given for various fiber reinforcement systems in Chapter 7. Alternately,the value of R for “U” wraps may be determined from tables given in Appendix A with d f /dfe equalto 1.0.

With the modified transverse reinforcement factor, the basic tension development lengthexpression given in ACI 318

2 as Equation 12-1 may be used to compute the development length.

9.2 References

1 Seible, F. and Innamorato, D. (1995), Earthquake Retrofit of Bridge Columns with Continuous

Carbon Fiber Jackets, Report to Caltrans, Division of Structures, La Jolla, CA, 56 pgs.

2 ACI 318 (1995), “Building Codes and Requirements for Reinforced Concrete,” AmericanConcrete Institute, Farmington Hills, MI 369 pgs



Chapter 10 Details of Reinforcement

10.1 GENERAL 10-2

10.1.1 Notation 10-2

10.1.2 General Detailing Guidelines 10-3

10.2 BOND AND DELAMINATION 10-3

10.2.1 Cover Tension 10-3

10.2.2 Beam Shear 10-4

10.2.3 Interfacial Shear and Peeling 10-4

10.2.4 Planar Surface Irregularities 10-5

10.2.5 Mechanical Anchorage 10-6

10.3 DEVELOPMENT LENGTH 10-6

10.4 SPLICES 10-7

10.4.1 Beams 10-7

10.4.2 Columns 10-8

10.5 CUTOFF POINTS 10-8

10.6 REFERENCES 10-10




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10.1 General

This chapter is presented to offer guidance in finalizing the design of an Wabo®MBrace

strengthening system. Full structural capacity of the FRP sheets will depend on the design, thetype of structure, and the quality and soundness of the concrete substrate.

Similar to designing traditional reinforced or prestressed concrete members, the procedure for designing FRP flexural reinforcement involves the following steps:

Determine the amount of FRP required at critical sections based on the analysis proceduresgiven in Chapter 6

Determine the development length of the laminate

Find the required length of the laminate based on development lengths and allowable cut-off points

Detail any additional anchorage and splices if required

Insure that the general detailing guidelines given in Section 10.1.2 are met

For FRP reinforcement used for shear strengthening or column wrapping the only detailingnecessary is determining splice dimensions and locations and insuring that the general detailingguidelines are met.

10.1.1 Notation


f'c = Nominal compressive concrete strength of unconfined concrete (psi)

f ct = Direct tensile strength of concrete determined by in-situ pull-off tests (psi)


n = Number of plies of FRP reinforcement with fibers oriented in the hoopdirection


Mcr = Moment to cause cracking of the concrete section (lb.-in.)

Mu = Design moment under factored loads (lb.-in.)

V = Shear force in the concrete section

= Interfacial bond stress between the FRP and the concrete substrate (psi)

df λ = Length required to develop the ultimate strength of the FRP laminate in tension(in.)




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10.1.2 General Detailing Guidelines

The following list provides general guidelines for detailing FRP reinforcement. Many bond-relatedfailures may be avoided by following these recommendations.

Do not turn inside corners

Provide a minimum ½” radius when the sheet is wrapped around outside corners

Inject all cracks prior to FRP installation

Do not use externally bonded reinforcement on a concrete substrate with a nominalcompressive strength, f’c, less than 2000 psi

Additionally, some standard details for FRP reinforcement are contained in Appendix B.

10.2 Bond and Delamination

Because of shear transfer mechanisms and local regions of tension at the interface between theconcrete and the FRP, delamination before ultimate design strength may be encountered. Thecause of this phenomenon is complex. However, schemes can be implemented to avoid thissituation.

The weak link in the concrete/FRP interface is the concrete. The soundness and tensile strengthof the concrete substrate will limit the overall effectiveness of the FRP bonded to it. It is importantto recognize the possible types of delamination failure. The basic types of delamination are

1:

1) Cover tension2) Beam shear 3) Interfacial shear 4) Planar surface irregularities

It is important to realize that delamination typically occurs at loads significantly higher thanservice loads.

10.2.1 Cover Tension

For externally bonded FRP reinforcement using sheet materials, the cover tension delaminationcondition starts developing at the location of flexural cracks and propagates towards the laminateend

2. This is different from the case of bonded steel plates where the delamination usually starts

at the plate end due to stress concentration and propagates toward the centerline of the beam3.

Because the reinforcing steel essentially acts as a bond breaker in a horizontal plane, thereduced area of bulk concrete pulls away from the rest of the beam. This situation is illustrated inFigure 10.1.

The use of over-wraps has been shown to lessen the effect of cover tension delamination. Over-wraps are highly efficient if distributed over the length of the member. If the over-wrap is simplyadded at the at the FRP curtailment, its function is simply to add a safety device.




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LC

Cover TensionFailure

FRP

Figure 10.1 – Delamination caused by tension failure of the concrete

cover

10.2.2 Beam Shear

Beams which are over reinforced for moment will fail by either shear or a combination of flexuraland shear. Typical behavior is governed by shear cracking near the high shear region. As theshear cracks open, local displacements along the tension face cause a delamination of the FRP,Figure 10.2. The delamination typically initiates at the shear crack and propagates toward the

support. This situation has been identified in steel plate bonding as well. A check of the repairedbeam with increased loads with respect to the nominal shear capacity of the beam will likely avoidthis situation.

Figure 10.2 – Delamination caused by beam shear cracks

10.2.3 Interfacial Shear and Peeling

Previous research on steel and FRP bonded plates has demonstrated that the interfacial shear and out-of-plane tension (peel) distribution in the vicinity of the plate end to be significantlydifferent than the average stress distribution

4, Figure 10.3. In situations where peel is the true

failure mode, the difference between the local peak stresses and the average stress partiallyexplains delamination.

In the case of the curtailment zone for externally bonded FRP sheets, the stress distributionshown in Figure 10.3 may not be highly relevant due to the relative small thickness of adhesiveand laminate. However, existing practice is to taper multiple sheets of FRP at 6 inches/ply.




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T e n s i o n

Interfacial Shear Stress,

Normal Stress,

Distance along FRP

End of FRP Centerline of beam

C o m p r e s s i o n

Figure 10.3 – Interfacial shear and normal stress (peel) distributions

along the length of a bonded FRP laminate

10.2.4 Planar Surface Irregularities

Because the MBrace sheet FRP can follow the contour of most concrete surfaces, it is importantto fill low spots and grind high spots flat. If the FRP follows the contour of a hole, snap-throughphenomenon caused by beam curvature can create a localized delamination. In the case of theFRP sheets “bridging” over protrusions (such as concrete filling formwork knotholes), the resultingbehavior is similar to the beam shear case on a much smaller scale. Proper surface preparationand use of Wabo

®MBrace Putty are the keys to avoiding these types of delaminations. Figures

10.4 and 10.5 illustrate what to avoid.

“Snap-through” forces

FRP

Figure 10.4 – Snap-through behavior of FRP bonded to contour

FRP

Figure 10.5 – FRP bridging over a protrusion




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10.2.5 Mechanical Anchorage

It is not recommended to use the Wabo®MBrace System with mechanical anchorage. Because of

complications regarding fastener shear out, corrosion, fiber crushing from fastener bearing stress,durability of fiber ends after drilling and significantly increased installation costs, use of mechanical fastening systems requires rigorous design and analysis.

10.3 Development LengthThe development length of externally bonded FRP in tension is based on an assumed bondstress distribution and the maximum tensile stress in the FRP. An appropriate bond stressdistribution for FRP bonded to cracked concrete is a triangular distribution starting at 0, rampingup to the direct tensile strength of the concrete, and ramping down to 0. This stress distribution isassumed to act over the development length of the FRP. This assumption for bond stressdistribution has been commonly used for bonded steel plates

5 and is appropriate for FRP. Its

validity has been confirmed in recently conducted tests using 4,000 psi concrete andWabo

®MBrace CF 130.

The tensile capacity of the in-situ concrete may be determined by approximation using a multipleof the square root of the nominal compressive strength or it may be determined directly byperforming direct pull-off tests on the concrete substrate to which the FRP is to be installed.

By equating the force developed in the sheet at ultimate to the area of the bond stressdistribution, Equations (10-1) and (10-2) result.

c

f fudf

f 3

tf

n

λ (10-1)

ct

f fudf

f

tf 2

n

λ (10-2)

10.4 Splices

Splices are often required for constructability and geometric reasons. Although Wabo®MBrace

fibers are delivered in rolls containing several hundred feet of continuous material, the installer istypically only capable of handling sheets in 6 to 8 ft lengths.* For most strengthening projects, ittherefore becomes necessary to incorporate splices. Furthermore, in cases where a section is tobe completely wrapped with the sheet (such as shear strengthening or column wrapping), splicingis necessary to maintain continuity of the laminate. The recommended method of splicingWabo

®MBrace laminates is simple lap splicing.

If the splice runs parallel to the direction of the fibers, the sheets being spliced may be buttedagainst one another. All of the design procedures assume that no force transfer exists in thedirection perpendicular to the fibers. Therefore, no overlap is required.

Full tensile capacity of the Wabo®MBrace CF 130 and CF 530 carbon fiber sheets are developed

within a 2-inch lap splice. However, for additional safety and application convenience, a 4 inch lapsplice is typically used. Design tensile capacity of the Wabo

®MBrace EG 900 glass fiber is

developed within 6 inches.

* 6 to 8 ft is a conservative length that all installers can manage; however some installers are capable of

handling sheets in excess of 25 ft. The designer is encouraged to consult the contractor involved in theinstallation for more specific guidance.




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For splices in the non-load carrying direction (90 to the longitudinal fibers), butting the sides of the sheets will be sufficient. For some applications where sheets wider than 20 inches arerequired (e.g. slabs), it may be prudent to detail the sheets with a space between each sheetinstead of continuous butt joints. The space between the sheets will allow the substrate to“breath” in case moisture vapor transmission (MVT) is a concern. Preventing equilibrium of MVTmay cause blistering of the FRP sheets.

10.4.1 Beams

Similar to lap splicing steel reinforcement, splices should be made away from areas of higheststress in the sheet (e.g., mid-span for positive moment strengthening) where possible. Wheremore than one splice is required, splices should be staggered. This includes splices for multipleply sheets. Each fiber layer in the multiple ply laminate should be spliced at a different location.Splices of sheets that are butted together or spaced evenly along the transverse direction shouldbe spliced at staggered locations as well.

Stirrup web reinforcement placed transverse to the longitudinal axis of the beam shouldcontinuous. If a splice is necessary, the splice location should be on the bottom face of the beam.

10.4.2 Columns

Lap splices along the circumference of a column are treated the same as on the tension face of beams. For round columns, a 4-inch lap splice for carbon fiber and a 6-inch lap splice for glassfiber is typically sufficient. For columns under 10 inches in diameter, more rigorous analysis isrequired of the hoop and radial stresses. This analysis is beyond the scope of this manual.

Splices of FRP jackets for columns should be staggered along the height of the column.

10.5 Cutoff Points

In lieu of a more detailed analysis, the following general guidelines for the location of cut-off points for the laminate may be used to avoid failures at the termination of the laminate.

For continuous beams, a single ply laminate should be terminated 6” beyond the inflectionpoint (point of zero moment resulting from factored loads). For multiple ply laminates, the

termination point of the fiber layers should be tapered. The outermost ply should be terminated6” beyond the inflection point. Each successive ply should be terminated an additional 6” beyondthe inflection point. For example if a 3-ply laminate is required, the ply directly in contact with theconcrete substrate should be terminated at least 18” past the inflection point (Figure 10.6). Theseguidelines apply for positive and negative moment regions.

For simply supported beams, the same general guidelines apply, however the plies shouldextend past the point on the beam corresponding to the cracking moment, Mcr , under factoredloads instead of the inflection point.

Similar to steel reinforcement, the FRP laminate must extend at least its development lengthfrom the point of maximum stress in the sheet.




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6” 6” 6” df λ

M = Mu

(b) Simply Supported Beam

M = Mcr

M = 0

(a) Continuous Beam

M = Mu

Figure 10.6 – Graphical representation of the guidelines for allowable

termination points of a 3-ply FRP laminate




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10.6 References

1 Blaschko, M., Niedermeier, R., and Zilch, K. (1998) “Bond Failure Modes of Flexural Members

Strengthened with FRP,” Proceedings of the Second International Conference on

Composites in Infrastructure, Tucson, AZ, Vol. 1, pp. 315-327.2 Arduini, M., A. Di Tommaso, and A. Nanni, "Brittle Failure in FRP Plate and Sheet Bonded

Beams," ACI Structural Journal, Vol. 94, No. 4, July-Aug. 1997, pp. 363-370.

3 Roberts, T.M. and Haji-Kazemi, H. (1989) “Theoretical Study of the Behavior of Reinforced

Concrete Beams Strengthened by Externally Bonded Steel Plates,” Proceedings of theInstitute of Civil Engineers, Part 2, Vol. 87, No. 9344, pp. 39-55.

4 Malek, A., Saadatmanesh, H., and Ehsani, M. (1998) “Prediction of Failure Load of R/C Beams

Strengthened with FRP Plate Due to Stress Concentrations at the Plate End,” Structural Journal , American Concrete Institute, Vol. 95, No. 1, January-February 1998, pp. 142-152

5 Brosens, K. and Van Gemert, D. (1997) “Anchoring Stresses Between Concrete and Carbon

Fibre Reinforced Laminates,” Non-metallic (FRP) Reinforcement for Concrete Structures,Proceedings of the Third International Symposium, Vol. 1, October 1997, pp. 271-278.



Chapter 11 Engineering Specifications



SPECIFICATION

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Wabo ® MBrace Composite Strengthening Systemwith Carbon Fiber Reinforcement

NOTE TO THE SPECIFIER

The specification information below is intended for use by architects, engineers, or other specifiers in defining thecriteria needed to specify carbon fiber reinforcement systems.

1. PART 1: General

1.01 Work Including

A. Existing concrete or steel surfaces shall be repaired and reinforced with dry, fiber fabric sheet.

B. The bid is deemed to include furnishings of materials, labor and equipment and all

items necessary for repair and reinforcing of the concrete or steel as specified oncontract drawings and specifications, complete.

C. Drawings and the general provisions of the contract, including general conditionsand general requirements are hereby made a part of this section.

D. Cooperate and coordinate with all other trades in executing the work described inthe contract.

E. Inspect the structural members specified to be reinforced with Carbon Fiber Reinforced Plastic (CFRP) on the contract drawings to check the location andinspect cracks and existing conditions of members.

F. Design and install CFRP laminates to reinforce (Beams, Slabs, Columns, Walls,Pipes, or other).

1.02 Codes and Reference Standards

A. Comply with provisions of the following codes, specifications and standards,except as otherwise indicated. Standard specifications of the applicablesocieties, Manufacturer's associations and agencies shall include the latestissues of the specifications. The Contractor shall have the following referencesand shall be familiar with the reference contents.

1. State of Art Report on Fiber Reinforced Plastic Reinforcement for Structures (ACI 44OR-96).

2. Building Code Requirements for Structural Concrete (ACI 318-95) and(ACI 318R-95).



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3. Pull-Out Test-Relates Pull-Out Resistance of Driven Pins to ConcreteStrength (ACI503R).

4. ICRI Surface Preparation Guidelines for Repair of Deteriorated ConcreteResulting from Reinforcing Steel Oxidation, selection of repair materialsand placement of repair materials.

5. SACMA 4-88 Test method for tensile properties of oriental fiber resincomposites.

6. Concrete Repair Guide (ACI546R).

7. Guide to the Use of Waterproofing, Dampproofing, Protective, DecorativeBarrier Systems for Concrete (ACI 515.R-85).

1.03 Quality Control and Quality Assurance

A. Manufacturer/Contractor Qualifications

Materials Manufacturer/Supplier Company must be specialized in themanufacturing of the products specified in this section.

Materials Manufacturer/Supplier Company must have been in business for aminimum of 5 years, with a program of training and technically supporting anationally organized Contractor Training Program.

Contractor shall be a trained Contractor of the Manufacturer/Supplier of thespecified product, who has completed a program of instruction in the use of thespecified material.

B. Quality Control

The Contractor shall conduct a quality control program that includes, but is notlimited to the following:

1. Inspection of all materials to assure conformity with contract requirements,and that all materials are new and undamaged.

2. Inspection of all surface preparation prior to CFRP laminate application.



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3. Inspection of work in progress to assure work is being done in accordancewith established procedures and established Manufacturer's instructions,specific Engineer Instructions, if given, or recommended practices listed inthe references of Section 1.02.

4. Inspection of all work completed including sounding all repairs to check for debonding and correction of all defective work.

C. Quality Assurance

1. Attend pre-installation conference to be held with a representative of theOwner, Engineer, the Contractor's Field Supervisor, and other tradesinvolved to discuss the conduct of the work of this Section.

2. In-situ load testing of concrete structural member prior to and after installation of CFRP sheets as required by these specifications. Quantityand location of member (s) to be tested shall be determined by Engineer of Record prior to proposal.

1.04 Submittals

A. Contractor's Qualifications

B. Manufacturer's product data indicating product standards, physical and chemicalcharacteristics, technical specifications, limitations, installation instructions,maintenance instructions and general recommendations regarding each material.

C. Test results on the properties of the epoxy and the carbon fiber (CF) sheet/systems to be used on the project.

D. Provide a record of performance of strengthening projects with CFRP laminates(in North America).

E. Provide Field Supervisor specifically trained in the installation of CRFP laminates.

F. Samples of all materials to be used, each properly labeled as specified in Section2.01.

G. Manufacturer's MSDS for all materials to be used.

H. Certifications (in time to prevent delay in the work) by the Producers of thematerials that all materials supplied comply with all the requirements andstandards of the appropriate ASTM and other agencies.



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I. Submit to the Owner's representative two copies of the strengthening layoutdetails prepared by the Contractor's and/or Owner’s professional Engineer usingthe CFRP laminates to be used on the job.

J. Submit design drawings by a professional Engineer, including the necessaryinformation listed above in a timely manner to obtain a building permit for thework.

K. Adhesion testing process for 3.07-D1.

L. Load testing program (process, loads, and shoring) as required.

1.05 Structural Design

A. Design the repair with CFRP laminates according to the design guides for theCFRP laminates and instructions supplied by the manufacturer.

B. Structural drawings of the existing structure included in the contract drawings.

1.06 General Procedures

A. Work only in areas permitted by the Owner approved schedule.

B. Remove all tools, buckets and materials from work areas and store neatly at anapproved location daily at the end of work.

C. Protect the building and its contents from all risks related to the work in thisSection. Schedule and execute all work without exposing adjacent building areasto water, dust, debris or materials used by the Contractor. Protect adjacent areasfrom damage and stains with appropriate barriers and masking. Repair alldamage as a result of the work to its condition at the start of work, or if suchcannot be determined, to its original condition.

D. Protect the work from damage such as impact, marring of the surfaces and other

damage.

E. Compliance with OSHA and all other safety laws and regulations is the exclusiveresponsibility of the Contractor, his Subcontractors, Suppliers, Consultants andServants.



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1.07 Technical Support

A. The contractor shall provide the services of a trained Field Supervisor at the worksite at all times to instruct the work crew in the CRFP application procedures.

1. The Field Supervisor must be fully qualified to perform the work.

2. The Contractor shall be completely responsible for the expense of theservices of Manufacturer's Field Representative if needed at the work siteand the contract price shall include full compensation for all costs in

connection therewith.

22.. PPAARRTT 22:: PPr r oodduuccttss

2.01 Product Delivery, Storage and Handling

A. Deliver materials clearly marked with legible and intact labels with Manufacturer'sname and brand name, product identification and batch number.

B. The products shall be in original, unopened containers (except carbon fiber material).

C. Store materials in areas where temperatures conform with Manufacturer'srecommendations and instructions.

2.02 Acceptable Manufacturere/Suppliers

A. The following vendors shall be used:

CFRP laminates: (dry sheet only). Wabo®MBrace Fiber Reinforcement Systems

supplied by Watson Bowman Acme Corp. 95 Pineview Drive, Amherst, NY14228 , 716-691-7566, 800-677-4WBA, FAX: 716-691-9239

Epoxy resin adhesive: an approved epoxy system for application of

Wabo®MBrace Composite System. The system shall include:

a. Primer b. Putty/Filler c. Saturantd. Topcoat

Substitutions: No substitutions allowed, except as requested by theManufacturer/Supplier of the product and approved by the Engineer of Record.



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3. Part 3: Execution

3.01 General Preparation for Application

The contract drawings show locations of CFRP reinforcement.

A. Ambient Temperature

Conditions of CFRP process application must be examined carefully during the

winter season and/or cold zones. DO NOT APPLY CFRP SHEET WHEN AMBIENT TEMPERATURES ARE LOWER THAN 40 DEGREES F (5 degrees

C). Auxiliary heat may be applied to raised surface and air temperature to asuitable range. Utilize "clean" heat source (electric, propane) so as not tocontaminate bond surfaces by the carbonation of the substrate.

B. Condensation

Presence of moisture may inhibit adhesion of primer and/or resin. DO NOT APPLY CFRP WHEN RAINFALL OR CONDENSATION IS ANTICIPATED.

C. Concrete Surface Defects and Corners

UNEVEN CONCRETE SURFACE IRREGULARITIES (OFF SETS) MUST BEGROUND AND SMOOTHED TO LESS THAN 0.04 in. (1 mm). WHEN CFRPSHEET IS TO RUN PERPENDICULAR TO CORNERS, CONCRETE CORNERSMUST BE ROUNDED TO A RADIUS OF AT LEAST 0.5 in. (15 mm). INTERNALCORNERS MUST BE SMOOTHED. NO DETAILING IS REQUIRED IF SHEETIS RUN PARALLEL TO CORNERS.

D. Handling of Primer and Resin

Refer to Manufacturer's specifications. DO NOT DILUTE PRIMER AND RESINWITH ANY SOLVENT. After the resin has been mixed with hardener, the mixed

resin batch must be used within its batch-life. The mixed batch resin must not beused after expiration of its batch-life because increased resin viscosity will preventproper impregnation of CFRP Sheet.



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E. Handling of CFRP Sheet

CFRP Sheet must not be handled roughly. CF Sheet must be stored either bybeing rolled to a radius greater than 12 in. (300 mm) or being dry stacked after cutting. When multiple lengths of CFRP Sheet are adhered to a concrete or steelsurface, a 4 in. (100 mm) OVERLAPPING LENGTH MUST BE APPLIED INLONGITUDINAL (FIBER) DIRECTION. No overlapping is required in the lateraldirection (unidirectional sheet only).

3.02 Surface Preparation

A. All substrates must be clean, sound and free of surface moisture and frost.Remove dust, laitance, grease, curing compounds, waxes, impregnations, foreignparticles and other bond inhibiting materials from the surface by blast cleaning or equivalent mechanical means. Any concrete surface including any exposed steelreinforcement or steel surface should be cleaned and prepared thoroughly byabrasive cleaning. Any spalled concrete areas should be patched prior toinstallation of CFRP laminates.

Any deteriorated concrete or corroded reinforcing steel must be repaired as per ICRI Specifications. Do not cover corroded reinforcing steel with CFRP.

B. Existing uneven surfaces must be filled with either the epoxy putty or a repair mortar or must be ground flat. If required, the strength of a concrete repair areacan be verified after preparation by random pull-off testing. Minimum tensilestrength required is 200 psi (1.4 MPa).

C. Prior to initiating surface preparation procedures, the Contractor shall first preparea representative sample area. The sample area shall be prepared in accordancewith the requirements of the Specification, and shall be used as a referencestandard depicting a satisfactorily prepared surface.

D. Where applicable for concrete members, Contractor shall install a sample area (2ft2 or 0.2 m2) of CFRP for purposes of in-situ bond testing to verify bond.

E. Maintain control of concrete chips, steel particles, dust and debris in each area of work. Clean up and remove such material at the completion of each day of blasting.



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3.03 Application Steps

A. The deteriorated surface layer of the base concrete or steel (weathered layer,laitance, surface lubricants, broken mortar pieces, paint coatings, staining, rust,etc.) must be removed and the surface ground using a grinder or abrasiveblasting.

Dusting from surface grinding must be removed using an air blower or other suitable means. If the dust has been removed by means of water washing, thesurface must be thoroughly dried.

B. Restoration of Concrete Cross Section

Defects in the concrete (such as broken pieces, voids, honeycomb, corrosion,etc.) must be chipped off and removed. If reinforcing bar has been exposed andcorrosion exists, it must be repaired before the concrete restoration commences.The repair material shall be selected as per ICRI "Guide to Selecting Repair Material", and project requirements.

Epoxy resin or similar material must be injected into concrete cracks greater than0.010 in. (0.25 mm) wide.

If water leaks through cracks or concrete joints are significant, water protectionand a water conveyance or run-off must be provided prior to concrete surfacerestoration.

3.04 Mixing Epoxy Resin

A. Epoxy based material used in the composite system may develop higher viscosityand/or slow curing and insufficient curing at low ambient temperature. Theambient temperature of the epoxy components shall be between 50 and 100

degrees F (10 to 38 degrees C) at the time of mixing. Presence of moisturemay inhibit adhesion of the system to the concrete or steel substrate. Providenecessary weather protection to protect surfaces from rain or cold.

B. Premix each component of the primer according to Manufacturer'srecommendation. Use the appropriate mixing tools, at proper speed to achievethe proper mix. Take care to scrape the sides of the pail during mixing.

C. Components which have exceeded their shelf-life shall not be used.

D. Mix only that quantity of epoxy which can be used within its pot life.



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3.05 Applications

A. No primer coat should be applied if the ambient temperature is lower than 40

degrees F (5 degrees C), or if rainfall or condensation is anticipated.

1. Primer must be thoroughly mixed with hardener at the specified ratio in themixing pot until it is uniformly mixed (about 2 minutes). Agitation shall beby means of electric hand mixer. Volume of primer prepared at one timemust be such that it can be applied within its batch life. A mixed primer

batch that has exceeded its batch life must not be used. (The batch lifemay vary subject to ambient temperature or volume of the mixed primer batch and care must be taken accordingly.)

2. Prime the concrete or steel surface with the penetrating primer prior toapplication of any subsequent coatings using brush or roller. Alternatively,the primer may be spray applied with airless spray equipment, followedimmediately by thorough back rolling to work the primer into the concretesurface. The primer shall be applied uniformly in sufficient quantity to fullypenetrate the concrete or cover the steel and produce a nonporous film onthe surface not to exceed two (2) dry mils (50 micrometers) in thicknessafter application. Volume to be applied may vary depending on directionand roughness of the concrete or steel surface.

3. Surface irregularities caused by primer coating must be ground andremoved using disc sander, etc. If any minor protrusions on the concreteor steel surface still remain, such surface defects may be corrected againusing epoxy resin base putty/filler as needed.

4. Apply base putty/filler to primed surfaces to fill all substrate voids andirregularities. (See 3.01-C.)

B. Adhesion of CFRP Sheet

CFRP Sheet shall not be applied whenever ambient temperature is lower than 40

degrees F (5 degrees C ), or whenever rainfall or condensation is anticipated.

1. CFRP Sheet must be cut beforehand into prescribed sizes using scissorsand/or cutter. The size of CFRP Sheet to be cut is preferable less than 10ft. (3 m) in length, but may be longer if access allows.

2. When the primer coat has been left unattended for more than one weekafter the application, the surface of the primer coat must be roughenedusing sandpaper. Do not solvent wipe.



SPECIFICATION

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3. Apply saturant coat to primed surface or CFRP sheet using a medium naproller (3/8 in. or 9.5 mm) to approximately 20 mil (500 micrometers) filmthickness.

4. CFRP Sheet is placed onto the concrete or steel surface where the wetsaturant coat has been applied. The surface of adhered CFRP sheet mustbe squeezed in the fiber direction(s) using a defoaming roller in order toimpregnate resin into CFRP Sheet and to defoam the resin coat.

For joining strips of CFRP Sheet in the fiber direction, a 4 in. (100 mm)overlapping length is required. At the overlapping location, additionalresin is applied to the outer surface of the CFRP Sheet layer to beoverlapped. No lapping is required in the fiber lateral direction(unidirectional sheet only).

Minimize the elapsed time between mixing and application of the saturantto ensure the material is applied to the sheet at least 15 minutes prior toany thickening or gelling.

5. The secondary saturant coat of mixed resin must then be applied onto thesurface of the CFRP Sheet. The surface onto which resin has beenapplied must be applied in fiber direction, in order to impregnate and

replenish resin into the CFRP Sheet using a roller in the same filmthickness as detailed in Item 3 above.

6. In case more than one layer of CFRP Sheet must be laminated, theprocesses as detailed in Items 3 through 5 must be repeated.

7. In the case of outdoor application, the work must be protected from rain,sand, dust, etc. by using protective sheeting and other barriers. Curing of adhered CFRP must be for no less than 3 hours (dry to touch) prior toapplication of topcoat.

3.06 Repair of Defective Work

A. Repair of all the defective work after the minimum cure time for the CFRPlaminates. Comply with material and procedural requirements defined in thisspecification. Repair all defects in a manner that will restore the system to thedesigned level of quality. Repair procedures for conditions that are notspecifically addressed in this specification shall be approved by the Owner'srepresentative. All repairs and touch up shall be made to the satisfaction of theOwner's representative.



SPECIFICATION

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3.07 Testing of the Installed CFRP Laminates

A. Test all the repaired areas to check for voids, bubbles and delaminations. Repair all voids, bubbles and delaminations by approved methods per manufacturer'sdirection.

B. Conduct direct pull-off test (concrete member only) to verify the tensile bondbetween the CFRP and the existing concrete substrate. Inspect the failuresurface of the core specimen. Failure at the bond line at tensile stress below 200psi (1.4 Mpa) is unacceptable.

C. Perform a minimum of one pull-off test (concrete member only) per_____ ft2

(___ m2) strengthened with the CFRP laminate system. The test is to becompleted prior to the application of topcoat finishes on the CFRP laminates.

D. Repair the test areas of the composite system to the satisfaction of the Owner'srepresentative.

3.08 Quality Control and Inspection

A. In Process Control

The Field Supervisor shall observe all aspects of onsite material preparation andapplication, including surface preparation, resin component mixing, application of primer, resin and CFRP Sheet, curing of composite, and the application of protective coating.

B. Inspection for Void/Delaminations

After allowing at least 24 hours for initial resin cure to occur, perform a visual andacoustic tap test inspection of the layered surface. Large delamination shall bemarked for repair. For small delaminations, which are typically less than 2 in.2

(1300 mm2 ) do not require corrective action.

C. Adhesion Testing

Adhesion Test: The Contractor will conduct adhesion testing of the fully curedCFRP Sheet concrete assembly. (See 3.07.)



SPECIFICATION

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D. Load Testing

If required by the Engineer, a representative area(s) shall be in-situ load testedbefore and after application of CFRP Sheet to verify results. The insitu test shallbe designed by the Engineer of Record and carried out by a designated thirdparty at owner’s expense.

E. Report

The Field Supervisor shall keep a copy of daily log report for inspection of the

Engineer of Record.



Appendix A Design Aids



MBrace Composite Strengthening System Design Guide

06/26/02A-2


Table A.1 – Design Material Properties for Various Fibers

Wabo®MBrace

Fiber

Design

Thickness,tf

(in/ply)

Design

Strength,f fu

(ksi)

Design

Strength/UnitWidth

(lb/in)

Design

Strain,fu

(in/in)

Tensile

Modulus,Ef

(ksi)

CF 130 High

Tensile Carbon

0.0065 550 3575 0.017 33,000

CF 530 High

Modulus Carbon

0.0065 510 3300 0.009 54,000

EG 900 E-Glass 0.0139 220 3050 0.021 10,500

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.001 0.0012 0.0014 0.0016 0.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003

c

3000 psi

4000 psi5000 psi

6000 psi8000 psi

10000 psi

Figure A.1 – as a Function of c, strain in the concrete




06/26/02 A-3

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.001 0.0012 0.0014 0.0016 0.0018 0.002 0.0022 0.0024 0.0026 0.0028 0.003

c

1

3000 psi4000 psi5000 psi6000 psi8000 psi10000 psi

Figure A.2 – 1 as a Function of the Strain in the Concrete

Table A.2 – Reduction factor for shear strength of U-wraps

R

f'c = 3000 psi 4000 psi 5000 psi

dfe/df = 1.0 0.9 0.8 1.0 0.9 0.8 1.0 0.9 0.8

1 ply 0.210 0.189 0.168 0.254 0.229 0.203 0.295 0.265 0.236

2 plies 0.148 0.134 0.119 0.180 0.162 0.144 0.209 0.188 0.167CF 130

3 plies 0.121 0.109 0.097 0.147 0.132 0.117 0.170 0.153 0.136

1 ply 0.298 0.268 0.238 0.361 0.325 0.289 0.419 0.377 0.335

2 plies 0.211 0.189 0.168 0.255 0.230 0.204 0.296 0.266 0.237CF 530

3 plies 0.172 0.155 0.138 0.208 0.187 0.167 0.242 0.218 0.193

1 ply 0.324 0.292 0.259 0.392 0.353 0.314 0.455 0.410 0.364

2 plies 0.229 0.206 0.183 0.278 0.250 0.222 0.322 0.290 0.258EG 900

3 plies 0.187 0.168 0.150 0.227 0.204 0.181 0.263 0.237 0.210




06/26/02A-4

C4-60.60.01

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Mn/Agh (ksi)

P n

/ A g

( k s i )

h

hf 'c = 4 ksi

f y = 60 ksi

= 0.60

g = 0.01

CF-130

f = 0.0015

f = 0

f = 0.003

f = 0.0045

f = 0.006

Figure A.3 – Interaction diagram for a column with f’ c = 4000 psi, =

0.60, and g = 0.01 wrapped with CF 130 FRP hoop reinforcement

C4-60.60.03

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Mn/Agh (ksi)

P n

/ A g

( k s i )

h

hf 'c = 4 ksi

f y = 60 ksi

= 0.60

g = 0.03

CF-130

f = 0

f = 0.0015

f = 0.003

f = 0.0045

f = 0.006

Figure A.4 – Interaction diagrams for a column with f’ c = 4000 psi, =





06/26/02 A-5

C4-60.90.01

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Mn/Agh (ksi)

P n

/ A g

( k s i )

h

hf 'c = 4 ksi

f y = 60 ksi

= 0.90

g = 0.01

CF-130

f = 0.0015

f = 0

f = 0.003

f = 0.0045

f = 0.006



C4-60.90.03

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Mn/Agh (ksi)

P n

/ A g

( k s i )

h

hf 'c = 4 ksi

f y = 60 ksi

= 0.90

g = 0.03

CF-130

f = 0

f = 0.0015

f = 0.003

f = 0.0045

f = 0.006






06/26/02A-6

C5-60.60.01

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Mn/Agh (ksi)

P n

/ A g

( k s i )

h

hf 'c = 5 ksi

f y = 60 ksi

= 0.60

g = 0.01

CF-130

f = 0.0015

f = 0

f = 0.003

f = 0.0045

f = 0.006



C5-60.60.03

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Mn/Agh (ksi)

P n

/ A g

( k s i )

h

hf 'c = 5 ksi

f y = 60 ksi

= 0.60

g = 0.03

CF-130

f = 0

f = 0.0015

f = 0.003

f = 0.0045

f = 0.006






06/26/02 A-7

C5-60.90.01

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Mn/Agh (ksi)

P n

/ A g

( k s i )

h

hf 'c = 5 ksi

f y = 60 ksi

= 0.90

g = 0.01

CF-130

f = 0.0015

f = 0

f = 0.003

f = 0.0045

f = 0.006



C5-60.90.03

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Mn/Agh (ksi)

P n

/ A g

( k s i )

h

hf 'c = 5 ksi

f y = 60 ksi

= 0.90

g = 0.03

CF-130

f = 0

f = 0.0015

f = 0.003

f = 0.0045

f = 0.006






06/26/02A-8

Table A.3 – Development Length of Sheets in Tension

n

dλ (in)

f'c = 3000 psi f'c = 4000 psi f'c = 5000 psi

CF 130 21.8 18.8 16.9

CF 530 20.2 17.5 15.6

EG 900 18.1 15.7 14.0



Appendix B Standard Details



Appendix C Equivalent Metric Equations




05/30/02C-2


The following lists metric equivalents of equations given in the text. Only thoseequations that are effected by the use of metric units are listed (any equations not listed

are applicable for U.S. or metric units). All the equations listed herein require units of

mm for lengths, MPa for stresses or pressures, and N for forces.

Chapter 6

008.0for 8.130065.0

52.0f

008.0for E

f p

p

pu

p p p

ps for Grade 270 steel (6-28M)

008.0for 8.13006.0

40.0f

008.0for E

f p

p

pu

p p p

ps for Grade 250 steel (6-29M)

Chapter 7

d bf 5.10

s

dcossinf AV wc

f

f fefvf

(7-2M)

fufu

e21 005.0

11900

Lk k R

(7-5M)

3/2

c1

27

f k

(7-7M)

d bf 5.32VV wcf s (7-10M)

Chapter 9

bf

fetf f ,tr

ns263

f AK

(9-2M)

wrapsFullfor 005.0

wraps"U"for 005.0

11900

Lk

R

fu

fufu

e1

(9-5M)

3/2

c1

27

f k

(9-6M)




Chapter 10

c

f fudf

f 25.0

tf

n

λ (10-1M)

wabo mbrace design guide

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