isis ec module 3 - notes (pdf)

8/11/2019 Isis Ec Module 3 - Notes (PDF)

1/35

ISIS Educational Module 3:

An Introduction to FRP-Reinforced Concrete

Prepared by ISIS Canada A Canadian Network of Centres of Excellencewww.isiscanada.com Principal Contributor: L.A. Bisby, Ph.D., P.Eng.Department of Civil Engineering, Queens UniversityContributors: M. Ranger and B.K. WilliamsMarch 2006

ISIS Education Committee:

N. Banthia, University of British ColumbiaL. Bisby, Queens UniversityR. Cheng, University of Alberta

R. El-Hacha, University of CalgaryG. Fallis, Vector Construction GroupR. Hutchinson, Red River College

A. Mufti, University of ManitobaK.W. Neale, Universit de SherbrookeJ. Newhook, Dalhousie UniversityK. Soudki, University of WaterlooL. Wegner, University of Saskatchewan


2/35

ISIS Canada Educational Module No. 3: An Introduction to FRP-Reinforced Concrete

1

Objectives of This ModuleThe objective of this module is to provide engineeringstudents with an overall awareness of the application anddesign of fibre reinforced polymer (FRP) reinforcingmaterials in new concrete structures. It is one of a series ofmodules on innovative FRP technologies available fromISIS Canada. Further information on the use of FRPs in avariety of innovative applications can be found atwww.isiscanada.com . While research into the use of FRPmaterials as reinforcement for concrete is ongoing, anoverall knowledge of currently available FRPreinforcements, and design procedures for their use, isessential for the new generation of structural engineers. The

problems of the future cannot be solved with the materialsand methodologies of the past. The primary objectives ofthis module are:1. to provide engineering students with a general

awareness of FRP materials and some of their potentialuses in civil engineering applications;

2. to introduce general philosophies and procedures fordesigning structures with FRP reinforcing materials;

3. to facilitate the use of FRP reinforcing materials in theconstruction industry; and

4. to provide guidance to students seeking additionalinformation on this topic.The material presented herein is not currently part of a

national or international code, but is based mainly on theresults of numerous detailed research studies conducted inCanada and around the world. Procedures, materialresistance factors, and design equations are based on therecommendations of the ISIS Canada Design Manual No. 3:Reinforcing Concrete Structures with Fibre ReinforcedPolymers. As such, this module should not be used as adesign document, and it is intended for educational use only.Future engineers who wish to design FRP-reinforcedconcrete structures should consult more complete designdocuments (refer to Section 10 of this document).


3/35


2

Additional ISIS Educational ModulesAvailable from ISIS Canada ( www.isiscanada.com )

Module 1 Mechanics Examples Incorporating FRPMaterials

Nineteen worked mechanics of materials problems are presentedwhich incorporate FRP materials. These examples could be usedin lectures to demonstrate various mechanics concepts, or could beassigned for assignment or exam problems. This module seeks toexpose first and second year undergraduates to FRP materials atthe introductory level. Mechanics topics covered at the elementarylevel include: equilibrium, stress, strain and deformation,elasticity, plasticity, determinacy, thermal stress and strain, flexureand shear in beams, torsion, composite beams, and deflections.

Module 2 Introduction to FRP Composites forConstruction

FRP materials are discussed in detail at the introductory level.This module seeks to expose undergraduate students to FRPmaterials such that they have a basic understanding of thecomponents, manufacture, properties, mechanics, durability, andapplication of FRP materials in civil infrastructure applications. Asuggested laboratory is included which outlines an experimental

procedure for comparing the stress-strain responses of steel versusFRPs in tension, and a sample assignment is provided.

Module 4 Introduction to FRP-Strengthening ofConcrete Structures

The use of externally-bonded FRP reinforcement for strengtheningconcrete structures is discussed in detail. FRP materials relevantto these applications are first presented, followed by detaileddiscussions of FRP-strengthening of concrete structures in flexure,shear, and axial compression. A series of worked examples are

presented, case studies are outlined, and additional, morespecialized, applications are introduced. A suggested assignmentis provided with worked solutions, and a potential laboratory forstrengthening concrete beams in flexure with externally-bondedFRP sheets is outlined.

Module 5 Introduction to Structural HealthMonitoring

The overall motivation behind, and the benefits, design,application, and use of, structural health monitoring (SHM)systems for infrastructure are presented and discussed at the

introductory level. The motivation and goals of SHM are first presented and discussed, followed by descriptions of the variouscomponents, categories, and classifications of SHM systems.Typical SHM methodologies are outlined, innovative fibre opticsensor technology is briefly covered, and types of tests which can

be carried out using SHM are explained. Finally, a series of SHMcase studies is provided to demonstrate four field applications ofSHM systems in Canada.

Module 6 Application & Handling of FRPReinforcements for Concrete

Important considerations in the handling and application of FRPmaterials for both reinforcement and strengthening of reinforcedconcrete structures are presented in detail. Introductoryinformation on FRP materials, their mechanical properties, andtheir applications in civil engineering applications is provided.Handling and application of FRP materials as internalreinforcement for concrete structures is treated in detail, includingdiscussions on: grades, sizes, and bar identification, handling andstorage, placement and assembly, quality control (QC) and qualityassurance (QA), and safety precautions. This is followed byinformation on handling and application of FRP repair materialsfor concrete structures, including: handling and storage,installation, QC, QA, safety, and maintenance and repair of FRPsystems.

Module 7 Introduction to Life Cycle Costing forInnovative Infrastructure

Life cycle costing (LCC) is a well-recognized means of guidingdesign, rehabilitation and on-going management decisionsinvolving infrastructure systems. LCC can be employed to enableand encourage the use of fibre reinforced polymers (FRPs) andfibre optic sensor (FOS) technologies across a broad range ofinfrastructure applications and circumstances, even where theinitial costs of innovations exceed those of conventionalalternatives. The objective of this module is to provideundergraduate engineering students with a general awareness ofthe principles of LCC, particularly as it applies to the use of fibre

reinforced polymers (FRPs) and structural health monitoring(SHM) in civil engineering applications.

Module 8 Durability of FRP Composites forConstruction

Fibre reinforced polymers (FRPs), like all engineering materials,are potentially susceptible to a variety of environmental factorsthat may influence their long-term durability. It is thus important,when contemplating the use of FRP materials in a specificapplication, that allowance be made for potentially harmfulenvironments and conditions. It is shown in this module thatmodern FRP materials are extremely durable and that they havetremendous promise in infrastructure applications. The objective of

this module is to provide engineering students with an overallawareness and understanding of the various environmental factorsthat are currently considered significant with respect to thedurability of fibre reinforced polymer (FRP) materials in civilengineering applications.


4/35


3

Section 1

Introduction and Overview

WHY USE FRPs?

The population of the modern developed world depends ona complex and extensive system of infrastructure formaintaining economic prosperity and quality of life. Theexisting public infrastructure of Canada, the United States,Europe, and other countries has suffered from decades ofneglect and overuse, leading to the accelerated deteriorationof bridges, buildings, and municipal and transportationsystems, and resulting in a situation that, if left unchecked,may lead to a global infrastructure crisis. Much of ourinfrastructure is unsatisfactory in some respect, and publicfunds are not generally available for the requiredreplacement of existing structures or construction of new

ones.

Fig. 1-1. Severely c orroded r einforcing steel in th isbridge column h as resulted in spalling of theconcrete cover and exposure of the steelreinforcement.

One of the primary factors which has led to the currentunsatisfactory state of our infrastructure is corrosion ofreinforcing steel inside concrete (Fig. 1), which causes the

reinforcement to expand, and results in delamination orspalling of concrete, loss of tensile reinforcement, or insome cases failure. Because infrastructure owners can nolonger afford to upgrade and replace existing structuresusing the same materials and methodologies as have been

used in the past, they are looking to newer technologies,such as non-corrosive FRP reinforcement, that will increasethe service lives of concrete structures and reducemaintenance costs.

FRPs have, in the last ten to fifteen years, emerged as a promising alternative material for reinforcement of concretestructures. FRP materials are non-corrosive and non-magnetic, and can thus be used to eliminate the corrosion

problem invariably encountered with conventionalreinforcing steel. In addition, FRPs are extremely light,versatile, and demonstrate extremely high tensile strength,making them ideal materials for reinforcement of concrete(refer to Figure 1-2).

Fig. 1-2. FRP Reinforcing bars being installed inthe conc rete deck of the Salmon River Bridge,British Columbia prior to pouring of the concrete.FRPs are particularly us eful for reinforc ingconcrete bridge decks which are highlysusceptible to corrosion.


5/35


4

Section 2

FRP Materials This section provides a brief overview of FRP materials andsome of their important characteristics and properties whenused as reinforcing materials for concrete. A more completediscussion of FRP materials and their applications in civilengineering can be obtained from ISIS EC Module 2: FRPComposites for Civil Engineering Applications, or from oneof a number currently available composite materialstextbooks.

GENERAL

FRP materials, originally developed for use in theautomotive and aerospace sectors, have been considered foruse as reinforcement of concrete structures since the 1950s.However, it is really only in the last 10 years or so thatFRPs have begun to see widespread use in large civilengineering projects, likely due to drastic reductions in FRPmaterial and manufacturing costs, which have made FRPscompetitive on an economic basis.

Many types and shapes of FRP materials are nowavailable in the construction industry. For the purposes oftensile reinforcement of concrete, the currently availablereinforcing products include unidirectional FRP bars, whichhave fibres oriented along the axis of the reinforcementonly, and orthogonal grids, which have unidirectional barsrunning in two (or sometimes 3) orthogonal directions. Inthis document, the focus is on unidirectional FRPreinforcing bars, since they are the most widely used of the

FRP reinforcing products currently available in NorthAmerica. Also, although it has been demonstrated throughresearch that FRP materials can be effectively used for

prestressed reinforcement of concrete structures, this is aspecialized topic and is beyond the scope of this module.Fig. 2-1 shows various types and shapes of currentlyavailable FRP materials.

ConstituentsFRP materials are composed of high strength fibresembedded in a polymer matrix. The fibres, which have verysmall diameters and are generally considered continuous,

provide the strength and stiffness of the composite, while

the matrix, which has comparatively poor mechanical properties, separates and disperses the fibres. The primaryfunction of the matrix is to transfer loads to the fibresthrough shear stresses that develop at the fibre-matrixinterface, although it is also important for environmental

protection of the fibres. In concrete reinforcingapplications, the fibres are generally carbon (graphite),glass, or aramid (Kevlar), and the matrices are typicallyepoxies or vinyl esters. Fig. 2-2 shows typical stress-straincurves for fibres, matrices, and the FRP materials that result

from the combination of fibres and matrix. The reader isreferred to ISIS EC Module 2 (ISIS, 2003) for furtherinformation on fibres and matrices.

Fig. 2-1. Various t ypes and sh apes of FRPs used inthe construction industry

Fig. 2-2. Stress-strain relationship s for fibres,matrix , and FRP.

Manufacturing ProcessAlthough a variety of techniques can be used to manufactureFRP shapes, a technique called pultrusion is used almostexclusively for the manufacture of FRP reinforcing rods. Inthis technique, continuous strands of the fibres are drawnfrom creels (spools of fibres) through a resin tank, wherethey are saturated with resin, pulled through a number ofwiper rings, and finally pulled through a heated die. This

process simultaneously forms and heat cures the FRP into a

matrix

Strain[%]

fibres

FRP

0.4 4.8 > 10

Stress[Mpa]

1800-4900

600-3000

34-130


6/35


7/35


6

Table 2-1. Selected Properties of Typical Currently Available FRP Reinforcing Products

Reinforcement Type Designation Diameter[mm] Area[mm 2]

Tensile Strength[MPa]

Elastic Modulus[GPa]

Deformed Steel #10 11.3 100 400* 200V-ROD CFRP Rod 3/8 9.5 71 1431 120V-ROD GFRP Rod 3/8 9.5 71 765 43NEFMAC GFRP Grid G10 N/A 79 600 30NEFMAC CFRP Grid C16 N/A 100 1200 100NEFMAC AFRP Grid A16 N/A 92 1300 54LEADLINE TM CFRP Rod -- 12 113 2255 147

* specified yield strength

Strain [%]

0 1 2 3

S t r e s s

[ M P a

]

0

500

1000

1500

2000

2500SteelISOROD CFRPISOROD GFRPNEFMAC GFRPNEFMAC CFRPNEFMAC AFRPLeadline TM CFRP

Fig. 2-7. Stress-strain plots for variou s reinforc ingmaterials

Advantages and DisadvantagesFRP materials for use in concrete reinforcing applicationshave a number of key advantages over conventionalreinforcing steel. Some of the most important advantagesinclude: FRP materials do not corrode electrochemically, and

have demonstrated excellent durability in a number ofharsh environmental conditions;

FRP materials have extremely high strength-to-weight ratios . FRP materials typically weigh less thanone fifth the weight of steel, with tensile strengths thatcan be as much as 8 to 10 times as high; and

FRP materials are electromagnetically inert . Thismeans that they can be used in specialized structuressuch as buildings to house magnetic resonance imaging(MRI) or sensitive communications equipment, etc.

There are, however, some disadvantages to using FRPs, asopposed to conventional reinforcing steel, as reinforcementfor concrete. The main disadvantage is the comparativelyhigh initial cost of FRP materials. Although prices havedropped drastically in recent years, most FRP materialsremain more expensive than conventional reinforcing steelon an initial material cost basis. However, because of the

high strength of these materials, they are often competitiveon a cost-per-force basis. Furthermore, the excellentdurability of FRP reinforcing materials in concrete, whichhas the potential to increase the service lives of structureswhile reducing inspection and maintenance costs, makesthem cost-effective when the entire life-cycle cost of astructure is considered, rather than the initial construction

cost alone.Another often cited potential disadvantage of FRP

materials is their relatively low elastic modulus as comparedwith steel. This means that FRP-reinforced concretemembers are often controlled by serviceability (deflection)considerations, rather than strength requirements.

ADDITIONAL CONSIDERATIONS

Coefficient of Thermal ExpansionThe thermal properties of FRP reinforcing products aresubstantially different than those of conventional reinforcingsteel and concrete, and can also vary a great deal in the

longitudinal and transverse directions. The characteristicsare highly variable among different FRP products, and it isdifficult to make generalizations regarding thermalexpansion or other properties. The thermal properties ofany FRP reinforcing material should be thoroughlyinvestigated before it is used as reinforcement for concrete,since differential thermal expansion of FRPs inside concretehas the potential to cause cracking and spalling of theconcrete cover.

Table 2-2. Typical Coeffic ients o f ThermalExpansion for FRP Reinforcin g Bars [ 10 -6/C]

MaterialDirectionSteel GFRP CFRP AFRP

Longitudinal 11.7 6 to 10 -1 to 0 -6 to 2Transverse 11.7 21 to 23 22 to 23 60 to 80

Effect of Elevated Temperature or FireElevated temperatures, as may be experienced in someindustrial settings or in the case of fire, adversely affect themechanical and bond properties of FRP reinforcingmaterials in concrete. Thus, special precautions are required


8/35


7

when FRPs are used in structures where elevatedtemperatures or fire are concerns. In most cases, thetemperature or the FRP reinforcement should be maintained

below the glass transition temperature (GTT) of the polymermatrix. For currently available FRP reinforcing productsthe GTT is generally in the range of 65 to 150C.

Bond PropertiesThe properties of the bond between FRP reinforcing barsand concrete depend on the surface treatment applied to theFRP reinforcing bar during manufacturing, the mechanical

properties of the FRP, and the environmental conditions towhich the bar is subjected during its lifetime. Again,generalizations are difficult to make, although the bond

between currently available FRP reinforcing materials andconcrete appears equivalent (or superior in some cases) tothat between steel reinforcement and concrete. The bond ofFRP bars to concrete does not depend on the concretestrength, as it does for steel reinforcement.

Creep and RelaxationWhen FRP materials are subjected to a constant elevatedstress level they can fail suddenly and unexpectedly. Thistype of failure is referred to as creep-rupture and is highly

undesirable. The larger the ratio of the sustained (deadload) stress to the transient (live load) stress in an FRPreinforcing bar, the more likely creep-rupture becomes.Susceptibility to creep rupture is also influenced by UVradiation, high temperature, alkalinity, and weathering.

Different FRP types have different susceptibilities tocreep-rupture. Carbon FRPs are the least susceptible,followed by aramid FRPs. Glass FRPs are the mostsusceptible. To protect against creep-rupture, the materialresistance factors suggested by ISIS Canada (ISIS, 2001) forFRP reinforcements have been adjusted to account for theeffect of sustained load. These resistance factors, frp, aregiven in Table 3-1.

DurabilityThe durability of FRP reinforcing bars in concrete is acomplex topic and research in this area is ongoing. Readersseeking additional information on the durability of FRPmaterials are encouraged to consult ISIS Educational

Module #8, also available from ISIS Canada atwww.isiscanada.com . To date, FRP reinforcing applicationsin concrete structures have performed well, and no failuresdue to durability problems have been reported.

Section 3

Design for Flexure

PHILOSOPHY AND ASSUMPTIONS

The design of FRP-reinforced concrete in Canada should beconducted under the unified limit-states philosophycurrently used by the existing design codes. For buildings,loads and load combinations for FRP-reinforced concretemembers should be determined in accordance with CSA-S806-02. For bridges, the Canadian Highway Bridge DesignCode, CSA-S6-05, should be used. Serviceability checksfor cracking and deflection must also be performed.

Resistance FactorsFollowing the recommendations of ISIS Canada DesignManual No. 3, the material resistance factor for concrete istaken as c = 0.60 for buildings, 0.65 for precast concrete,and 0.75 for bridges. The material resistance factor forFRPs depends on the type of FRP material, and is based onthe variability of material characteristics, the effect ofsustained load, and various durability considerations. Table3-1 provides resistance factors for steel, concrete, and FRPmaterials as specified by relevant Canadian codes.

AssumptionsIt is assumed that FRPs are perfectly linear-elastic materials.Thus, failure of an FRP-reinforced section in flexure can bedue to FRP rupture or concrete crushing. The ultimateflexural strength for both of these failure modes can becalculated using a similar methodology as that used forsteel-reinforced sections. Hence, the following additionalassumptions are required:1. the failure strain of concrete in compression is

3500 10 -6;2. the strain in the concrete at any level is proportional to

the distance from the neutral axis (plane sectionsremain plane);

3. FRPs are linear elastic to failure;4. concrete compressive stress-strain curve is parabolic

and concrete has no strength in tension;5. perfect bond exists between FRP reinforcement and

concrete; and6. neglect FRPs strength in compression.


9/35


8

Table 3-1. Resistanc e Factors f or FRP BarsMaterial Notation Factor

Building Components: CSA-S806-02 Concrete cast in situ c 0.60Precast concrete c 0.65Steel reinforcement s 0.85

Carbon FRP f 0.75Glass FRP f 0.75

Aramid FRP f 0.75Bridge Components: CSA-S6-05

Concrete c 0.75Carbon FRP f 0.75

Aramid FRP f 0.60Glass FRP f 0.50

Fig. 3-1. Assumed stress-strain behaviour of FRP.

Fig. 3-2. Assumed stress-strain behaviour ofconcrete.

FAILURE MODESThere are three potential flexural failure modes for FRP-reinforced concrete sections: Balanced failure simultaneous FRP tensile rupture

and concrete crushing Compression failure concrete crushing prior to FRP

tensile rupture Tension Failure tensile rupture of the FRP prior to

concrete crushing

Compression failure is the most desirable of the abovefailure modes. This failure mode is less violent than tensionfailure, and is similar to the failure of an over-reinforcedsection when using steel reinforcement.

Tension failure is less desirable, since tensile rupture ofFRP reinforcement will occur with less warning. Tensionfailure will occur when the reinforcement ratio is below the

balanced reinforcement ratio for the section. This failuremode is permissible with certain safeguards.

Balanced FailureAs mentioned above, balanced failure will occur whenconcrete crushing occurs simultaneously with FRP tensilerupture. It is important to remember that the balancedfailure condition is drastically different for FRP-reinforcedconcrete than it is for members reinforced with steel.Because FRPs will not yield at the balanced condition, anFRP-reinforced concrete member at the balanced conditionwill fail suddenly, although accompanied by cracking and a

significant amount of deflection. At balanced failure, thestrain in the concrete reaches its ultimate value, cu =0.0035, while the FRP reinforcement simultaneouslyreaches its ultimate strain, frpu . The ultimate strain of theFRP depends on the specific FRP reinforcing material beingused (refer to Table 2-1), and is determined from the FRPultimate stress, f frpu , and tensile elastic modulus, E frp, using:

frp

frpu frpu E

f = (Eq. 3-1)

Using strain compatibility, for a rectangular cross-sectionwith a single layer of FRP reinforcement, the distribution ofstrains across the member can be illustrated as shown in Fig.3-3a. Thus, the ratio of the balanced neutral axis depth, cbto the effective depth of the section, d , at the balancedreinforcement ratio, frpb , can be expressed in terms ofknown quantities as follows:

frpucu

cub

d c

+

= (Eq. 3-2)

To determine the balanced reinforcing ratio, forceequilibrium over the cross-section is utilized, and thecompressive and tensile stress resultants, C and T , areequated as follows:

T C = (Eq. 3-3)

The true distribution of stress in the concrete in thecompression zone is non-linear, as shown in Figure 3-3a.However, as is the case for steel-reinforced concretemembers, we can replace the non-linear stress distributionwith an equivalent rectangular stress-block. To do this, the

f fr u

Strain

fr u

Stress

E fr

1

f c

Strain

cu

Stress

1

E c

c c

f c


10/35


9

same stress-block parameters, 1 and 1, are used as thosesuggested in CSA A23.3-94/CHBDC for steel-reinforcedconcrete, namely:

67.0'0015.085.01 = c f (Eq. 3-4)67.0'0025.097.01 = c f (Eq. 3-5)

Thus, the compressive stress resultant is:

bc f C bcc 11 ' = (Eq. 3-6)

The tensile stress resultant is determined from the FRPultimate stress and the cross-sectional area of FRPreinforcement:

frp frp frpu frp A E T = (Eq.3-7)

Now, equating the compressive and tensile stress resultantsand rearranging, the balanced failure reinforcement ratio, frpb , is obtained:

+

== frpucu

cu

frpu

c

frp

c frpb frpb f

f bd

A

'

11 (Eq. 3-8)

For a given FRP-reinforced concrete member, an FRPreinforcement ratio less than frpb will result in tensionfailure, and an FRP reinforcement ratio greater than frpb will result in compression failure. Next, we will examinethe two potential failure modes that are of practical interest.

Compression FailureIf an FRP-reinforced concrete section contains sufficienttensile reinforcement, then failure of the section will beinduced by crushing of the concrete in the compression zone

before the FRP reaches its ultimate strain. This type offailure is highly unlikely for a T-section in positive bending,since the width of the compression zone, b, is very large,and so only rectangular sections are considered.

For the case of compression failure, the strains in thecross-section can be illustrated as shown in Figure 3-3b.Again, the strain in the extreme compression fibre isassumed to be cu = 0.0035, and the non-linear stressdistribution in the concrete can be replaced by the CSA

A23.3-94/CHBDC equivalent rectangular stress block(using parameters 1 and 1 as defined previously).The compressive and tensile stress resultants can be

determined as follows:

cb f C cc 1'

1 = (Eq. 3-9)

frp frp frp f AT = (Eq. 3-10)

A complication in the analysis arises from the fact that FRPreinforcement does not yield, and hence the stress in theFRP at compression failure of the member, f frp, is unknown.Equating the tensile and compressive stress resultantsyields:

b f

f Aac

cc

frp frp frp

'1

1

== (Eq. 3-11)

And from strain compatibility (refer to Fig. 3-3b) we canderive the following:

aad

E f

ccd

ccd

cu frp frp

cu frp

cu

frp

=

=

=

1

1

11

(Eq. 3-12)

Now, substituting Eq. 3-11 into Eq. 3-12, and solving forthe stress in the FRP reinforcement at compressive failure,gives:

+= 141

21 2

1'

11

cu frp frp frp

cccu frp frp E

f E f

(Eq. 3-13)

Once the stress in the FRP reinforcement is known, Eq. 3-11can be used to determine the depth of the equivalentrectangular stress block, a , and the flexural capacity, M r , can

be obtained in a similar fashion as for steel-reinforcedconcrete:

=

2a

d f A M frp frp frpr (Eq. 3-14)

NOTE:Rather than using Eq. 3-13 to determine the stress in theFRP at compressive failure, an iterative procedure can be

performed using Eqs. 3-9, 3-10, and 3-11 by assuming aneutral axis depth, calculating the compressive and tensilestress resultants using strain compatibility, and checking ifC = T . If C T , the neutral axis depth is updated and the

procedure is repeated until convergence of the neutral axisdepth is achieved within a suitable tolerance.


11/35


10

Fig. 3-3. Flexural failure mod es for FRP-reinfo rced co ncrete beams.

Tension FailureIf the FRP reinforcement ratio is less than the balancedfailure reinforcement ratio, then the section will fail by FRPtensile rupture before the concrete in the compression zonecrushes (Fig. 3-3c). This situation is different from anunder-reinforced concrete member with steel reinforcementin that there is no yielding of the FRP. In this case, the

strain in the concrete at failure is less than cu = 0.0035, andthe strain in the FRP reinforcement is given by:

frp

frpu frpu E

f = (Eq. 3-15)

Because the concrete in the compression zone is not atultimate, the stress distribution in the concrete cannot be

Cross-section Strain Distribution Stress Distribution EquivalentStress Distribution

b

d

A frpb

cb

cu

frpu

1 cfc

C

Tf frpu

a = 1cb

d

A frp

c

cu

frp < frpu

1 cfc

C

Tf frp

a = 1c

d

A frp

c

c < cu

frpu

cfc

C

Tf frpu

a = c

(a)

BALANCEDFAILURE

c = cu frp = frpu

(b)COMPRESSION

FAILUREc = cu

frp < frpu

(c)

TENSION FAILUREc < cu

frp = frpu


12/35


11

described using the equivalent rectangular stress block parameters used previously. The 1 and 1 parameterssuggested by CSA A23.3-94/CHBDC are valid only for thecase of c = cu. Thus, modified stress block parameters arerequired. These modified parameters, and , can bedetermined either from tabulated values available in ISISDesign Manual No. 3, or from Figs. 3-2 and 3-3 below,which give and as functions of the strain in the concretefor a variety of concrete strengths.

Fig. 3-2. Equivalent stress-block parameter forconcrete.

Fig. 3-3. Equivalent stress-block parameter forconcrete.

Once and have been determined, the tensile andcompressive stress resultants can be determined for anassumed value of the neutral axis depth using:

frp frpu frp frp frpu frp frp E A f AT == (Eq. 3-16)

cb f C cc '= (Eq. 3-17)

Again, for equilibrium it is required that:

T C = (Eq. 3-18)

If the above equation is not satisfied, then a new value of theneutral axis depth is assumed, and are reevaluated, andEq. 3-18 is checked. This process is repeated in an iterativefashion until Eq. 3-18 is satisfied. For each iteration, theupdated neutral axis depth, c, can be determined using:

b f

E Ac

cc

frp frpu frp frp

'

= (Eq. 3-19)

where and are determined at the following concretestrain (from strain compatibility, Fig. 3-3c):

cd c

frpuc = (Eq. 3-20)

Once the tensile and compressive stress resultants areknown, the moment resistance of the member can bedetermined by taking moments about the compressive stressresultant. Thus:

=

2c

d f A M frpu frp frpr

(Eq. 3-21)

Due to the brittle failure associated with failure by ruptureof the FRP reinforcement, it is recommended that andadditional safety requirement of:

f M r M 5.1 (Eq. 3-22)

be applied when failure is by tensile rupture of the FRP.

MINIMUM FLEXURAL RESISTANCE

Three criteria are suggested by ISIS Canada Design Manual No. 3 to provide minimum tensile reinforcement for an

FRP-reinforced concrete member.Failure of a member immediately after cracking, which

occurs suddenly and without warning, should be avoided.Thus, the moment resistance of an FRP-reinforced concretemember, M r , should be at least 50% greater than thecracking moment, M cr . Hence:

cr r M M 5.1 (Eq. 3-23)


13/35


12

The cracking moment is determined from the modulus ofrupture of the concrete, f r , the moment of inertia of thetransformed section, I t , and the distance from the centroidalaxis of the transformed section to the extreme tension fibre,

yt , using:

t

t r cr y

I f M = where cr f f '6.0= (Eq. 3-24)

As the minimum reinforcement condition is usuallygoverned by tensile rupture of the FRP reinforcement, themoment resistance, M r , must be at least 50% greater thanthe moment due to the factored loads, M f . Thus:

f M r M 5.1 (Eq. 3-25)

ADDITIONAL CONSIDERATIONS

Beams with FRP Rebars in MultiplelayersFor the case of FRP-reinforced concrete beams withreinforcement in two or more layers, the strain in the outerlayer of FRP reinforcement is the critical strain. This meansthat lumping of reinforcement, as is commonly performedin the analysis of steel-reinforced concrete beams, is not

permitted (refer to Figure 3-4). Members can be easilydesigned on the basis of the strain in the outermost layer ofFRP reinforcing bars by assuming strain compatibility.

Fig. 3-4. Lumping o f reinforcement is no tpermitted.

Beams with CompressionReinforcementFRP reinforcing materials are generally weak incompression. Although these materials may be used ascompression reinforcement, their contribution to the flexuralstrength of FRP-reinforced concrete members should beneglected.

Section 4

ServiceabilityGENERAL

Serviceability considerations, relating both to cracking andto deflection, are crucial factors in the design of FRP-reinforced concrete flexural members. FRP reinforcing barsgenerally have much higher strengths than the yield strengthof conventional steel reinforcement. However, the modulusof elasticity of FRP materials is generally less than that ofreinforcing steel, and this can lead to the formation of largecracks or to unserviceable deflections. The result is that, inmany cases, serviceability considerations may control thedesign of FRP-reinforced concrete members.

CRACKING

In steel-reinforced concrete members, it is necessary tocontrol crack widths both for aesthetic reasons and to

prevent corrosion of reinforcing steel. For FRP-reinforcedmembers, there is no such corrosion requirement (FRP barsare non-corrosive) and so cracking must be limited

primarily for aesthetic reasons, as well as to control serviceload stresses in the reinforcement (to prevent creep-rupture).

If there is a need to calculate the crack width at serviceload levels for an FRP-reinforced concrete member,guidance is available in Section 7.4.1 of ISIS DesignManual No. 3. The limiting crack width for FRP-reinforcedmembers is recommended by CHBDC (CSA, 2005) to be0.7 mm, except for members subjected to aggressiveenvironments where 0.5 mm is recommended. Alternatively,as a conservative approach, the ISIS design guidelinessuggest, to control cracking, that the maximum strain intensile FRP reinforcement at service should not exceed0.2%. Thus:

002.0 frps (Eq. 4-1)

The strain in the FRP at service load levels can bedetermined using the concept of transformed sections ineither cracked or un-cracked sections.


14/35


13

If there is a need to calculate the crack width at serviceload levels for an FRP-reinforced concrete member,guidance is available in Section 7.3.1 of ISIS DesignManual No. 3.

DEFLECTION

Since the modulus of elasticity of FRP reinforcement isgenerally substantially lower than for conventional steelreinforcement, FRP-reinforced members typically displaysignificantly more deflection than equivalent steel-reinforced members. This means that the minimumthickness (overall member depth) requirements used in CSAA23.3-94 or CSA S6-05 for steel-reinforced concrete areunconservative, and are thus not directly applicable tomembers reinforced with FRPs. Furthermore, deflectionsfor FRP-reinforced concrete members must be checkedagainst the requirements of CSA A23.3-94 or CSA S6-05using the effective moment of inertia, as described below.

MINIMUM THICKNESS

For steel-reinforced concrete structures, CSA A23.3-94recommends span-to-depth ratios for a variety of membertypes and end conditions to ensure adequate deflectioncontrol. For FRP-reinforced concrete members, thefollowing equation should be used to ensure similar span todeflection ratios as for steel-reinforced beams:

d

frp

s

s

n

frp

n

hh

=

ll

(Eq. 4-2)

where: n is the member length [mm]h is the member thickness [mm] s is the maximum strain allowed in the steel

reinforcement in servicefrps is the maximum strain allowed in the FRP

reinforcement in service d is a dimensionless coefficient taken as 0.50 for

a rectangular section

The ratio ( l n /h) s is the equivalent ratio for steel-reinforcedconcrete and is obtained from Table 9-1 of CSA A23.3-94.

EFFECTIVE MOMENT OF INERTIA

If a member remains uncracked under service loads, then

deflection requirements can be checked using the concept oftransformed sections. However, if the member is crackedunder service load, the effective moment of inertia should

be calculated (for a rectangular section) using the followingequation, which was empirically derived from test data onFRP-reinforced concrete members:

( )cr t a

cr cr

cr t e

I I M M

I

I I I

+

=2

5.01

(Eq. 4-3)

where: I cr is the moment of inertia of the cracked sectiontransformed to concrete with concrete in tensionignored, calculated using the Eq. 4-4 below [mm 4]

I t is the moment of inertia of a non-cracked sectiontransformed to concrete [mm 4]

M cr is the cracking Moment [Nmm] M a is the maximum moment in a member at theload stage at which deflection is being calculated[Nmm]

23

)1(3

)(k d An

kd b I frp frpcr += (Eq. 4-4)

where: b is the width of the compression zone [mm]d is the effective depth of the section [mm]n frp is the modular ratio E frp/ E c

The neutral axis depth, kd , can be calculated using thefollowing equation:

( ) ++= frp frp frp frp frp frp nnnk 22 (Eq. 4-5)

where: frp is the FRP reinforcement ratio.


15/35


14

Section 5

DeformabilityIn the past, the concept of a balanced section was used toimplicitly design steel-reinforced concrete structures forductile behaviour. Traditionally, a balanced section is onein which the steel reinforcement reaches the yield strainsimultaneously with the crushing strain being reached in theconcrete. It was recognized that an under-reinforced design,having reinforcement less than the balanced condition, gaveductile behaviour, with very large curvature observed priorto failure. Conversely, an over-reinforced design, withreinforcement above the balanced condition, gave a verysafe structure with comparatively less deformation observed

prior to failure. Thus, a trade-off between ductility andsafety was recognized.

Unlike steel, FRP reinforcement has a linear strain-stress relationship. For FRP reinforcement there is no

plastic phase. However, because of the comparatively lowmodulus of elasticity of FRP reinforcing materials, an FRP-reinforced member will also exhibit sufficiently largecurvature at failure. Because of this important difference inthe characteristics of FRP reinforcement, in comparisonwith steel, it is important that issues of deformability andsafety be thoroughly investigated.

ISIS Canada Design Manual No. 3 suggests that theFRP reinforcement ratio can be less than the balanced FRP

reinforcement ratio, provided that the curvature at serviceloads is an acceptably low proportion of the curvature atultimate. This concept is referred to as deformability andcan be summarized, for rectangular and T-beams in flexure,

by the following equation:

=

s s

uu

M M

DF 4 for rectangular sections (Eq. 5-1)

=

s s

uu

M M

DF 6 for T-sections (Eq. 5-1)

In the previous expressions, u and M u are the curvature andmoment at ultimate conditions, respectively, and s and M are the curvature and moment at service conditions, but notexceeding the condition where the maximum concretecompressive strain = 0.001.

The concept of deformability, while extremelyimportant, is rather complex and is not discussed further.Deformability is discussed in significant detail in Chapter 9of ISIS Design Manual No. 3.

Section 6

Spacing and CoverConcrete CoverAdequate concrete cover to the FRP-reinforcement isrequired to prevent cracking due to thermal expansion,swelling from moisture, and to protect the FRPreinforcement from fire. Due to the wide variety of FRPreinforcing products available, it is difficult to makegeneralizations as to the required concrete cover for varioustypes of FRP reinforcing materials. CHBDC (CSA, 2005)recommends that the minimum clear cover shall be 35 mm

with a construction tolerance of 10 mm. The overallguidelines suggested by ISIS Canada Design Manual No. 3are as follows;

Table 6-1. Cover to Flexural ReinforcementExposure Beams SlabsInterior 2.5 d b or 40mm 2.5 d b or 20mmExterior 2.5 d b or 50mm 2.5 d b or 30mm

* d b is the bar diameter in mm

CSA-S806-02 provides additional information on concretecover requirements if fire rating requirements area designconsideration.

Bar SpacingTo ensure that concrete can be placed properly and thattemperature cracking will be avoided, the minimum barspacing for longitudinal reinforcing bars in FRP-reinforcedconcrete members should be taken as the maximum of: 1.4 d b 1.4 times the maximum aggregate size (MAS) 30 mm the concrete cover obtained above

The maximum spacing of flexural reinforcement should be taken, in the same manner as suggested by CSA A23.3-94 for steel-reinforced concrete, as the smaller of: 5 times the slab thickness 500 mm


16/35


15

ConstructabilityThe following are additional considerations which must beaccounted for when designing with FRP reinforcement: All FRP materials should be protected against UV

radiation. Storage and handling requirements for FRPs may vary

significantly depending on the specific product beingused.

FRPs should not come into contact with reinforcingsteel in a structure.

FRP reinforcement is light and must be tied, with plastic ties, to formwork to prevent it from floatingduring concrete placing and vibrating operations.

Care must be taken when vibrating concrete to ensurethat the FRP reinforcement is not damaged (plastic

protected vibrators should be used).

Additional information on the appropriate handling andapplication of FRP materials is given in ISIS EducationalModule 6.

Section 7

Additional TopicsDEVELOPMENT LENGTH ANDANCHORAGE

For concrete to be reinforced with FRPs, there must be forcetransfer from the FRP to the concrete through bond. Therequired development length for FRP reinforcement isdependent on the bond between FRP and concrete, which inturn depends on the bar diameter, surface condition,embedment length, and bar shape. Because the bond ofFRP bars to concrete differs depending on the specific FRPreinforcement being used, the development length for anyspecific product should be determined from experimentaltests. Most FRP reinforcement manufacturers can provideguidance in this regard for any specific FRP product.

FLEXURAL DESIGN AIDS

To assist in the flexural design of FRP-reinforced concretemembers, ISIS Canada has produced a series of designsaids. The design aids consist of a series of charts that weredeveloped for rectangular sections with a specific type ofreinforcement in a single layer. They were developed basedon the serviceability requirement that the strain in the FRPat service load levels should not exceed frp = 0.002, andthey can be used for the design of section dimensions andreinforcement details to satisfy both serviceability and

ultimate limit states requirements. The design charts havenot been included herein, but are available in Chapter 10 ofISIS Design Manual No. 3.

DESIGN FOR SHEAR

FRP are widely used in a variety of shapes andconfigurations for flexural reinforcement of concrete

members. FRPs have been used successfully as shear

reinforcement in full-scale field applications, although thetopic is not covered in any significant detail in this manual.

If steel stirrups are used in an FRP reinforced concretemember, and the shear design is conducted according toexisting standards, such as CSA A23.3-94, then no

problems with the shear capacity of the member areexpected.

Further information on the shear design of concretemembers reinforced with FRPs for both flexure and shearcan be found in Chapter 11 of ISIS Design Manual No. 3.

Fig. 7-1. CFRP stirrups for shear reinforcement ofa prestressed concrete bridge girder.


17/35


16

Section 8

ExamplesEXAMPLE 1

Moment Capacity Analysis of a Rectangular Beam with FRP Reinforcement(Tension Failure)

Problem:

Calculate the factored moment resistance, M r , for a precast(c = 0.65) FRP-reinforced concrete section with thefollowing dimensions:

Section width b = 350 mmSection depth h = 600 mm

The tensile reinforcement consists of eight 12.7 mmdiameter GFRP ISOROD bars (bundled in pairs) in a single

layer. Assume that the shear reinforcement consists of 5

mm diameter Leadline TM stirrups and that the beam has aninterior exposure condition.

Given information:

Concrete compressive strength, f c = 35 MPa.ISOROD GFRP tensile strength, f frpu = 617 MPaISOROD GFRP tensile modulus, E frp = 42 GPaThe area of one 12.7 mm bar, A bar = 129 mm

2

Solution:

1. Determine the concrete cover and the effective depth ofthe section.

The required concrete cover to the flexural reinforcement is(Table 6-1):

mm40or mm32)7.12)(5.2(5.2 ==bd

40 mm governs.

The effective depth, d , is calculated from:

mm5542

7.1240600

2cover === bd hd

2. Calculate the FRP reinforcement ratio:

00532.0554350

1298 =

==bd

A frp frp

3. Calculate the balanced FRP reinforcement ratio (Eq. 3-8):

( )

0125.00146.00035.0

0035.061735

4.065.0

88.080.0

'11

=

+=

+

== frpucu

cu

frpu

c

frp

c frpb frpb f

f bd

A

Where:

80.0'0015.085.01 == c f (Eq. 3-4)88.0'0025.097.01 == c f (Eq. 3-5)

0146.01042

6173 =

== frp

frpu frpu E

f (Eq. 3-1)

4. Check if the section will fail by tension failure orcompression failure. In this case:

0125.000532.0 =


18/35


17

610144850554

0146.050

=

=c

Fig. 9-1. Strain compatibility analysis.

The tensile stress resultant can be calculated directly usingEq. 3-16:

( )( )kN255

N25469861712984.0=

=== frpu frp frp f AT

where frp is determined according to Table 3-1.

The compressive stress resultant is more difficult to obtain.It is given by Eq. 3-17:

cb f C cc '=

Because the strain in the extreme concrete compressionfibre is less than ultimate, the equivalent rectangular stress

block factors, and , must be determined from Figs. 3-2and 3-3.

From Fig. 3-2, with a concrete strain of c = 1448 10 -6 and interpolating between the curves for 30 and 40 MPaconcrete, we find that = 0.75. Using Fig. 3-3, with the

same concrete strain as above, we find = 0.69. Now, the compressive stress resultant can be obtained:

( )( )( )( )( )kN206

N0300623505069.03565.075.0

'

===

= cb f C cc

Now we must check for equilibrium of the stress-resultantson the cross-section:

255206 =


19/35


18

cr f f '6.0= inertiaof momentsectionedtransform=t I

fibretensionextremeto N.A.fromdistance=t y

Thus we have:

mkN1110.745.15.1mkN136 === cr r M M OK

Thus, the beam has satisfactory capacity to avoid failureupon cracking.

The reader should note that the beam in the precedinganalysis may not be adequate with regard to serviceabilityrequirements, particularly given that the modulus ofISOROD GFRP reinforcement is less than that ofconventional steel reinforcement. Serviceabilityrequirements for cracking and deflection should also beinvestigated, although they are not covered here.

EXAMPLE 2Moment Capacity Analysis of a Rectangular Beam with Tension Reinforcement(Compression Failure)

Problem:

Calculate the factored moment resistance, M r , for a precast(c = 0.65) FRP-reinforced concrete section with thefollowing dimensions:

Section width b = 300 mmSection depth h = 500 mm

The tensile reinforcement consists of six #10 ISORODCFRP bars in a single layer. Assume that the shearreinforcement consists of 5 mm diameter Leadline TM

stirrups and that the beam has an interior exposurecondition.

Given information:

Concrete compressive strength, f c = 35 MPa.ISOROD CFRP tensile strength, f frpu = 1596 MPaISOROD CFRP tensile modulus, E frp = 111 GPaThe area of one #10 bar, A bar = 71 mm

2 The diameter of one #10 bar, d b = 9.3 mm

Solution:

1. Determine the concrete cover and the effective depth ofthe section.

The required concrete cover to the flexural reinforcement is(Table 6-1):

mm40or mm23)3.9)(5.2(5.2 ==bd

The effective depth, d , is calculated from:

mm45523.9

405002

cover === bd hd


( )( )

%312.000312.0455300716 ====

bd

A frp frp

3. Calculate the balanced FRP reinforcement ratio(Eq. 3-8):

( )

%245.000245.00144.00035.0

0035.01596

358.0

65.088.080.0

'11

==

+=

+== frpucu

cu

frpu

c

frp

c frpb

frpb f f

bd

A

Where:

80.0'0015.085.01 == c f (Eq. 3-4)

88.0'0025.097.01 == c f (Eq. 3-5)

0144.010111

15963 =

== frp

frpu frpu E

f (Eq. 3-1)



20/35


19

00245.000312.0 =>= frpb frp

Therefore, we have COMPRESSION FAILURE , and thestrain distribution is as follows:

Fig. 9-1. Strain compatibility analysis.

5. Determine the tensile stress in the FRP reinforcement atcompressive failure of the section (Eq. 3-8):

( )( )

( )( )( )( )( )( )( )

MPa1396

10035.01110008.01012.3

3565.088.080.041

0035.01110005.0

14

15.0

21

3

21

'11

=

+

=

+=

cu frp frp frp

cccu frp frp E

f E f

6. Determine the stress block depth, a (Eq. 3-11):

( )( )( )( )( )

mm873003565.080.0

13877168.0

'1

1

=

=

==b f

f Aac

cc

frp frp frp

7. Determine the flexural capacity, M r (Eq. 3-14):

( )( )mkN196mm N10196

2

87

45513967168.0

2

6 ==

=

= ad f A M frp frp frpr

Thus, the moment capacity of the section is 196 kNm.

Finally, we must check that the minimum flexural capacityrequirements are satisfied. Using Eq. 3-23:

cr r M M 5.1

The cracking moment is determined using Eq. 3-24:

( )( )

mkN8.45mm N108.45248

1020.3356.0

6

9

==

=

=t

t r cr y

I f M

where:

cr f f '6.0=

inertiaof momentsectionedtransform=t I fibretensionextremeto N.A.fromdistance=t y

Thus we have:

mkN7.688.455.15.1mkN196 === cr r M M OK

Thus, the beam has satisfactory capacity to avoid failureupon cracking.

The reader should note that the beam in the precedinganalysis may not be adequate with regard to serviceabilityrequirements, particularly given that the modulus ofISOROD CFRP reinforcement is less than that ofconventional steel reinforcement. Serviceabilityrequirements for cracking and deflection should also beinvestigated, although they are not covered here.

frp < frpu

cu = 0.0035

d= 455 mm

c

300 mm


21/35


20

Section 9

Field ApplicationsThe following case studies provide examples of fieldapplications where FRP reinforcement has been usedsuccessfully for reinforcement of concrete. Furtherinformation on a variety of additional field applications can

be obtained from the ISIS Canada website(www.isiscanada.com ).

TAYLOR BRIDGE

A significant research milestone was achieved on October 8,1998 when Manitobas Department of Highways andTransportation opened the Taylor Bridge in Headingley,Manitoba. The two-lane, 165.1-metre-long structure hasfour out of 40 precast concrete girders reinforced withcarbon FRP stirrups. These girders are also prestressed with

carbon FRP cables and bars. Glass FRP reinforcement has been used in portions of the barrier walls.

Fig. 10-1. The Taylor Br idge, in HeadinglyManitoba, during construc tion.

As a demonstration project, it was vital the materials betested under the same conditions as conventional steelreinforcement. Thus only a portion of the bridge wasdesigned using FRPs.

Two types of carbon FRP reinforcements were used inthe Taylor bridge. Carbon fibre composite cables produced

by Tokyo Rope, Japan, were used to pretension two girders,while the other two girders were pretensioned usingLeadline bars produced by Mitsubishi ChemicalCorporation, Japan.

Two of the four FRP-reinforced girders were reinforcedfor shear using carbon FRP stirrups and leadline bars in arectangular cross section. The other two beams werereinforced for shear using epoxy coated steel reinforcement.

The deck slab was reinforced by Leadline bars similarto those used for prestressing. Glass FRP reinforcement

produced by Marshall Industries Composites Inc. was usedto reinforce a portion of the barrier wall. Double-headed

stainless steel tension bars were used for the connection between the barrier wall and the deck slab.

The bridge incorporates a complex embedded fibreoptic structural sensing system that will allow engineers tocompare the long-term behaviour of the various materials.This remote monitoring is an important factor in acquiringlong-term data on FRPs that is required for widespreadacceptance of these materials through national andinternational codes of practice.

Fig. 10-2. Placing the FRP-reinforced concretedeck of the Taylor Bridge.

JOFFRE BRIDGE

Early in August of 1997, the province of Qubec decided toconstruct a bridge using carbon FRP reinforcement. TheJoffre Bridge, spanning the Saint Francois River, wasanother contribution to the increasing number of FRP-reinforced bridges in Canada. A portion of the Joffre Bridgeconcrete deck slab is reinforced with carbon FRP, as are

portions of the traffic barrier wall and the sidewalk.The bridge is outfitted extensively with various kinds of

monitoring instruments including fibre optic sensorsembedded within the FRP reinforcement (these are referredto as smart reinforcements). Over 180 monitoring

instruments are installed at critical locations in the concretedeck slab and on the steel girders, to monitor the behaviourof the FRP reinforcement under service conditions. Theinstrumentation is also providing valuable information onlong-term performance of the concrete deck slab reinforcedwith FRP materials.


22/35


21

Fig. 10-3. Placement of FRP grid for Joff re Bridgesconcrete deck reinforcement (yellow coils aresensor lead wires).

Fig. 10-4. Aerial view of Joffre Brid ge durin gconstruction.

WOTTON BRIDGE

Wotton Bridge, in the municipality of Wotton, Qubec, is asingle span prestressed concrete girder bridge with a totallength of 30.6 metres and a width of 8.9 metres. The deckslab rests on four prestressed concrete girders, spaced at 2.3metres, with a cantilever slab of one metre on either side.The deck slab is reinforced internally with ISOROD GFRPand CFRP reinforcing bars with diameters of 15 mm and 10mm respectively. FRP reinforcement is used both for topand bottom slab reinforcement.

MORRISTOWN BRIDGE

The Morristown Bridge, in the State of Vermont, USA, is asingle-span integral abutment bridge with a total length of43 metres and a width of 11.3 metres. The deck slab has athickness of 230 mm and rests on 5 steel girders spaced at2.4 metres. The deck slab cantilevers on either side of the

bridge are 0.92 metres in length. Top and bottom deckreinforcement consists of ISOROD GFRP reinforcing bars.

Fig. 10-5. Placement of GFRP and CFRPreinforcement in the Wotton Bridge deck.

Fig. 10-6. The completed Wotton Br idge.

Fig. 10-7. The GFRP-reinforced Morristow n Bridgedeck just before placement of the concrete deckslab.


23/35


24/35


23

C n nominal compressive stress resultant (N)

c depth of neutral axis (mm)

cb depth of the neutral axis at the balanced failure condition (mm)

d effective depth of the section (mm)

d b diameter of the reinforcement (mm)

E c elastic modulus of the concrete (MPa)

E frp elastic modulus of the FRP (MPa)

f c compressive strength of the concrete (MPa)

f frp stress in the FRP reinforcement at failure (MPa)

f frpu ultimate tensile strength of the FRP (MPa)

f r modulus of rupture of the concrete (MPa)

h overall member depth (mm)

I cr moment of inertia of the cracked section transformed to concrete with concrete in tension ignored (mm4)

I t moment of inertia of the transformed section (mm4

) n member length (mm)

M a maximum moment in a member at the load stage at which deflection is being calculated (Nmm)

M cr cracking moment of the cross-section (Nmm)

M f moment due to the factored loads (Nmm)

M r factored moment resistance of the cross-section (Nmm)

n frp modular ratio E frp/ E c

T tensile stress resultant (N)

T n nominal tensile stress resultant (N)

yt distance from the centroidal axis of the transformed section to the extreme tension fibre (mm) stress-block parameter for concrete at a strain less than ultimate

1 CSA A23.3-94 stress-block parameter for concrete at ultimate

d dimensionless coefficient taken as 0.50 for a rectangular section

stress-block parameter for concrete at a strain less than ultimate

1 CSA A23.3-94 stress-block parameter for concrete at ultimate

cu ultimate concrete strain

frp strain in the FRP reinforcement at compression failure

frps strain in the tensile FRP reinforcement at service load

frpu ultimate strain of the FRP in tension

s maximum strain allowed in the reinforcement in service

c material resistance factor for concrete

frp material resistance factor of FRP reinforcement

frpb balanced failure reinforcement ratio

frp FRP reinforcement ratio


25/35


24

Appendix A:Suggested Student Assignment

Problem #1:

Calculate the factored moment resistance, M r , in positive bending, for the precast ( c = 0.65) FRP-reinforced concretesection shown below. Assume that the beam has an interiorexposure condition:

Material Properties:

Concrete Compressive Strength, f c = 45 MPaFRP Ultimate Strength, f frpu = 1596 MPaFRP Elastic Modulus, E frp = 111 MPaArea of FRP Bars, A bar = 71 mm

2

Problem #2:

Calculate the factored moment resistance, M r , in positive

bending, for the precast ( c = 0.65) FRP-reinforced concretesection shown below. Assume that the beam has an interiorexposure condition:

Material Properties:Concrete Compressive Strength, f c = 40 MPaFRP Ultimate Strength, f frpu = 2255 MPaFRP Elastic Modulus, E frp = 147 MPaArea of FRP Bars, A bar = 113 mm

2

5 0 0 m m

250 mm

3 9.3 mm diametercarbon ISOROD bars

2 9.3 mm diametercarbon ISOROD bars

4 0 0 m m

300 mm

6 12 mm diametercarbon Leadline TM bars

in two la ers


26/35


25

Appendix B: Assignment SolutionsProblem #1:



2

Solution:

1. First, note that we always assume FRP reinforcement isineffective in compression. Thus, we can completely ignorethe compression reinforcement for the purposes of this

problem. Next, determine the concrete cover and theeffective depth of the section.

The required concrete cover to the main reinforcement is(Table 6-1):

mm40or mm23)3.9)(5.2(5.2 ==bd

40 mm cover governs.

The effective depth, d , is thus:

mm45523.9

405002

cover === bd hd


( )( )

31087.1455250713 ===

bd

A frp frp

3. Calculate the balanced FRP reinforcement ratio

(Eq. 3-8):

( )3

11

1002.3

0143.00035.00035.0

159645

8.065.0

86.078.0

'

=

+=

+

== frpucu

cu

frpu

c

frp

c frpb frpb f

f bd

A

Where:

78.0'0015.085.01 == c f (Eq. 3-4)

86.0'0025.097.01 == c f (Eq. 3-5)

0143.010111

15963 =

== frp

frpu frpu E

f (Eq. 3-1)


33 1002.31087.1 =


27/35


26

5. Perform an iterative strain-compatibility analysis:

Assume the neutral axis depth, c = 60 mm. Using straincompatibility:

610217260455

0143.060 =

=

= c

frpuc

cd c

The tensile stress resultant can be calculated directly usingEq. 3-16:

( )( )kN272

N27200015967138.0=

=== frpu frp frp f AT

where frp is determined according to Table 3-1.

The compressive stress resultant obtained using Eq. 3-17:

cb f C cc '=

The strain in the extreme compression fibre is less thanultimate, and , must therefore be determined from Figs.3-2 and 3-3. From Fig. 3-2, with a concrete strain of c =2172 10 -6 and interpolating between the curves for 40 and50 MPa concrete, we find that = 0.90. Using Fig. 3-3 wefind = 0.70.

The compressive stress resultant can be obtained:

( )( )( )( )( )kN276

N2764122506070.04565.090.0

'

===

= cb f C cc

Check for equilibrium of the stress-resultants on the cross-section:

272276 == T C

Since C T , further iteration is not required.

6. Determine the moment capacity using Eq. 3-21:

( )( )

mkN118mm N10118

26070.045515967138.0

2

6 ==

=

= cd f A M frpu frp frpr

Thus, the moment capacity of the section is 118 kNm.

7. Check that the minimum flexural capacity requirementsare satisfied. Using Eq. 3-23:

cr r M M 5.1 The cracking moment is determined using Eq. 3-24:

( )( )

mkN42mm N1042250

1088.2636456.0

6

6

==

=

=t

t r cr y I f

M

Thus we have:

mkN63425.15.1mkN118 === cr r M M OK Therefore, the flexural resistance of the carbon FRP-reinforced concrete beam is 118 kNm.


28/35


27

Problem #2:



2

Maximum aggregate size, MAS = 14 mm

Solution:

1. Determine the concrete cover and the effective depth ofthe section. The required concrete cover to the flexuralreinforcement is (Table 6-1):

mm40or mm30)12)(5.2(5.2 ==bd The bar spacing requirements dictate that the spacing

between layers of reinforcement must be the greater of:

mm17)12)(4.1(4.1 ==bd ;

mm20)14)(4.1(4.1 == MAS ;mm30 ; or

the concrete cover of mm40 Governs

The effective depth to the bottom layer of reinforcement, d ,is (note that we may not lump the reinforcement as wewould normally do for steel reinforced concrete):

mm3542

1240400

2cover === bbottom

d hd

The depth to the top layer of reinforcement is:

mm31440212

40400

402

cover

==

= btopd

hd

2. Calculate the FRP reinforcement ratio (here we will usethe average value of effective depth, THIS STEP ONLY!):

( )( )

3

1076.6334300

1136

=

== bd A frp

frp

3. Calculate the balanced FRP reinforcement ratio(Eq. 3-8):

( )3

11

1084.1

0153.00035.00035.0

225540

8.065.0

87.079.0

'

=

+=

+

== frpucu

cu

frpu

c

frp

c frpb frpb f

f bd

A

Where:

79.0'0015.085.01 == c f (Eq. 3-4)

87.0'0025.097.01 == c f (Eq. 3-5)

0153.010147

22553 =

==

frp

frpu frpu E

f (Eq. 3-1)


33 1084.11076.6 =>= frpb frp

Therefore, we have COMPRESSION FAILURE , and thestrain distribution is as follows:

4 0 0 m m

300 mm

6 12 mm diametercarbon Leadline TM bars

in tw o l a ers


29/35


28

5. Assume the neutral axis depth, c = 115 mm (educated

guess).6. Now we must determine the actual stresses in thedifferent layers of FRP reinforcement ( NO LUMPING ) andcheck that the compression and tensile forces are equal.From the strain profile shown above:

( ) 6,

,

1072741150035.0

115354 ==

=

bottom frp

bottom

bottom frpcu

cd c

( ) 6,

,

1060571150035.0

115314 ==

=

top frp

top

top frpcucd c

Now, the tension force is calculated by summing thecontributions of both layers of FRP:

( )( )( )kN290 N290000

14700010727411338.0 6,

===

=

frpbottom frp frp frpbottom E AT

( )( )( )kN241 N241000

14700010605711338.0 6,

===

=

frptop frp frp frptop E AT

So the total tensile force is T = 290 + 241 = 531 kN. Now,the compression force is

( )( )( )( )( )kN617 N617000

30011587.04065.079.0

'1

==== cb f C cc

Since C = 616 T = 531, we must try a different neutralaxis depth. Try c = 104 mm. As before:

( ) 6, 1084361040035.0

104354 ==bottom frp

( ) 6, 1070881040035.0

104314 ==top frp

Now, the tension force is calculated by summing thecontributions of both layers of FRP:

( )( )( )kN336 N336000

14700010843611338.0 6

=== bottomT

( )( )( )kN282 N282000

14700010708811338.0 6

=== topT

So the total tensile force is T = 336 + 282 = 618 kN. Now,the compression force is

( )( )( )( )( )kN613 N613000

30010487.04065.087.0

===C

Since C = 613 T = 618, we will use a neutral axis depth ofc = 104 mm.

7. We can now determine the flexural capacity, M r (Eq. 3-14):

4 0 0 m m

300 mm

frp < frpu

cu = 0.0035

d b o t t om =

3 5 4 mm

c

d t o p=

3 1 4 mm frp,top

frp,bottom


30/35


29

mm N10175

2104

31410282

210435410336

2

2

6

3

3

,,

,,

=

+

=

+

=

ad f A

ad f A M

toptop frptop frp frp

bottombottom frpbottom frp frpr

Thus, the moment capacity of the section is 175 kNm.Finally, we must check that the minimum flexural capacityrequirements are satisfied. Using Eq. 3-23:

cr r M M 5.1 The cracking moment is determined using Eq. 3-24:

( )

mm N103.30200

12400300

406.0

6

3

=

=

=t

t r cr y

I f M

Thus we have:

( ) 5.453.305.15.1175 === cr r M M OK Thus, the beam has satisfactory capacity to avoid failureupon cracking.

Therefore, the flexural resistance of the carbon FRP-reinforced concrete beam is 175 kNm.


31/35


30

Appendix C:Suggested Laboratory

The following laboratory procedure is given as an exampleof a reinforced concrete laboratory that can be given inconjunction with an undergraduate course on reinforcedconcrete design, and that includes both conventionalreinforcing steel and internal FRP reinforcement. Given thewide variety of laboratory and testing facilities available atvarious Canadian universities, this laboratory is given

primarily as an example for professors of what can be doneusing FRP reinforcement to increase the impact and studentunderstanding of traditional reinforced concrete labs.

Inclusion of FRP reinforcement into traditionalreinforced concrete laboratories is advantageous for anumber of reasons, including:

it introduces students to a new and innovative materialwhich is gaining acceptance within the reinforcedconcrete industry;

it increases student understanding of the fundamentalconcepts and assumptions, including serviceability and

deflection, used in reinforced concrete beam design andanalysis;

it forces students to consider and understand importantmechanics concepts such as elasticity, plasticity, andductility; and

it exposes students to the state-of-the-art in reinforcedconcrete design and thus increases student enthusiasmfor the course content, subsequently, in many cases,increasing student participation and effort.The laboratory presented herein suggests the use of

glass FRP reinforcing bars, ISOROD, manufactured byPultrall Inc. It is important to recognize that the laboratory

procedures can be adapted to include the use of any specific

type of FRP reinforcement, and this specific type ofreinforcement has been used here only as an example.

Caution:FRP MaterialsFRPs are linear elastic materials. As such, these materialsdo not display the yielding behaviour observed when testingsteel and they provide little warning prior to failure . Inaddition, beams which fail in shear or due to FRP rupturemay fail suddenly and with little warning. It is important

that instructors, students, laboratory demonstrators, andtechnical staff be made aware of the specific failure modesto be expected when testing FRP materials, and thatappropriate safety precautions be taken in addition tothose precautions that are normally enforced.


32/35


31

Concrete Beam LaboratoryOVERVIEW

This laboratory is intended to increase studentsunderstanding of the effects of various amounts and types ofinternal reinforcement, both steel and fibre reinforced

polymer (FRP), on the flexural and shear behaviour ofreinforced concrete beams. The laboratory consists of thefabrication and testing of five concrete beams with varyingamounts and types of reinforcement. The laboratoryillustrates the following important concepts:1. the flexural and shear behaviour of reinforced concrete

beams;2. under-reinforced versus over-reinforced concrete

beams;3. the effect of shear reinforcement on the load capacity,

deflection, ductility, and failure of reinforced concrete

beams;4. the effect of reinforcement type (steel or FRP) on the

load capacity, deflection, ductility, and failure ofreinforced concrete beams; and

5. the concepts of cracking, yielding, and moment-curvature.The class will be divided into five groups, and each

group will be responsible for the fabrication and testing ofone of the five beams. Experimental data obtained duringtesting for all beams will be made available to all groups foruse in writing the laboratory report. Each group will submitone report only, but will comment on the results for all five

beams.

Beam DetailsAll beams will be fabricated from concrete with a specified28-day concrete strength of 35 MPa (compression tests will

be conducted to determine the true 28-day strength of theconcrete). Steel reinforcement will consist of deformedreinforcing bars with a specified yield strength of 400 MPa.FRP reinforcement will consist of glass FRP reinforcing

bars with a specified ultimate strength of 691 MPa and atensile elastic modulus of 40 GPa. Note that the beamssuggested herein are given as an example only, since GFRP

bars should not directly contact steel bars in an actual fieldapplication of GFRP reinforcement. The five beams to be

tested in this laboratory are:1. an under-reinforced beam without shear reinforcement(steel reinforcing bars);

2. an under-reinforced beam with shear reinforcement(steel reinforcing bars);

3. an over-reinforced beam with shear reinforcement (steelreinforcing bars);

4. an under-reinforced beam with shear reinforcement(glass FRP reinforcing bars); and

5. an over-reinforced beam with shear reinforcement

(glass FRP reinforcing bars).Dimensions and reinforcement details of the beams are

given on the following page.

Instrumentation and TestingAll beams will be tested in four-point bending to failure, asshown in the figure below. Strain gauges will be mountedon the tensile reinforcement, prior to casting the concrete,and on the concrete compression fibre. Load, deflection,and reinforcement and concrete compressive strain will bemeasured and recorded during testing. Cracking patternswill also be marked and photographed during testing. Anysignificant visual observations will be recorded throughout

the tests.

Laboratory ReportThe laboratory report should consist of the following:1. A title page giving the group name and number.2. An abstract , briefly stating the purpose and procedure

of the lab and the major conclusions drawn.3. An introduction providing information on the material

properties, beam details, testing setup, instrumentation, procedures, etc.

4. A calculations and analysis section detailing allcalculations performed for the laboratory. Where acalculation has been performed more than once only asample calculation should be provided. A summary oftheoretical calculations should be presented in tabularform.

5. An experimental results and discussion section,summarizing the test results obtained for all beamstested. This section should include photographs and

plots showing beam behaviour along with a thoroughcomparison of theoretical and observed results, and acomparison of the behaviour of the various beams.

6. A conclusion in which the major points of interest fromthe above sections are highlighted. The focus in theconclusion should be on the consequences of theobserved behaviour on the practical design of

reinforced concrete beams.7. A list of references . All tests referenced during thecourse of the laboratory project should be listed usingan accepted referencing format.


33/35


32

200

4 0 0

100

25

2 20M bars1 15M bar

40 mm coverto reinforcement

* all dimensionsin millimeters

3000

200

4 0 0

10025

25

150 150Etc..

2 20M bars1 15M bar10M stirrups

30 mm coverto stirrups

* all dimensions inmillimeters

200

4 0 0

10025

25

150 150Etc..

4 25M bars10M stirrups


35 mm verticalspacing betweenbars

* all dim. in mm

200

4 0 0

10025

25

150 150Etc..

2 25 mm glass FRP bars10M stirrups



200

4 0 0

10025

25

150 150Etc..

2 10 mm glass FRP bars10M stirrups



BEAM #1

BEAM #2

BEAM #3

BEAM #4

BEAM #5

100


34/35


33

CALCULATIONS AND ANALYSIS

The calculation and analysis section of your report shouldinclude calculations of the following parameters accordingto traditional reinforced concrete theory, as presented inclass. Each group should perform the calculations for theirspecific beam and then forward their results to all othergroups:1. Issues related to flexural strength :

a. The bending moment at first cracking of theconcrete in tension (cracking moment, M cr ).

b. The bending moment at an extreme fibre concretecompressive stress of 0.4 f c.

c. The nominal (predicted) moment capacity of thesection.

d. The design (ultimate) moment capacity of the beamaccording to CSA A23.3-94 for steel-reinforced

beams and according to ISIS Design Manual No. 3for FRP-reinforced concrete beams.

2. Issues related to strain and deformation :a. The strain in the reinforcement and in the concrete

compression fibre at first cracking of the concretein tension.

b. The strain in the reinforcement and concrete at anextreme fibre concrete compressive stress of 0.4 f c.

c. The strain in the reinforcement and concretecompression fibre at ultimate.

3. Issues related to curvature and deflection :a. The midspan curvature and deflection at first

cracking of the concrete in tension.

b. The midspan curvature and deflection at twice thecracking moment, 2 M cr .c. The midspan curvature and deflection at a concrete

compressive stress of 0.4 f c.d. The midspan curvature at ultimate.

RESULTS AND DISCUSSION

In addition to presenting, through the use of graphs andtables, a summary of experimental data obtained for all five

beams, the results and discussion section of each reportshould contain, for all five beams, discussions on thefollowing topics:1. A comparison of the theoretical calculations versus the

results obtained during testing and a discussion ofdiscrepancies between theory and observation.

2. Plots showing:a. Load versus deflection for all 5 beams.

b. Midspan bending moment versus deflection for all5 beams.

c. Midspan moment versus strain in the reinforcementfor all 5 beams.

d. Midspan moment versus concrete extreme

compression fibre strain.Each plot should include points showing: the crackingmoment, steel yielding (where applicable), acompressive fibre concrete stress of 0.4 f c, acompressive fibre concrete strain of 0.0035, and themaximum load/moment. A bar chart should also beincluded showing a comparison of the five beams basedon selected important criteria (left to the discretion ofthe student). Each plot should be followed by a briefcommentary and discussion.

3. A comparison should be made between the calculateddesign ultimate load, the calculated nominal loadcapacity, and the observed load capacity for all beams.

What does this imply for the design of actual reinforcedconcrete beams in practice?Students are expected to provide clear and concise

discussions of the above-listed topics and to add additionalcommentary and calculations as they see fit. The reportswill be graded in part on the quality of independent thoughtand discussion brought to bear on the various conceptsdemonstrated in this laboratory, and on the students explicitrecognition of the greater significance of the resultsobtained.

1

2

3

4

1000 mm 1000 mm900 mm

1 Load cell2 Concrete compression strain gauge3 Reinforcement strain gauge4 Displacement transducer


35/35


isis ec module 3 - notes (pdf)

Documents