isis ec module 9 - notes (pdf)

7/30/2019 Isis Ec Module 9 - Notes (PDF)

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ISIS Educational Module 9:

Prestressing Concrete Structures with Fibre

Reinforced Polymers

Prepared by ISIS CanadaA Canadian Network of Centres of Excellencewww.isiscanada.comPrincipal Contributor: Raafat El-Hacha, Ph.D., P.Eng.

Department of Civil Engineering, University of CalgaryContributor: Cynthia CoutureJune 2007

ISIS Education Committee:

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


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ISIS Canada Educational Module No. 10: Prestressing Concrete Structures with FRP

2

Objectives of This Module

Fibre reinforced polymer (FRP) reinforcing materials for

concrete structures have high strength-to-weight ratios that

can provide high prestressing forces while adding only

minimal additional weight to a structure. They also havegood fatigue properties and exhibit low relaxation losses,

both of which can increase the service lives and the load

carrying capacities of reinforced concrete structures. Thismodule is intended to:

1. provide students with a general awareness ofguidelines and procedures that can be used for the

design of concrete components prestressed with

FRPs in buildings and bridges.2. to facilitate the use of FRP reinforcing materials in

the construction and structural rehabilitation

industries; and

3. to provide guidance to students seeking additionalinformation on this topic.

Information is presented for both internal and external

prestressing applications with FRP bars, rods, and tendons.

Design considerations for serviceability, strength and

ductility, as well as anchorage of FRP prestressing tendonsare addressed.

The material presented herein is not currently part of a

national or international design code, but is based mainly onthe results of numerous detailed research studies conducted

in Canada and around the world. Procedures, material

resistance factors, and design equations are based primarily

on the recommendations of ISIS Canada Design ManualNo. 5: Prestressing Concrete Structures with Fibre

Reinforced Polymers. As such, this module should not be

used as a design document, and it is intended for educational

use only. Future engineers who wish to design FRP-strengthening schemes for reinforced concrete structures

should consult more complete design documents (refer to

Section 11 for further guidance)

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

Module 1 Mechanics Examples Incorporating

FRP Materials

Nineteen worked mechanics of materials problems are

presented which incorporate FRP materials. These

examples could be used in lectures to demonstrate variousmechanics concepts, or could be assigned for assignment or

exam problems. This module seeks to expose first and

second year undergraduates to FRP materials at the

introductory level. Mechanics topics covered at theelementary level include: equilibrium, stress, strain and

deformation, elasticity, plasticity, determinacy, thermal

stress and strain, flexure and shear in beams, torsion,composite beams, and deflections.

Module 2 Introduction to FRP Composites for

Construction

FRP materials are discussed in detail at the introductorylevel. This module seeks to expose undergraduate students

to FRP materials such that they have a basic understanding

of the components, manufacture, properties, mechanics,

durability, and application of FRP materials in civilinfrastructure applications. A suggested laboratory is

included which outlines an experimental procedure for

comparing the stress-strain responses of steel versus FRPs

in tension, and a sample assignment is provided.

Module 3 Introduction to FRP-Reinforced

Concrete

The use of FRP bars, rods, and tendons as internal tensile

reinforcement for new concrete structures is presented and

discussed in detail. Included are discussions of FRP

materials relevant to these applications, flexural designguidelines, serviceability criteria, deformability, bar

spacing, and various additional considerations. A number

of case studies are also discussed. A series of workedexample problems, a suggested assignment with solutions,

and a suggested laboratory incorporating FRP-reinforced

concrete beams are all included.

Module 4 Introduction to FRP-Strengthening

of Concrete Structures

The use of externally-bonded FRP reinforcement for

strengthening concrete structures is discussed in detail. FRPmaterials relevant to these applications are first presented,

followed by detailed discussions of FRP-strengthening of

concrete structures in flexure, shear, and axial compression.


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3

A series of worked examples are presented, case studies are

outlined, and additional, more specialized, applications are

introduced. A suggested assignment is provided with

worked solutions, and a potential laboratory forstrengthening concrete beams in flexure with externally-

bonded FRP sheets is outlined.

Module 5 Introduction to Structural Health

Monitoring

The overall motivation behind, and the benefits, design,

application, and use of, structural health monitoring (SHM)

systems for infrastructure are presented and discussed at theintroductory level. The motivation and goals of SHM are

first presented and discussed, followed by descriptions of

the various components, categories, and classifications of

SHM systems. Typical SHM methodologies are outlined,

innovative fibre optic sensor technology is briefly covered,

and types of tests which can be carried out using SHM areexplained. Finally, a series of SHM case studies is provided

to demonstrate four field applications of SHM systems in

Canada.

Module 6 Application & Handling of FRP

Reinforcements for Concrete

Important considerations in the handling and application of

FRP materials for both reinforcement and strengthening of

reinforced concrete structures are presented in detail.

Introductory information on FRP materials, their

mechanical properties, and their applications in civil

engineering applications is provided. Handling andapplication of FRP materials as internal reinforcement for

concrete structures is treated in detail, including discussions

on: grades, sizes, and bar identification, handling andstorage, placement and assembly, quality control (QC) and

quality assurance (QA), and safety precautions. This is

followed by information on handling and application of

FRP repair materials for concrete structures, including:

handling and storage, installation, QC, QA, safety, and

maintenance and repair of FRP systems.

Module 7 Introduction to Life Cycle

Engineering & Costing for InnovativeInfrastructure

Life cycle costing (LCC) is a well-recognized means ofguiding design, rehabilitation and on-going management

decisions involving infrastructure systems. LCC can beemployed to enable and encourage the use of fibre

reinforced polymers (FRPs) and fibre optic sensor (FOS)technologies across a broad range of infrastructure

applications and circumstances, even where the initial costsof innovations exceed those of conventional alternatives.

The objective of this module is to provide undergraduate

engineering students with a general awareness of theprinciples 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 for

Construction

Fibre reinforced polymers (FRPs), like all engineering

materials, are potentially susceptible to a variety of

environmental factors that may influence their long-termdurability. It is thus important, when contemplating the use

of FRP materials in a specific application, that allowance be

made for potentially harmful environments and conditions.

It is shown in this module that modern FRP materials areextremely durable and that they have tremendous promise in

infrastructure applications. The objective of this module is

to provide engineering students with an overall awareness

and understanding of the various environmental factors that

are currently considered significant with respect to the

durability of fibre reinforced polymer (FRP) materials incivil engineering applications.


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4

Section 1

Introduction

BACKGROUND

The non-corrosive, high strength, and light weight

characteristics of fibre reinforced polymers (FRPs) make

them attractive for use as either internal or externalreinforcement of concrete structures. Using FRPs in new

structures offers numerous potential benefits:

Longer life cycles and reduced life cycle costs Reduced maintenance costs Enhanced durability Overall cost efficiencies New and innovative design options

FRP reinforcements have high strength-to-weight ratios

that can provide high prestressing forces with only minimaladditional weight on a structure. They also have good

fatigue properties and exhibit low relaxation losses, both of

which can increase the service lives and the load carrying

capacities of reinforced and/or prestressed concretestructures. Full scale FRP prestressed concrete bridges have

been constructed in North America, Europe, and Japan.

During the 1990s, several demonstration projects in Canada

showed the potential of FRP applications. In 1993, the

Beddington Trail Bridge was built in Calgary, Alberta,

using FRP pretensioned tendons and incorporating fibre

optic sensors for ongoing structural health monitoring (referto ISIS Canada Educational Module 5). This was the first

bridge of its kind in North America, and one of the first inthe world. A second bridge, Taylor Bridge, incorporating

FRP prestressing tendons was built at Headingly, Manitoba

in 1997. In the United States, the Bridge Street Bridge in

Southfield, Michigan was completed in 2001, and used

bonded and unbonded carbon FRP (CFRP) prestressingtendons.

The current educational module provides information

on available guidelines that can be used to design concrete

members fully prestressed with carbon FRP, aramid FRP(AFRP), and glass FRP (GFRP) tendons, in both buildings

and bridges. The reader will note that this module is not part

of national or an international standard.

Section 2

FRP Tendon Characteristics & Properties

GENERAL

Fibre reinforced polymers are anisotropic composite

materials, consisting of high-strength fibres embedded in a

light polymer resin matrix. The mechanical properties of anFRP product such as strength and stiffness are highly

dependent on (ISIS, 2001):

the mechanical properties of the fibre and the matrix; the fibre volume fraction of the composite; the degree of fibre matrix interfacial adhesion; the fibre cross section, quality, and orientation within

the matrix;

the loading history and duration, as well asenvironmental conditions; and

the method of manufacturing.These factors are interdependent, and consequently it is

difficult to determine the specific effect of each factor in

isolation. FRP tendons may be produced from a widevariety of fibres and polymer resins, and they are typically

identified by the type of fibre used to make the tendon.

COMMERCIALLY AVAILABLE FRP

PRESTRESSING TENDONS

FRP prestressing tendons are available in a variety of shapes

and sizes; they may be in the form of bars, multi-wire

strands, ropes, or cables. The properties of FRP prestressing

tendons are typically available from the manufacturer. Table

2.1 provides a comparison of typical mechanical propertiesof selected commercially available structural AFRP and

CFRP prestressing tendons, together with those of steel

prestressing tendons for the purposes of comparison.The two main types of FRP prestressing

reinforcements, namely CFRP and AFRP, used in North

America, Japan and Europe are described briefly in the

following subsections.


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5

Table 2-1. Typical Uniaxial Tensile Properties of Prestressing Tendons (CAN/CSA-S806-02)

Mechanical Properties Prestressing Steel AFRP Tendon CFRP Tendon GFRP Tendon

Nominal yield stress (MPa) 10341396 N/A N/A N/ATensile strength (MPa) 13791862 12002068 16502410 1379-1724Elastic Modulus (GPa) 186200 5074 152165 48-62Yield Strain (%) 1.42.5 N/A N/A N/ARupture Strain (%) >4 22.6 11.5 3-4.5Density (kg/m

3) 7900 12501400 15001600 1250-2400

Carbon FRP (CFRP)

Carbon fibres provide numerous potentially advantageousproperties, including: high strength and high stiffness to

weight ratios, excellent fatigue properties, excellentmoisture resistance, high temperature and chemical

resistance, and electrical and thermal conductivity. Due to

their low ultimate strains, carbon fibres typically havecomparatively low impact resistance. Two types (grades) of

carbon fibres are widely available: (1) synthetic fibres

known as polyacrylonitrile (PAN), which are similar to

fibres used for making textiles, and (2) pitch-based carbon

fibres, obtained from the destructive distillation of coal(Hollaway, 1989).

Polyacrylonitrile (PAN) CFRPs are used to make

unidirectional Carbon Fibre Composite Cables (CFCC),

developed by Tokyo Rope Mfg. Co. Ltd. and Toho RayonMfg. Co. Ltd., both in Japan. The cables are made of carbon

fibre yarns twisted together, similar in may ways to 7-wiresteel tendons which are widely used in the prestressed

concrete industry. Carbon Fibre Composite Cables can bemanufactured as a single rod, which may be used in

isolation, or combined in sets of seven, nineteen, or thirty-

seven to form multiple strand cables (refer to Figure 2-1).

CFCC has a lower modulus (137GPa) in comparison to steel(198GPa). This is considered to be an advantage for CFCC

since smaller losses of prestress will be experienced as

compared with steel tendons due to shrinkage and creep of

the concrete. In addition, the same weight of CFCC carriesabout four times the load carried by an equivalent amount of

conventional steel tendon.

Fig. 2-1. Carbon Fibre Composite Cables (TokyoRope, 1993)

Pitch-based CFRP is used by Mitsubishi Kasei Chemical

Company of Japan for both round and deformed LeadlineCFRP rods. Plain round bar diameters range from 3mm to17mm, and deformed bar diameters from 5mm to 12mm(refer to Figure 2-3). These rods have a tensile strength of

1813MPa, a tensile modulus of elasticity of 147GPa, and an

elongation at failure of 1.3%.

Fig. 2-2. Carbon Fibre Reinforced Polymer

Leadline Tendons (Mitsubishi KaseiCorporation, 1993)


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6

Aramid FRP (AFRP)The term aramid is derived from the chemical names of thebase compounds from which it is manufactured: ARomatic

polyAMIDe. Aramid fibres have lower weights and a lowertensile moduli of elasticity than carbon fibres, but are

generally superior to carbon fibres in terms of toughness and

impact resistance (hence their widespread use in armor and

ballistics applications). The cost of aramid fibres is also

typically less than carbon fibres. While various modulus

grades are available the modulus of elasticity of aramidfibres is generally about one quarter that of conventional

cold-drawn prestressing steel, and the specific density is one

sixth that of prestressing steel. Prestressing reinforcementformed from this material is manufactured into rods or

ropes, which are created from six main types of fibres, four

different grades of proprietary aramid fibres called Kevlar

(Grades 29, 49, 129, 149), and various other proprietary

aramid fibres called Twaron, Technora, Arapree,FiBRA, and Parafil (ISIS, 2001). The fibre tensile strengthfor these fibres varies considerably and ranges from 2800 to

4210 MPa, with moduli of elasticity ranging from 74 GPa to

179 GPa. Figure 2-4 shows Technora rods.

Fig. 2-3. Technora AFRP Tendons

Fig. 2-4. Arapree AFRP Tendons

Arapree comprises aramid Twaron fibres embedded inepoxy resin, with two types of cross sectional shapes

available, rectangular and circular. (refer to Figure 2-4).FiBRA (Fibre BRAiding) is an FRP rod formed by braiding

high strength fibre tows, followed by epoxy resin

impregnation and curing (Figure 2-5). Two types of rods are

produced for concrete reinforcement, rigid and flexible.

Parafil, is a parallel lay rope composed of dry (non-

impregnated) fibres within a protective polymeric sheath. Itcan not be bonded to concrete and contains no polymer

resin. Figure 2-6 shows a Parafil Rope with end fittings.

ANCHORAGE SYSTEMS

Numerous anchoring devices have been developed for steelprestressing tendons, and these are widely available, cost-

effective, and reliable. However, these existing anchorage

devices cannot be applied directly to FRP tendons, sinceFRPs are sensitive to transverse pressure when subjected to

high axial stress. The very high ratio of axial to lateral

strength and stiffness of FRPs (which can be as high as 30:1in some cases) translates into a need to rethink and redesign

the anchoring system for cables made from FRP materials.

Anchors for FRP tendons are required to have at least the

same nominal load capacity as the FRP tendons, even

though the full capacity of the tendon is typically not

utilized in practice (because the tendons are generallystressed well below their tensile failure load during the

prestressing operations). The reason for this is that anchors

having a smaller capacities than the FRP tendons are

inefficient in that they may overstress some fibres (whichcould cause premature failure of a tendon) and understress

others (an inefficient use of material).

Fig. 2-5. FiBRA (Kevlar) (Mitsui Constructi on Co.)

Fig. 2-6. Parafil Rope and Fittings (LinearComposites Limited)

Existing FRP tendon anchorages have to be designed insuch a way that the tensile strength of the FRP is not

significantly reduced by anchorage effects when subjectedto both static and dynamic actions. This requires limiting the

anchoring stresses on the tendon such that failure of the

cable will take place outside the anchoring zone. Some of


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7

the available anchorage systems, shown schematically in

Figure 2-7, include: clamp anchor, plug and cone (or barrel

and spike) anchor, resin sleeve anchor, resin potted anchor,

metal overlay anchor, and split wedge anchor.

Clamp Anchor

In a clamp anchor, the FRP rod is sandwiched between twogrooved steel plates, which are held together by bolts. The

shear-friction mechanism that transfers the force from the

tendon to the anchor is influenced by parameters such as the

roughness of the interface surfaces and the lateral clamping

force applied by the bolts. The performance of the anchorcan be improved by using a sleeve of soft metal such as

aluminum or copper to encase the rod and distribute the

gripping force. The length of the anchor may varydepending on the sleeve material chosen to insure that the

ultimate strength of the rod can be developed.

Plug & Cone Anchor

The plug and cone anchor is made of a metallic socket

housing and a conical spike (refer to Figure 2-6). Thegripping mechanism is similar to that in a wedge anchor, in

that the rope is held by the compressive force applied to the

fibres when the plug is inserted into the barrel. This

compressive stress generates friction between the rodmaterial and the socket and plug, resulting in a frictional

stress that resists the slipping of the rod from the socket.

Resin Sleeve Anchor

This anchor system functions by embedding the FRP tendon

in a potting material that fills a tubular metallic housingcomprising steel or copper. Non-shrink cement grout, with

or without sand filler, expansive cement grout, or an epoxy-based material may all be used as the potting material. The

mechanism of load transfer is by shear and bond at theinterface between the rod and the filling material, and

between the filling material and the metallic sleeve.

Resin Potted Anchor

This type of anchor varies depending on the internal

configuration of the socket; which may be straight, linearly

tapered, or parabolically tapered. This type of anchor has the

same components as the resin sleeve anchorage. The loadtransfer mechanism from the rod to the sleeve is by interface

shear stress, which is influenced by the radial stress

produced by the variation of potting material profile.

Metal Overlay Anchor

In this system, a metal overlay is added to each end of the

tendon by means of die-molding during the manufacturing

process. This enables the tendon to be gripped at thelocations of the metal material using a typical wedge anchor

as would be used for a steel tendon. The use of this system

is limited because of the length of the tendon between

anchorages must be predefined during the manufacturingprocess. The load transfer in this anchor is achieved by

shear (friction) stress, which is a function of the

compressive radial stress and friction at the contact surfaces.

Split Wedge Anchor

The split wedge anchorage, which contains steel wedges in

a steel tube with an inner conical profile and outer

cylindrical surface, has been widely used for anchoring steelprestressing tendons. The number of the wedges within the

anchors barrel may vary from two to six, depending on the

specific system. Increasing the number of wedges induces a

contact pressure that is more uniformly distributed around

the rod. This type of anchor is comparatively convenientbecause of its compactness, ease of assembly, reusability,

and reliability. The gripping mechanism relies on both

friction between the FRP rod and the wedges, as well as theclamping force between the wedges, barrel and tendon.

CFCC Anchoring System

In some cases, combinations of the above noted anchorage

systems may be used in combination. As an example, Figure

2-8 shows a wedge system used in conjunction with die-casting, while Figure 2-9 shows different anchoring systems

used by Tokyo Rope Mfg. Co. for anchoring CFCC cables.

Steel cone

CFCC

Die-cast

Steel wedges

Fig. 2-8. CFCC system (El-Hacha, 1997)

LEADLINE Anchoring SystemSeveral types of multi-rod anchorages are available for each

size of Leadline CFRP rod and tension capacity (refer toFigure 2-10). In addition, a metallic anchor was developed,as part of the ISIS Canada research program for 8mmdiameter LEADLINE

TMCFRP prestressing tendons. This

stainless steel wedge-type anchorage, requires no new

technology for manufacture and is relatively simple to

assemble in the field (it is shown in Figure 2-11).

ARAPREE, FIBRA, TECHNORA & PARAFIL

Anchoring System

The anchoring systems developed for Arapree aramidprestressing rods, both flat and round rod types, consist of

tapered metal sleeves into which the tendon is either grouted

(in post-tensioning applications) or clamped between twowedges (refer to Figure 2-12).


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FRP Rod

Steel Plates

Bolts

(a)

Conical socket

Multiple rods

Plug(b)

Sleeve

Resin

Rod

(c)

Conical Sleeve

(d)

Resin

Rod

Conical Socket

(f)

Wedge

Rod

SleeveRod

(e)

Fig. 2-7. Anch oring Systems (ACI 440.4R, 2004)


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Fig. 2-9. Various Anchor ing Systems for CFCC(Tokyo Rope, 1993)

Fig. 2-10. Anchori ng Systems for CFRP

LEADLINE (Mitsubishi Kasei Corporation, 1993)

tendonwithcoppersleevethreaded

barrel

wedges

barrel elastic band tosecure wedges

Fig. 2-11. Calgary Anchor for LEADLINE (Sayed-Ahmed and Shr ive, 1998)

Fig. 2-12. Wedge Anchor System for Arapree

FiBRA has two different types of anchoring systems: a

resin-potted anchor used for single tendon anchoring, and awedge anchor for either single or multiple tendon anchoring

(shown in Figure 2-13).

Fig. 2-13. Anchorage Systems for Fibra (Kevlar 49)(Mitsui Construction Co. Ltd).

Parafil ropes are anchored by means of a barrel and spikefitting, which grips the fibres between a central tapered

spike and an external matching barrel (Figure 2-6). Because

of problems in finding a standard FRP anchorage system,pretensioning rather than post-tensioning prestressed

systems using FRP have gained increased popularity


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10

CREEP RUPTURE OF FRP TENDONS

Creep-rupture is the failure of a material subjected to a

sustained load level less than its short-term load tensilecapacity. FRP tendons used as prestressed reinforcement for

concrete members are, their very application as prestressed

reinforcement, subjected to long-term static stresses, and as

a result the long-term tensile strength of the FRP tendons

may be reduced. To assure that FRP tendons do not fail due

to creep rupture, the initial prestress in the tendon must be

limited to some prescribed percent of its ultimate short-term

tensile stress. To prevent creep-rupture failure, and to have

the design life of the tendon exceed 100 years, it has been

recommended (Burke and Dolan (2001) that the maximumprestress level should be limited to 60% of the ultimate

capacity for carbon tendons, and to 50% of the ultimate

capacity for aramid tendons. Glass tendons are used only

very rarely, but the stress limits for GFRP tendons aretypically lower than either carbon or aramid tendons.

Section 3

Placement, Handling, Construction &

Protection

PRECUATIONS

FRP tendons can be damaged due to poor handling and

storage, if sharp or heavy objects pierce the surface or crush

the bars. Surface defects could lead to lower strength

capacity. To avoid damage to FRP tendons, instructionsrequiring careful handling, storage and placement shall be

specified in the work plans. FRP tendons must be protected

from damage during transportation, and should be stored insuch a way that they are not exposed to rain, excessive heat,

or direct sunlight for a prolonged period of time. When

placing concrete, care should be taken not to damage the

FRP tendons by vibrators, tamping rods, or other placementequipment. Concrete with FRP tendons should typically be

moist-cured, but should not be heat-cured or autoclaved, as

this may lead to damage to the polymer resin of the tendons,

(CAN/CSA, 2005).

Installation & Prestressing PrecautionsClearly, the tendons must be installed as specified in the

design plans and construction drawings. Inspection should

be made frequently to ensure that the tendons have minimal

surface damage, kinks, or exposure to adverse environmentsor chemicals.

When installing FRP tendons, care should be taken not

to cause damage by trampling or bending. The cutting of the

tendons should be done using a high-speed cutter. Heatingand cutting with the help of gas torches can damage the

tendons and should not be used. During re-stressing of a

tendon, the gripping mechanism should not be applied at the

same location. Because FRP tendons are brittle and may

break suddenly during prestressing, precautions to safeguard

against the explosive release of energy stored in thesetendons must be considered (CAN/CSA, 2005).

Cover to ReinforcementAccording to CAN/CSA-S806-02 (CAN/CSA, 2002), the

minimum clear concrete cover in pretensioned members

shall be 3.5 times the diameter of the tendon or 40mm,

whichever is greater. If concrete of higher compressive

strength than 80MPs is used, the cover may be reduced to 3times the diameter or 35mm, whichever is greater.

According to CAN/CSA-S6-06 (CAN/CSA, 2006), the

minimum clear cover shall be 50mm 10mm for FRPtendons. For pretensioned concrete, the cover and

construction tolerance shall not be less than the equivalent

diameter of the tendons 10mm. For post-tensioned

concrete, the cover shall not be less than one-half thediameter of the post-tensioning duct 10mm.

End Zone in Prestressed ComponentsThe end zones of pretensioned concrete components are

required to be reinforced against splitting, using additionalclosed stirrups added to the stirrups which are already

provided at the ends of a typical prestressed beam.

Reinforcement of the anchorage zones of beams post-tensioned with FRP tendons should consist of an anchor

bearing steel plate provided at both ends of the beam to

transfer the prestress force into the concrete beam and to

resist high bearing stresses. Spiral reinforcement behind the

bearing area should be provided around each tendon toconfine the concrete, so as to improve the bearing capacity

and resist splitting forces.


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Section 4

Stress Limitations for FRP Tendons

STRESSES AT JACKING & TRANSFER

The maximum permissible stresses in FRP tendons at jacking and transfer for concrete beams and slabs are given in Table

4.1. As previously discussed, the stresses are typically limited to values significantly less than the tensile capacity of the FRP

tendon itself.

Table 4-1. Maximum Permissible Stresses in FRP Tendons at Jacking and Transfer for Concrete Beamsand Slabs (CAN/CSA-S6-06, and CAN/CSA-S806-02)

At Jacking At TransferTendon

Pretensioned Post-tensioned Pretensioned Post-tensioned

AFRP 0.40ffrpu 0.40ffrpua) 0.35ffrpub) 0.38ffrpu

0.35ffrpu

CFRP 0.70ffrpu 0.70ffrpua) 0.65ffrpub) 0.60ffrpu

0.65ffrpu

GFRP 0.30ffrpu 0.30ffrpu 0.25ffrpu 0.25ffrpuonly permitted by CAN/CSA-S6-06 (CAN/CSA, 2006) a)

by CAN/CSA-S6-06

b)by CAN/CSA-S806-02

Correction of Stress for Harped or

Draped TendonsOccasionally, the profile of a pretensioned FRP tendon isaltered by harping at the mid-span or the third points of a

member before casting of the concrete. Because FRP

tendons exhibit linear elastic behaviour to failure, draping or

harping of tendons results in a loss of tendon strength. Thus,

when an FRP tendon is bent, the jacking stresses must be

reduced to account for stress increases. The degree of thestress increase is dependent on the radius of curvature of the

tendon at the harping point(s), the tendons modulus of

elasticity, and the cross-sectional properties of the tendon.

Dolan et al. (2000) proposed that the stress increase due toharping in both solid and stranded tendons can be defined

by the following equation:

ch

frp

hR

yE= (Eq. 4.1)

where

frpE = Modulus of elasticity of the FRP tendon

y = Distance from the centroid to the tensile face of the

bent tendon (radius of tendon)

chR = Radius of curvature of the harping saddle

Research carried out at the University of Waterloo (Quayle,

2005) indicates that this approach may overestimate the

harping stress, and recommends that the value ofRch inEquation 4.1 be taken as the greater of the radius of

curvature of the harping saddle or the natural radius of

curvature,Rn, of the harped tendon given by:

( )

cos12

2

=

P

ErR

frp

n(Eq. 4.2)

where

r = Radius of the FRP tendonP = Force in the tendon

= Angle of deviation of tendon at the deviator point

The efficiency of the prestressing tendons can be

significantly reduced when this stress is deducted from the

permissible stress at jacking. The combined stress in atendon of cross-sectional area,Afrp, at a harping saddle, due

to the jacking load, Pj,, is given by:

..hc

frp

frp

j

R

yE

A

P+= (Eq. 4.3)

PRESTRESS LOSSES

Prestress loss in concrete structures is an important design

parameter which must be taken into consideration with FRP

materials (as in the case of prestressing with conventional


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steel prestressing strands). Losses due to initial elastic

shortening (ES), concrete creep (CR), and concrete

shrinkage (SH), can be computed according to CAN/CSA-

S6-06 in the same manner as for beams prestressed withsteel tendons (taking into account the typically lower

modulus of elasticity of FRP tendons).

Elastic Shortening (ES)The loss due to elastic shortening (ES), should be calculated

as follows. For pretensioned members:

cir

ci

pf

E

EES= (Eq. 4.4a)

for post-tensioned members:

cir

ci

pf

E

E

N

NES

=

2

1(Eq. 4.4b)

where

pE = Modulus of elasticity of tendonsN = Total number of post-tensioning tendons

cirf = Concrete stress at the level of the tendon

g

d

g

i

g

i

I

eM

I

eP

A

P+=

2

(Eq. 4.5)

Creep of Concrete (CR)Prestress losses due to creep of concrete (CR) may becalculated as follows (using an empirical equation):

( )[ ] ( )cdscirc

p

cr ffE

EKRHCR =

201.077.037.1

(Eq. 4.6)

where

RH is the mean annual relative humidity expressed aspercentage

crK = 2.0 for pretensioned members

crK = 1.6 for post-tensioned members

cdsf = Concrete stress at the centre of gravity of the

tendons due to all dead loads except the dead load present attransfer, the stress being positive when tensile, given by:

g

sdcds

I

eMf = (Eq. 4.7)

Note that cirf should be taken as positive in Equation 4.6

Shrinkage of Concrete (SH)Prestress losses due to shrinkage of concrete (SH) may be

calculated, again using empirically-derived equations, as

follows. For pretensioned members:

RHSH 05.1117 = (Eq. 4.8a)

for post-tensioned members:

RHSH 85.094 = (Eq. 4.8b)

Since the modulus of elasticity of FRP tendons is typicallylower than a corresponding steel tendon, losses for

prestressed FRP tendons due to elastic shortening, creep,

and shrinkage of concrete will be less than for prestressed

steel tendons.

Relaxation Losses (REL)According to Rostsy (1988), the losses due to relaxation

for carbon FRPs is negligible when the initial stress is equal

to 50% of the ultimate tensile stress. However, relaxation

losses vary with the fibre type. The relaxation losses in FRP

tendons are a combination of three sources, and the totalrelaxation loss (as percentage of transfer stress), REL, can

be calculated by assessing these three effects separately.

ACI 440.4R (ACI, 2004) describes these three effects asfollows:

321 RELRELRELREL ++= (Eq. 4.9)

Relaxation of Polymer(REL1)When a tendon is initially stressed, a portion of the loadis carried in the resin matrix. The matrix, which is a

visco-elastic material, relaxes and loses its contributionto the load carrying capacity. This relaxation is given by

the modular ratio of the resin to the fibre, rn , and the

volume of fibres in the tendon, fv ,. The modular ratioof the resin is defined as the ratio of the elastic modulus

of the resin, rE , to the modulus of the fibre, fE , as

given in Equation 4.5:

f

r

rE

En = (Eq. 4.10)

The volume of fibres in the tendon can be determined

from 0.1=+ rf vv ,where fv and rv are the volume

fractions of fibre and resin, respectively. The relaxation


13/30


loss is the product of the volume fraction of resin,

fr vv = 0.1 , and the modular ratio of the resin, rn ,

giving:

rr vnREL =1 (Eq. 4.11)

Straightening of Fibres(REL2)The fibres in a pultruded section are nearly but not

completely parallel. Therefore, stressed fibres flowthrough the matrix and straighten, and this straighteningappears as a relaxation loss in typical applications. Anassumed one to two percent relaxation of the transferstress is adequate to predict this portion of the relaxationloss calculation.

Relaxation of Fibres (REL3)Fibre relaxation is dependent upon the fibre type.

According to CAN/CSA-S806-02, in the absence ofspecific information, the following values of relaxation

may be used (with t = time in days), expressed as apercentage of the transfer stress. For CFRP:

)log(345.0231.0(%) tRelaxation += (Eq. 4.12)

For AFRP:

)log(88.238.3(%) tRelaxation += (Eq. 4.13)

Friction Losses (FR)In assessing friction loss, relevant curvature friction and

wobble coefficients must be used, as would typically beused when designing with steel prestressing tendons. Such

data are sparse. Burke and Dolan (2001) found that, for a

CFRP tendon in a PVC duct, the curvature friction

coefficient could range from 0.25 for stick-slip behaviour to0.6 for no stick-slip behaviour. Since the wobble coefficient

relates primarily to the type of duct, values specified for

steel prestressing systems may be applied for this

component.

Section 5

Flexural Design

The overall design approach for flexure in concrete beams

prestressed with FRP tendons is based on the concept ofdetermining the area of the prestressing tendons required to

meet the strength requirements of the section. A prestress

level of 40 to 70 percent of the ultimate tensile strength ofthe tendons can be selected for the initial applied prestress

force, and service level of stresses in the concrete are

checked on this basis. If the stresses meet the prescribed

requirements (discussed below), the flexural design is

complete; otherwise, the number or size of the tendons isadjusted to meet serviceability requirements (i.e. stress

limits), and the strength capacity is rechecked until an

appropriate solution is obtained.

Flexural Service StressesFlexural service level stresses, which may be computedusing techniques similar to conventional steel prestressed

concrete members, should not exceed the stress levels given

in Table 5.1. These are the same concrete service stresslimits imposed by Canadian codes for steel prestressed

concrete. As is the case for steel prestressed concrete, the

stresses in the concrete in tension at transfer may be

exceeded, provided that bonded reinforcement is added to

resist the total tensile force in the concrete.

DESIGN PROCESS

Under the overarching philosophy of Limit States Design

(LSD), structures are designed in Canada such that the

factored resistance of a given structural member is greaterthan the effect of the factored loads (NBCC, 2005, Sentence

4.1.3.2(1)). This requirement can be expressed as:

LoadsFactoredofEffectResistanceFactored (Eq. 5.1)

where

Factored Resistance is the resistance of a cross-section,

including application of the appropriate resistance factors,

, to the specified material properties.

Effect of Factored Loads means the structural effect due to

the factored loads and load combinations as specified in

CAN/CSA-A23.3-04 (CAN/CSA, 2004) Clause 8.3.2 and

8.3.3 or Sentence 4.1.3.2 of NBCC 2005.

Resistance Factors()

The material resistance factor for concrete in buildings is

given as c = 0.65 for cast-in-place and precast concrete

strength (CAN/CSA-A23.3-04, clause 8.4.2). For bridges

c = 0.75 in accordance with CAN/CSA S6-06.


14/30


The material resistance factor for FRP, frp , is based

on variability of the material characteristics, the effect of

sustained load and the type of fibres. Values of resistance

factors, frp , for various types of prestressed FRP

reinforcement in buildings, according to CAN/CSA-S806-

02, are given in Table 5.2.

CAN/CSA-S6-06 gives a value for the resistance factor

of 0.55 for AFRP, 0.75 for CFRP, and 0.50 for GFRPtendons in bridges, respectively.

Table 5-1. Allowable Concrete Stresses (CAN/CSA-A23.3-04)

Allowable stresses at transfer of prestress (immediately after prestress transfer due toprestress and the specified load present at transfer, prior losses)

Limits (MPa)

(a) Extreme fibre stress in compression cif6.0

(b) Extreme fibre stress in tension except for (c)cif25.0

(c) Extreme fibre stress in tension at endscif5.0

Allowable stresses under service or specified loads and prestress (after allowance for allprestress losses)

(a) Extreme fibre stress in compression due to prestress plus sustained loadscf45.0

(b) Extreme fibre stress in compression due to prestress plus total loadscf6.0

(c) Extreme fibre stress in precompressed tensile zonecf5.0

Table 5-2. Resistance Factors for Prestressed FRP Reinforcement for Buildings (CAN/CSA-S806-02)

Tendon Type Pretensioned Post-tensioned (bonded) Post-tensioned (unbonded)

CFRP 0.85 0.85 0.80

AFRP 0.70 0.70 0.65

Assumptions for Flexural DesignThe analysis of prestressed concrete beams should be

performed using a simple plane sections, straincompatibility analysis. The main standard assumptions are

summarized below:

1. Plane sections before bending remain plane afterbending, leading to a linear strain distribution over thecross section.

2. The concrete is assumed to have a maximum usablecompressive strain capacity of 0.0035 at the extreme

compression fibre, in accordance with existingprestressed concrete design codes in Canada

(CAN/CSA, 2004; CAN/CSA, 2006; CAN/CSA, 2002).

3. After cracking the tensile strength of concrete may beneglected.

4. Flexural deformations are small, and sheardeformations are negligible.

5. The stress-strain relationships for the constituentmaterials are known from experimental tests andtheoretical curves.

Two additional assumptions are required specifically for the

design of FRP prestressed concrete members:

6. Nominal balanced strain conditions for FRP prestressedmembers are assumed to exist at a cross section wherethe tensile FRP reinforcement reaches its ultimate

strain, frpu, at the same instant as the concrete in

compression reaches its maximum usable strain, cu, of

0.0035. At the balanced strain condition, an FRPprestressed member will fail suddenly and with little

warning, since the FRP does not yield like conventional

steel reinforcement.

7. For all FRP prestressed concrete members, it ispermissible to allow rupture of the FRP, provided that

the structure as a whole contains supplementary

reinforcement designed to carry the unfactored dead

loads or has alternative load paths such that the failureof the member does not lead to progressive collapse of

the structure (CAN/CSA-S6-06 and CAN/CSA-S806-

02).

FAILURE MODES & STRENGTH DESIGN

The approach to strength design of an FRP prestressed beam

is based on the mode of failure. Three possible failure

modes exist (if it is assumed that premature failure modes

such as anchorage failure do not occur):

Balanced strain condition - Simultaneous failure byrupture of the FRP tendons in tension and crushing of

the concrete in compression at the extreme compressionfibre. The balanced failure of FRP prestressed beams is

similar to the balanced strain condition used in

reinforced concrete design, and defines the point at

which the failure mode changes. However, thebehaviour is somewhat different than for steel tendons

in that the FRP tendons rupture at the balanced point,


15/30


rather than yield as is the case for steel tendons. This

leads to the FRP balanced ratio being an indicator of the

failure mode, rather than any measure (or assurance) of

ductility.

Tension failure - Tensile rupture of the FRP tendonsoccurs before crushing of the concrete, i.e., the strain in

the most highly stressed FRP tendon reaches the

ultimate tensile strain of the FRP, frpu , while the strainin the concrete at the extreme fibre of the compression

zone is less than 0.0035. This type of failure is typicallyvery sudden and occurs when the reinforcement ratio is

less than the balanced failure reinforcement ratio.

Compression failure - Concrete crushing incompression occurs while the FRP tendons have atensile strain level smaller than their ultimate strain.

Compression failure, which occurs when the

reinforcement ratio is more than the balanced ratio, is

less violent and more desirable than tension failure, andis similar to that of an over-reinforced concrete beam

with internal steel reinforcement. Because the strain at

failure for an FRP tendon is greater than the yield strain

of a typical steel prestressing tendon, beams prestressedwith FRP tendons will generally exhibit larger

deformations prior to compression failure than beams

prestressed with steel tendons; therefore, the beams

provide warning of failure in the form of large

deformations.

Reinforcement Ratio at Balanced Strain

ConditionThe balanced strain condition occurs when the concrete

strain reaches its ultimate compressive strain value,

0035.0=cu , while the most highly stressed layer of FRP

tendons reaches their ultimate strain, frpu . At the balanced

failure strain condition the FRP tendons will fail suddenly

and without warning, since FRPs do not yield. Figure 5-1

shows the stress and strain conditions for an FRP

prestressed concrete section at the balanced condition. The

balanced reinforcement ratio, b, is based on strain

compatibility in the cross section and is calculated using the

assumptions listed previously.

Fig. 5-1. Stress and Strain Conditions for Balanced Reinforcement Ratio

An FRP reinforcement ratio above the balanced ratio, b ,

results in failure due to concrete crushing, while a

reinforcement ratio below the balanced ratio results in

failure due to tendon rupture in tension. Using straincompatibility and similar triangles from Figure 5-1, the

depth to the Neutral Axis at the balanced strain condition

can be determined from:

fcu

cub

d

c

+= (Eq. 5.13)

where, the strain in the FRP which contributes to flexuralstrength (again, refer to Figure 5-1) can be determined from:

prdpefrpuf =

thus, we have:

prdpefrpucu

cub

d

c

+= (Eq. 5.14)

where,

Strain distribution

Rectangular T

Sections

a =1c

1cfc

T

bb cu

pefConcrete stress

distribution (idealized)

and internal forces

Tension Compression

Effective

Prestrain

Strain atultimate

chf

d

d

C

Comment [LB1]: Shoutext not equation editorbecause the equation edmesses up the line spacand the formatting wheninserted into paragraphs

Comment [LB2]: Shoushow how to calculate threinforcement ratio


16/30


bc = Depth neutral axis at balanced condition (mm).

d = Effective depth of outermost layer of FRP tendons intension (mm).

cu = Ultimate strain of concrete in compression (i.e.,

0.0035 in Canada).

frpu = Ultimate tensile strain of FRP tendons.

pe = Effective strain in the FRP tendon due to

prestressing. In a typical design, pe is known because it is

specified and selected by the designer based upon the levelof desired prestress, the type of tendons being used, and the

ultimate stress and strain capacity of the tendons provided

by the manufacturer.

d = Strain used to decompress the precompressed zone,

which can be usually ignored (this is a conservativeassumption), because it is a negative value and is an order of

magnitude smaller than the other strains.

pr = Loss of strain capacity due to sustained loads. This

strain loss due to sustained loads is nearly zero, if thesustained load is less than the load corresponding to 50% of

the ultimate tensile strain (Dolan et al., 2000), and, thus, can

be ignored. This condition is typically satisfied, because the

prestress strain is around 50% of the ultimate strain in orderto leave some capacity for flexural strain needed for strength

requirements.

Now taking equilibrium of forces in the cross section(Figure 5-1):

CT= (Eq. 5.15)

where,

bcc cbfC 11 = (Eq. 5.15(a))

ufrpfrpbfrp fAT = (Eq. 5.15(b))

bdA bbfrp = (Eq. 5.15(c))

ufrpf = Ultimate tensile stress of FRP tendons (MPa).

frpufrp E=

bfrpA = Area of FRP for balanced conditions (mm2).

frpE = Modulus of elasticity of FRP tendons (MPa).

Thus, we have:

frpufrpbbcc fbdcbf = 11 (Eq. 5.16)

where

1 = Ratio of average concrete strength in the rectangular

compression block to the specified concrete strength, given

by the following (CAN/CSA-A23.3-04, CAN/CSA-S6-06

and CAN/CSA-S806-02):

67.00015.085.01 = cf (Eq. 5.17)

1 = Factor defined as the ratio of depth of equivalent

rectangular compression stress block to the depth of the

neutral axis, given as (CAN/CSA-A23.3-04, CAN/CSA-S6-

06 and CAN/CSA-S806-02):

67.00025.097.01 = cf (Eq. 5.18)

b = Width of compression face of a member (mm).

d = Effective depth of outermost layer of FRP (mm).

cf = Compressive strength of concrete (MPa).

Thus, solving equation 5.16 for the balanced reinforcement

ratio gives:

d

c

f

f b

frpufrp

ccb

'11= (Eq. 5.19)

Substituting the expression forcb/dfrom Equation 5.14 into

Equation 5.19 gives the balanced reinforcement ratio interms of basic material properties as follows:

+=

prdpefrpucu

cu

frpufrp

ccb

f

f

'11

(Eq. 5.20)

As explained previously, the strain loss due to sustained

loads, pr , and the decompression strain, d , can typically

be ignored (Dolan et al., 2000), giving the following

simplified definition for b :

+=

pefrpucu

cu

frpufrp

ccb

f

f

'11 (Eq. 5.21)

Equation 5.21 is valid for both flanged and rectangularsections, provided that the depth of the compression block

remains within the flange.

Failure Due to Concrete Crushing

In a beam which has b> , flexural failure will occur bycrushing of the concrete before rupture of the FRP tendons

in tension. The stress and strain distributions at ultimate

condition for this type of section are shown in Figure 5-2. In


17/30


this case, the strain in the FRP tendon is not known since

frpufrp < , the strain in the extreme compression fibre of

the concrete is equal to the ultimate compressive strain of

concrete in compression, again 0035.0=cu , and thenonlinear concrete stress field in the compression zone is

replaced by an equivalent uniform rectangular stress block

(as is done for conventional reinforced or prestressedconcrete flexural design). The ultimate moment resistance

for such an over-reinforced section is determined as follows.The compressive force in the concrete is calculated as:

bcfC cc 11 = (Eq. 5.22)

and the tensile force in the FRP tendon at failure is:

frpfrpfrp fAT = (Eq. 5.23)

where,

c = Depth of neutral axis (mm).

c = Material resistance factor for concrete.

frpA = Area of FRP )( bdA frpfrp = (mm2).

frp = Material resistance factor of FRP.

frpf = Stress in FRP tendon at failure, which is smaller

than the ultimate tensile strength of the FRP tendon (MPa).

From strain compatibility in the cross section (Figure 5-2):

fcu

cu

d

c

+= (Eq. 5.24)

The strain in the FRP tendon, p , is equal to the effective

prestrain, pe , plus the flexural strain, f , which is not

known:

pefp += (Eq. 5.25)

Thus, Equation 5.24 can be rewritten as follows:

( )pepcucu

d

c

+= (Eq. 5.26)

Substituting the neutral axis depth from Equation 5.26 into

Equation 5.22, and satisfying equilibrium of forces on the

cross section, by equating Equation 5.22 to Equation 5.23,

gives a quadratic equation in terms of the stress in the FRP

tendon at failure frpf . An iterative process may be adopted

in solving this quadratic equation. In each iteration, for an

assumed depth of neutral axis the strain in the FRP tendon

( p ) is calculated from Equation 5.26, the internal forces in

the concrete and the FRP tendon are calculated using

Equations 5.22 and 5.23, and their equilibrium is checked:

frppfrpfrpcc EAbcf = 11 (Eq. 5.27)

If equilibrium is not satisfied, a new value of depth ofneutral axis is chosen and the compressive force in the

concrete and the tensile force in the FRP tendon are

recalculated. When equilibrium of internal forces is satisfied

(i.e., CT= ), the moment resistance can be calculated as:

=

2

1cdCMr

(Eq. 5.28)

Fig. 5-2. Strain and Stress Distributi on at Ultimate for Concrete Crushing Failure Mode

Strain distribution

Rectangular

section

a =1c

1cfc

T

b cu

pef Concrete stressdistribution (idealized)and internal forces

Tension Compression

EffectivePrestrain

Strain atultimate

c

d

dAfrp

C


18/30


Failure Due to Tendon Rupture

A beam which has b will fail by rupture of the FRP

tendons before crushing of the concrete. In this case, the

strain in the FRP tendons reaches their ultimate tensile

strain, frpu , before the strain in the concrete in the extreme

compressive fibre reaches its ultimate value. The strain in

the FRP tendon at failure is thus given by:

frp

frpu

frpuE

f= (Eq. 5.29)

Because the corresponding strain in the concrete at theextreme compression fibre is less than the ultimate strain,

the traditional rectangular stress block, and the stress block

factors 1 and 1 , cannot be used to idealize the

distribution of concrete stress in the compressive zone.

However, Tables 5.6, 5.7 and 5.8 provide stress block

factors and for the stress blocks at extreme fibre

concrete compressive strains of less than ultimate, and are

given in Tables 5.6, 5.7 and 5.8 for different ratios of

'cc and different concrete compressive strengths.

Using these tables and an iterative process assumingstrain compatibility and force equilibrium, the flexural

strength can be determined. The process begins by

specifying the strain in the FRP tendon equal to the ultimate

tensile strain, frpu , and assuming a value of the depth of

neutral axis, c . The strain in the extreme compression

concrete fibre, c , is then calculated using strain

compatibility from similar of triangles (refer to Figure 5-3),

assuming 0=d ; this value must be less than the ultimate

strain of concrete in compression, cu . The compressive

force in the concrete can be calculated as:

bcfC cc = (Eq. 5.30)

The tensile force in the FRP tendon at failure is

subsequently calculated as:

frpfrpufrpfrp EAT = (Eq. 5.31)

And equilibrium of forces requires that TC= , hence:

frpfrpufrpfrpcc EAbcf =

If equilibrium is not satisfied, another iteration is made

using a new value of depth of neutral axis, c , while the

strain in the FRP tendon is kept equal to the ultimate tensile

strain, frpu . When equilibrium of internal forces is

satisfied, the moment of resistance of the section can be

found by taking moments about the resultant of thecompressive stresses in concrete, C, giving the followingequation for flexural capacity:

=

2

cdTMr

(Eq. 5.32)

Fig. 5-3. Strain and Stress Distributi ons at Ultimate for Rupture of FRP

a = c

cfc

T

b c < cu

pefrpu-pe Concrete stressdistribution (idealized)

and internal forces

Rectangular

section

Tension Compression

Effective

Prestrain

Strain atultimate

Strain distribution

c

d

dAfrp

C

actual stress

diagram


19/30


Table 5-6. Stress Block Factors and for 20 to 30 MPa Concrete (ISIS,

2001a)cf=20 MPa cf=25 MPa cf=30 MPa

oc

0.1 0.184 0.602 0.111 0.163 0.600 0.098 0.150 0.600 0.090

0.2 0.325 0.639 0.208 0.293 0.636 0.186 0.271 0.634 0.172

0.3 0.455 0.657 0.299 0.418 0.650 0.272 0.390 0.647 0.252

0.4 0.569 0.672 0.382 0.533 0.661 0.353 0.503 0.656 0.330

0.5 0.666 0.686 0.457 0.636 0.672 0.428 0.609 0.664 0.404

0.6 0.746 0.700 0.522 0.724 0.684 0.495 0.702 0.674 0.473

0.7 0.810 0.714 0.578 0.796 0.697 0.555 0.781 0.685 0.535

0.8 0.860 0.728 0.626 0.853 0.711 0.606 0.844 0.698 0.589

0.9 0.897 0.743 0.666 0.894 0.726 0.649 0.890 0.713 0.635

1.0 0.923 0.757 0.699 0.923 0.742 0.685 0.921 0.729 0.671

1.1 0.941 0.772 0.726 0.940 0.758 0.713 0.938 0.747 0.700

1.2 0.952 0.786 0.748 0.948 0.775 0.734 0.942 0.766 0.722

1.3 0.958 0.800 0.766 0.949 0.791 0.751 0.938 0.785 0.736

1.4 0.959 0.813 0.780 0.943 0.808 0.762 0.926 0.805 0.745

1.5 0.956 0.827 0.791 0.934 0.825 0.770 0.909 0.825 0.750

1.6 0.951 0.840 0.798 0.921 0.841 0.774 0.887 0.846 0.750

1.7 0.944 0.852 0.804 0.905 0.857 0.776 0.864 0.866 0.748

1.8 0.935 0.864 0.807 0.888 0.873 0.775 0.839 0.885 0.743

1.9 0.924 0.876 0.809 0.870 0.888 0.773 0.813 0.905 0.736

2.0 0.913 0.887 0.810 0.851 0.903 0.769 0.787 0.924 0.727


20/30


Table 5-7. Stress Block Factors and for 35 to 45 MPa Concrete (ISIS, 2001a)cf=35 MPa cf=40 MPa cf=45 MPa

oc

0.1 0.141 0.600 0.085 0.134 0.600 0.080 0.129 0.600 0.077

0.2 0.255 0.634 0.161 0.243 0.633 0.154 0.23 0.633 0.148

0.3 0.368 0.645 0.238 0.352 0.645 0.227 0.339 0.645 0.218

0.4 0.479 0.653 0.313 0.459 0.651 0.299 0.443 0.651 0.288

0.5 0.584 0.660 0.385 0.564 0.657 0.370 0.546 0.655 0.358

0.6 0.681 0.667 0.454 0.662 0.663 0.438 0.644 0.660 0.425

0.7 0.765 0.676 0.518 0.750 0.670 0.503 0.735 0.666 0.489

0.8 0.834 0.688 0.574 0.823 0.680 0.560 0.812 0.675 0.548

0.9 0.885 0.702 0.621 0.879 0.694 0.610 0.872 0.687 0.599

1.0 0.918 0.719 0.660 0.915 0.710 0.650 0.911 0.703 0.641

1.1 0.934 0.738 0.689 0.931 0.730 0.679 0.926 0.724 0.671

1.2 0.936 0.759 0.710 0.929 0.753 0.699 0.920 0.749 0.689

1.3 0.926 0.781 0.723 0.912 0.778 0.710 0.898 0.777 0.697

1.4 0.907 0.804 0.729 0.885 0.805 0.713 0.863 0.808 0.697

1.5 0.881 0.828 0.730 0.852 0.833 0.710 0.821 0.840 0.690

1.6 0.852 0.853 0.726 0.814 0.862 0.702 0.776 0.874 0.678

1.7 0.820 0.877 0.719 0.775 0.891 0.691 0.730 0.907 0.662

1.8 0.788 0.901 0.710 0.736 0.920 0.677 0.686 0.940 0.645

1.9 0.755 0.925 0.699 0.698 0.948 0.662 0.643 0.973 0.626

2.0 0.723 0.948 0.686 0.662 0.976 0.646 0.604 1.005 0.607


21/30


Table 5-8. Stress Block Factors and for 50 to 60 MPa Concrete (ISIS, 2001a)cf=50 MPa cf=55 MPa cf=60 MPa

oc

0.1 0.125 0.600 0.075 0.122 0.600 0.073 0.119 0.600 0.071

0.2 0.226 0.633 0.143 0.220 0.633 0.141 0.216 0.633 0.136

0.3 0.328 0.644 0.211 0.320 0.644 0.206 0.313 0.644 0.202

0.4 0.430 0.650 0.280 0.419 0.650 0.272 0.410 0.650 0.266

0.5 0.531 0.654 0.347 0.518 0.654 0.339 0.507 0.654 0.331

0.6 0.629 0.658 0.414 0.615 0.657 0.404 0.603 0.656 0.396

0.7 0.721 0.663 0.478 0.708 0.661 0.468 0.696 0.660 0.459

0.8 0.802 0.670 0.537 0.791 0.667 0.528 0.781 0.665 0.519

0.9 0.866 0.682 0.590 0.859 0.677 0.581 0.852 0.674 0.574

1.0 0.907 0.697 0.632 0.902 0.693 0.625 0.898 0.688 0.618

1.1 0.921 0.719 0.662 0.917 0.715 0.655 0.912 0.711 0.648

1.2 0.912 0.746 0.680 0.902 0.744 0.671 0.892 0.742 0.662

1.3 0.882 0.777 0.685 0.865 0.779 0.673 0.847 0.781 0.662

1.4 0.839 0.812 0.681 0.813 0.818 0.665 0.788 0.825 0.650

1.5 0.789 0.849 0.670 0.756 0.860 0.650 0.723 0.871 0.630

1.6 0.737 0.887 0.654 0.698 0.902 0.630 0.661 0.918 0.607

1.7 0.686 0.925 0.634 0.643 0.945 0.608 0.603 0.965 0.582

1.8 0.637 0.963 0.614 0.593 0.986 0.584 0.552 1.009 0.557

1.9 0.593 0.999 0.592 0.547 1.026 0.561 0.507 1.052 0.533

2.0 0.552 1.035 0.571 0.506 1.064 0.539 0.467 1.092 0.510


22/30


Flexural Capacity for Multiple Layers of

FRP TendonsAt the ultimate limit state in flexure, the resistance of a

concrete beam prestressed with steel tendons is calculated

by assuming that all the tendons have yielded. Thisassumption is valid whether the steel tendons are in one or

more layers. Unlike steel tendons, however, FRP tendons donot yield, and, therefore, they cannot all be assumed to be at

the same stress at ultimate when they are in multiple layers.

If FRP tendons are placed in multiple layers, at theultimate limit state the strain in the outermost layer of the

prestressed FRP tendons is the critical strain, since this will

be first layer to reach the rupture strain. Thus, the depth of

multi-layer FRP tendons cannot be considered as the

distance from the compression face to the centroid of all the

FRP tendons, as would be assumed for steel reinforcement,and the strain in tendons in multiple layers should be

calculated by assuming a linear variation of strain throughthe depth of the section.

Minimum Factored Flexural Resistance

At every section in an FRP prestressed flexural member,

failure of the member immediately after cracking should be

avoided, and the following two criteria should be satisfied:

crr MM 5.1 (Eq. 5.33a)

fr MM 5.1 (Eq. 5.33b)

Minimum Area of Bonded Non-

Prestressed ReinforcementDue to the brittle nature of the failure of beams with FRP

tendons, supplementary non-prestressed reinforcement

capable of sustaining the unfactored dead loads must be

provided to control cracking. Such non-prestressed

reinforcement should be provided on the basis of the limitsprescribed in Table 5.9.

Table 5-9. Minimum Area of Bonded Non-Prestressed Reinforcement (CAN/CSA-S806-02)

Concrete Tensile Stress

cf 5.0 cf> 5.0

Type of Tendon Type of Tendon

Type of Member

Bonded Unbonded Bonded Unbonded

CFRP 0 0.0044Ag 0.0033Ag 0.0055AgBeamsAFRP 0 0.0048Ag 0.0036Ag 0.0060Ag

CFRP 0 0.0033Ag 0.0022Ag 0.0044AgOne-way slabs

AFRP 0 0.0036Ag 0.0024Ag 0.0048Ag

*whereAg is the concrete gross section area.

Section 6

Serviceability Limit States

GENERAL

The allowable stresses specified for concrete in Table 5.1must be enforced in order to ensure that the tensile strength

of the concrete will not be exceeded, and thus that FRP

prestressed concrete members will remain uncracked underservice loads.

DEFLECTIONS

Short-Term DeflectionsDeflections for FRP prestressed beams can be divided into

two categories, namely short-term deflections and long-term

deflections. The gross moment of inertia can typically be

used to calculate the short-term deflections along with

traditional mechanics of materials.

Long-Term DeflectionsFor long-term deflections, camber and deflection areseparated into individual components, adjusted by a

modifier, and then superimposed to obtain final deflections

in a similar manner as for conventional steel prestressed

members (CPCI, 1996). The modifiers for FRP tendons are

given in Table 6.1. The CPCI Design Handbook (CPCI,

1996) indicates that multipliers for topped members aresmaller than for un-topped members and the use of values

in Table 6.1 will be conservative for topped members.


23/30


14

Table 6-1. Suggested PCI Modifiers for FRP Tendons (Currier, 1995)

Without Composite ToppingDeflection or Camber

Carbon Aramid

Deflection due to self-weight 1.85 1.85At Erection

Camber due to prestress 1.80 2.00

Deflection due to self-weight 2.70 2.70

Camber due to prestress 1.00 1.00At Final

Deflection due to applied loads 4.10 4.00

Section 7

Ductility & DeformabilityGENERAL

Ductility and deformation require special consideration and

explanation for FRP prestressed members, as there is amarked difference between the two. Under load, a

prestressed concrete beam with steel tendons deforms

elastically until cracking, and then the member deflections

will progressively increase as the steel tendons yield.However, due to the linear elastic behaviour of FRP

tendons, FRP prestressed members also deform elastically

until cracking, but under increasing applied load they

continue to deform elastically until failure occurs either bytendon rupture or crushing of the concrete.

For either reinforced or prestressed concrete members,

ductility is defined as the ability of the member to sustain

large plastic deformations, and thus absorb energy, beforefailure, while deformability reflects the amount of

deformation that occurs prior to failure. Consequently,deformability is a key issue in determining the safety of

FRP prestressed structures (i.e. warning of failure).

Deformability

For a steel prestressed concrete member, the deformabilityindex, , is defined as the ratio of the deflection at ultimateto the deflection at yield of the tension reinforcement. This

definition cannot be applied directly in case of FRPprestressed member because the FRP exhibits linear elastic

behaviour up to rupture.

The use of a curvature approach is simpler and easier to

accomplish by using quantities calculated during the design

process. The deformability index, , for this approach isgiven by (Dolan and Burke, 1996):

( )

frps

frpu

ad

kdd

=

1

(Eq. 7.1)

where,

a = Depth of equivalent stress block at ultimate (mm)

d = Depth to FRP tendon (distance from the extremecompression fibre to the centroid of longitudinal tensionforce) or the effective depth of the outermost layer of FRP

tendon in tension (mm).

kd = Depth of neutral axis of cracked section at serviceconditions (mm).

1 = Stress-block reduction factor for concrete based on

Eq. 5.18.

frps = Strainin FRP tendon at service condition.

frpu = Ultimate strainin FRP tendon

CAN/CSA-S6-06 gives a value for the deformability indexto be at least 4.0 for rectangular concrete sections and 6.0

for concrete T-sections.


24/30


14

Section 8Bond, Development & Transfer LengthsGENERAL

In pretensioned concrete systems, stresses are transferred by

bond between the concrete and the reinforcement, and,

therefore, adequate transfer length and flexural bond lengthmust be provided. The mechanism of bond differs between

FRP and steel strands, due to the large variation of types,shapes, elastic moduli, and surface treatments of FRP bars.

The minimum development length should be calculated

as the summation of the transfer length and the flexural

bond length, as follows:

fbtd LLL += (Eq. 9.1)

in which

tL = Transfer length

fbL = Flexural bond length

Transfer LengthThe transfer length in pretensioned concrete is defined asthe length over which the prestressing force is totally

transferred to the concrete. The following equation can beused to determine the transfer length of carbon CFRP

reinforcement (Mahmoud and Rizkalla, 1996; Mahmoud et

al., 1997):

( )mmf

dfL

cit

tpi

t 67.0=

(Eq. 9.2)

where9.1=t for CFRP Leadline bars

8.4=t for CFCC strands

Flexural Bond LengthThe flexural bond length is defined as the embedment length

beyond the transfer length which is required to develop the

full tensile strength of the tendon in tension. The following

is an equation for the flexural bond length of carbon CFRPreinforcement (Mahmoud and Rizkalla, 1996; Mahmoud et

al., 1997):

( )( )mm

f

dffL

cf

tpefrpu

fb 67.0

=

(Eq. 9.3)

where

0.1=t for CFRP Leadline bars

8.2=t for CFCC strands

Typical values for transfer and development lengths of

various FRP tendons are given in Table 9-1.

Table 9.1 Development length and Transfer Length for Certain Types of FRP (CAN/CSA-S806-02)

FRP tendon type Diameter (mm) Development length Transfer length

CFRP strand N/A 50db 20dbCFRP rebar N/A 180db 60db

AFRP 8 db


25/30


Section 11

References and Additional Information

Additional information on the use of FRP materials can be obtained in various documents available from ISIS Canada. The

following publications have been used in the preparation of this module and can be consulted for a more complete discussionof the various topics presented herein:

ACI 440.4R-04. Prestressing Concrete with FRP Tendons American Concrete Institute, Detroit, Michigan, USA, 35pp. ACI 440.1R-03: Guide for the design and construction of concrete reinforced with FRP bars. American Concrete

Institute, Farmington Hills, MI.

ACI 440.2R-02: Guide for the design and construction of externally bonded FRP systems for strengthening concretestructures. American Concrete Institute, Farmington Hills, MI.

ACI 440R-96: State-of-the-art report on fiber reinforced plastic reinforcement for concrete structures. AmericanConcrete Institute, Farmington Hills, MI.

Burke, C.R., and Dolan, C.W., 2001. Flexural Design of Prestressed Concrete Beams using FRP Tendons. PCIJournal, March-April 2001, pp. 76-87.

CAN/CSA-S806-02: Design and Construction of Building components with Fibre Reinforced Polymers. CanadianStandards Association, Ottawa, Ontario, Canada, May 2004.

CAN/CSA-S06-06: The Canadian Highway Bridge Design Code (CHBDC). Canadian Standards Association, Ottawa,Ontario, Canada, November 2006.

CAN/CSA-S6.1-05, Commentary on CAN/CSA-S6-05, Canadian Highway Bridge Design Code, Canadian StandardAssociation, Toronto, Ontario, Canada, May 2005.

CAN/CSA Standard A23.2-04 Design of Concrete Structures. Canadian Standard Association, 2006.

CPCI, 1996. Design Manual 3rd

edition, Canadian Prestressed Concrete Institute, Ottawa, Canada. Dolan, C.W., and Burke, C.R., 1996. Flexural Strength and Design of FRP Prestressed Beams. Proceedings of the 2nd

International Conference on Advanced Composite Materials in Bridges and Structures, ACMBS II, El-Badry, M.M.,(Editor), Montral, Canada, August 11-14, 1996, pp. ACMBS-II, pp. 383-390.

Dolan, C.W., Hamilton, H. R., Bakis, C. E., and Nanni, A., 2000. Design Recommendations for Concrete StructuresPrestressed with FRP Tendons, Draft Final Report, University of Wyoming, Department of Civil and Architectural

Engineering Report DTFH61-96-C-00019, Laramie Wyoming, 2000.

Ehsani, M.R., Saadatmanesh, H., and Tao, S., 1995. Bond of Hooked Glass Fibre Reinforced Plastic (GFRP)Reinforcing Bars to Concrete, ACI Materials Journal, V. 92, No. 4, pp. 391-400.

Hollaway, L.C. 1989. Polymers and polymer composites in construction. Thomas Telford Ltd., London, UK. ISIS, 2001. Reinforcing Concrete Structures with Fibre Reinforced Polymers, Design Manual, ISIS-M03-00, The

Canadian Network of Centres of Excellence on Intelligent Sensing for Innovative Structures (ISIS Canada), September

2001.

Mahmoud, Z.I. and Rizkalla, S. H., 1996. Bond of CFRP Prestressing Reinforcement, Advanced Composite Materialsin Bridges and Structures (ACMBS-II), Montreal, Quebec, August, pp. 877-884.

Mahmoud, Z.I, Rizkalla, S.H., and Zaghloul, E., 1997. Transfer and Development Length of CFRP Reinforcement,Proceedings of the 1997 CSCE Annual Conference, Sherbrooke, Quebec, May, pp. 101-110.Mitsui Construction Co. LtdProduct Information on FiBRA High performance Reinforcing Fiber Rod, Japan.

Naaman, A.E., Burns, N, French, C., Gamble, W.L., and Mattock, A.H., 2002, Stresses in Unbonded PrestressingTendons at Ultimate: Recommendation, ACI Structural Journal, Vol. 99, No.4, pp. 520-531.

National Building Code of Canada 2005- Volumes 1 and 2, National Research Council of Canada, Ottawa, 2005, andUser's Guide - NBC 2005 Structural Commentaries (Part 4 of Division B), Canadian Commission on Building and Fire

Codes, National Research Council of Canada, 2005.

Quyale, T., 2005. Tensile-Flexural Behaviour of Carbon-Fibre Reinforced Polymer Prestressed Tendons Subjected toHarped Profiles, M.A.Sc. Thesis, University of Waterloo, Ontario, Canada, 156pp.

Shehata, E.F.G., 1999. Fibre-Reinforced Polymer (FRP) for Shear Reinforcement in Concrete Structures, PhD Thesis,Department of Civil and Geological Engineering, University of Manitoba, Winnipeg, Manitoba, Canada.


26/30


Section 12

Example: Flexural Design

Fig. A1. Details of beam

The pretensioned concrete beam shown in Figure A1 is

designed to carry a superimposed dead load sdw of

2.3 N/mm and a live load lw of 3.2 N/mm. Check the

adequacy of the beam with regard to flexural stresses and

strength (i.e., both service and ultimate conditions).

Assume a non-corrosive exposure condition.

Material properties:

Concrete:

65.0=c MPafc 40=

MPafE cc 284604045004500 ===

at transfer:

MPafci 30= MPafE cici 246483045004500 ===

Prestressed reinforcement (10mm CFRP Leadlinetendons):

2

6.71 mmAfrp = each2

tot4.2866.714 mmAp ==

MPaffrpu 2860= MPaEp 147000=

85.0=frp

Section properties:

2100000400250 mmAg ==

4633

103.133312

400250

12mm

bhIg =

==

mmyy bt 200==

Loads:

Self-weight:

mmNwsw /35.21081.91000

2400400250 6 ==

Service load moments:

( )mmNMsw =

= 6

2

1079.238

900035.2

( )mmNMsd =

= 6

2

1029.238

900030.2

( )mmNMl =

= 6

2

1040.328

900020.3

mmNMMMM lsdswserv =++=6

. 1048.79

Factored load moments:

( ) lsdswf MMMM 5.125.1 ++= ( )

( )

mmN

mmN

mmN

=

+

+=

6

6

6

1045.107

1040.325.1

1029.2379.2325.1

Prestressing force:

cgf

cgc

140

100

2509000

100400

(Dimensions in mm)


27/30


Select a tendon stress at transfer of frpuf4.0 , less than

the maximum permissible stress specified in Table 4.1, to

accommodate additional stress due to harping and loss

due to elastic shortening.

N

AfPpfrpui

3

tot

106.3274.28628604.0

4.0

==

=

Stresses in concrete at transfer:

At mid-span section:

MPaA

P

g

i 28.3100000

106.327 3=

=

( ) ( )MPa

I

eyPi 88.6103.1333

200140106.3276

3

=

=

( ) ( )MPa

I

yMsw 57.3103.1333

2001079.236

6

=

=

Concrete stress at extreme top fibre:

MPafMPa ci

T

37.13025.025.003.0

57.388.628.3

+=+=+


28/30


( )MPa

I

eMf

g

sd

cds 45.2103.1333

1401029.236

6

=

==

Assuming 60% relative humidity gives:

( )

( )

MPa

CR

2.35

2846045.260.510147

0.26001.077.037.1

3

2

=

=

Shrinkage of concrete for pretensioned member:

MPaRHSH 0.546005.111705.1117 === Relaxation of FRP:

321 RELRELRELREL ++=

As outlined in Section 4.4 taking:

%6.01 =REL of transfer stress

%0.22 =REL of transfer stress

03 =REL (for carbon)

giving,

( ) ( ) MPaREL 7.2928604.00%0.2%6.0 =++=

Alternatively, assuming transfer occurs 2 days after

tensioning of the tendons, and using Eqn 4.12 gives the

relaxation prior to transfer as:

( ) ( ) %33.02log345.023.0log345.023.01 =+=+= tREL and after transfer as:

%27.233.06.22 ==REL

Hence

MPaREL 8.328604.00033.01 ==

MPaREL 0.2628604.00227.02 ==

( )[ ]

N

Pe3106.294

4.2860.26542.3528604.0

=

++=

MPaA

Pf

p

epe 6.1028

4.286

106.294 3

tot

=

==

[ ] NPjack3103.3384.2868.34.3328604.0 =++=

Stress due to harping:

Angle of deviation:

o509.0180

4500

40==

The natural radius of curvature, nR , of the harped tendon

given by Equation: 4.2:

( )

( )mm

P

ErR

frp

n

2325509.0cos1103.338

147000

2

5

cos12

3

2

2

=

=

=

The stress increase due to harping tendons given byEquation 4.1:

( )MPa

R

yE

ch

frp

h 3162325

510147 3=

==

where the value of Rch is taken as the greater of the

radius of curvature of the harping saddle or the natural

radius of curvature, Rn , of the harped tendon.

Maximum stress in tendon at jacking =

MPaMPa

R

yE

A

P

ch

frp

frp

j

171628606.01497

3164.286

103.338 3

=


29/30


MPafMPa c

T

184045.045.068.8

92.1119.695.2

==


30/30


=

2

1cdCMr

mmN=

=

6

33

109.146

102

11387.034010505

mmNMmmNMfr

=>= 66 104.107109.146Strength is adequate

since fr MM 5.1< then crr MM 5.1> must be

checked. Check against crM to verify minimum

resistance.

y

I

I

Pey

A

PfM ccr

= 6.0

=

200

103.1333

103.1333

200140108.294

100000

108.294406.0

6

6

3

3

crM

mmNMcr =6102.86

and

( ) mmNMcr ==6103.1292.865.15.1

thus,

crr MM 5.1> OK

isis ec module 9 - notes (pdf)

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