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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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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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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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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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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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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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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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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
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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.
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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,
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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
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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.
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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)
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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
+=+=+
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ISIS Canada Educational Module No. 10: Prestressing Concrete Structures with FRP
( )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
=
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ISIS Canada Educational Module No. 10: Prestressing Concrete Structures with FRP
MPafMPa c
T
184045.045.068.8
92.1119.695.2
==
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ISIS Canada Educational Module No. 10: Prestressing Concrete Structures with FRP
=
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