Adil Al-MayahResearch Assistant

Department of Civil EngineeringUniversity of Waterloo

Ontario, Canada

Khaled A. Soudki, Ph.D., P.E.Associate Professor Department of Civil EngineeringUniversity of WaterlooOntario, Canada

This paper presents the results of laboratory testingand mathematical modeling which describe theperformance of a stainless steel wedge anchoragesystem for Carbon Fiber Reinforced Polymer(CFRP) tendons under static loading conditions. Itwas found that as the presetting load increased, thedisplacement of the rod and sleeve decreased. Afinite element model (FEM) consisting of threecontact surfaces was applied to simulate theanchor components and successfully model thedisplacement of the rod. An analytical modelbased on thick cylinder analogy was used to verifythe contact pressure on the CFRP rod determinedby FEM. A parametric study was conducted usingFEM to investigate the effects of varying thepresetting load and coefficient of friction betweenthe anchor components. It was found that theeffect of the coefficient of friction at the wedgebarrel surface was minimal in comparison to theeffect of the presetting load and coefficient offriction between the rod and sleeve.

Prestressing concrete with Fiber Reinforced Polymer(FRP) tendons is increasing in popularity becausethese composites have many attractive features com-

pared to prestressing steel. Their high strength-to-weightand stiffness-to-weight ratios, as well as corrosion resis-tance, are extremely attractive properties which structuraldesigners can exploit, in much the same way as aerospaceengineers applied FRP materials 20 years ago.

Experimental and Analytical Investigation of a Stainless Steel Anchorage for CFRP Prestressing Tendons

88 PCI JOURNAL

Alan Plumtree, Ph.D., P.E.Professor

Department of MechanicalEngineering

University of WaterlooOntario, Canada

March-April 2001 89

The use of these materials allows thedesign of new structures as well as therehabilitation or strengthening of struc-tures with post-tensioning by usingFRP rod-anchor systems. Oftentimes,repairs with prestressing steel are sus-ceptible to corrosion and environmen-tal changes not experienced by FRP.

Anchorage Systems

A problem facing the use of FRP inprestressing applications is their an-chorage.1 Different types of anchorshave been used with FRP tendons,such as a clamp,2,3,4 plug and cone,5

resin sleeve,3,6 potted resin,7 expansivecement,8 metal overlay,1 and splitwedge.5,9,8,10

Split wedge anchors which do notuse resins are preferred because oftheir compactness, ease of assembly,reusability and reliability. These mayconsist of two, four or six wedges in-serted into a barrel. Split wedge an-chors are similar to those used forsteel strands but are longer and have asoft metal sleeve encapsulating therod to prevent notching.

Unfortunately, the anchors that arecommercially available today aremade of plain carbon steel which canbe susceptible to corrosion.

The failure modes that have beenobserved using wedge anchors andFRP rods fall into two main categories:

The first is failure of the anchor sys-tem, including slip of the rod out ofthe anchor, slip of the sleeve and rodrelative to wedges, slip of the wedgesrelative to the barrel, and rupture ofthe rod inside the anchor.

The second category is failure of therod outside the anchor, thereby not in-volving the anchor.

To improve the performance of theanchor system, Shrive et al.11 at theUniversity of Calgary, as part of theISIS Canada Programme, introduced acorrosion-resistant stainless steel an-chorage system designed for 8 mm(5/16 in.), 104 kN (23.4 kips) speci-fied tensile strength, LeadlineTM CFRPtendons manufactured by Mitsubishi.12

In an attempt to improve the perfor-mance of the stainless steel anchorsystem, several developmental stageswere undertaken.

To improve anchor grippage, differ-ent interference angles between the

Fig. 1. Components of anchorage system: (a) Photographic; (b) Schematic. Note: dimensions in mm; 1 in. = 25.4 mm.

Property Rod Sleeve Wedge Barrel

(1) (2) (3) (4) (5)

Material CFRP Aluminum Stainless steel Stainless steel

Elastic modulus

-Longitudinal direction, GPa 147 68.9 200 200

-Transverse direction, GPa 10.3 68.9 200 200

Shear modulus

-Longitudinal direction, GPa 7.2 26 77 77

-Transverse direction, GPa 7.2 26 77 77

Major Poisson’s ratio 0.27 0.35 0.33 0.33

Minor Poisson’s ratio 0.02 0.35 0.33 0.33

Table 1. Mechanical properties of anchor components.

Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

(a)

(b)

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contact surfaces at the inner face of thebarrel and the wedges were tested. Asandblasted copper sleeve of 0.48 mm(0.019 in.) thickness was also used.

The main purpose of this soft metalsleeve was to produce a larger contactsurface and to minimize stress concen-trations between the tendon and thewedges. Further details of the wedge-anchor system are presented elsewhere.8

The present work presents a furtherdevelopment of this system, includingthe results of laboratory testing andmathematical modeling. Although de-scribed later, it is important to notethat following these developments,failure always occurred outside the an-chor.

Previous Experimental Studies

Most of the tests to date have con-centrated on proof testing the rod-anchor system by determining its loadcapacity.

Nanni et al.9 carried out static loadtests to failure to determine the stress-strain relationship using Carbon FiberReinforced Polymer (CFRP), GlassFiber Reinforced Polymer (GFRP),and Aramid Fiber Reinforced Polymer(AFRP) rods.

The CFRP-rod anchor system con-sisted of 8 mm (0.31 in.) diameterLeadlineTM and a two-wedge anchorwith a shredded aluminum sleevemade by Mitsubishi.12 Although someslipping in the anchor components oc-curred, it was reported that the systemwas able to carry the fracture load ofthe rod.

Hodhod and Uomoto10 conductedsimilar tests using two-wedge anchorswith 6 mm (0.24 in.) diameter CFRProds without a soft metal sleeve. Theinner faces of the wedges were rough-ened by coating them with an adhesiveand iron powder. Failure of the anchorsystem was caused by rupture of therod due to non-uniform distribution ofthe radial stresses on the rod caused bythe wedges.

Sayed-Ahmed et al.8 conducted pre-liminary static tests on an anchor sys-tem similar to that used in the presentstudy. The anchor comprised a coppersleeve, four stainless steel wedges anda stainless steel barrel. It was reportedthat the ultimate strength of the CFRProd was achieved on loading.

Fig. 2. Presetting load versus wedge displacement. Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

Fig. 3. Loading frame andtest setup.

Short-term sustained loading tests ofdifferent FRP rod-anchor systems wereconducted by Nanni et al.13 The tendonswere stressed to 65 percent of their ulti-mate tensile strength for a three-day pe-riod, and load, strain and displacementreadings were monitored during loadingand under sustained load. For wedgeanchor systems, steel wedges with orwithout a sleeve performed well in

comparison to other wedge materialssuch as aluminum and plastic.

Cyclic, as well as static tests havebeen conducted by Grace and Sayed14

on a highway bridge system. Externalpost-tensioning was implementedusing a LeadlineTM CFRP rod anchorsystem supplied by Mitsubishi. Nosignificant effect on the internal andexternal prestressing was reported.

March-April 2001 91

Sayed-Ahmed et al.8 conducted sat-isfactory cyclic proof tests on thestainless steel anchor developed at theUniversity of Calgary.

Previous Analytical Studies

Mitchell et al.14 modeled an FRProd-anchor system by using finite ele-ment analysis. The axisymmetricmodel consisted of an FRP rod bondedto the outer metal casing by a layer ofpotting material. Adhesive bonding oc-curred between the three parts of theanchor. The load was transferred fromthe FRP rod to the other parts by highshear stresses combined with relativelylow normal stresses (shear fitting).

A parametric study was conductedto determine the effect of anchorlength, modulus of elasticity of thepotting material and its thickness atthe inner end of the anchor, and thesocket thickness. Strain of the rodwithin the anchor was measured fordifferent parameters. The experimen-tal and analytical results showed thatthe anchor was unable to carry the ul-timate design load of the rod throughlack of grip or rod failure.

The anchor system under considera-tion was modeled using finite ele-ments by Sayed-Ahmed et al.8 andCampbell et al.15 Both models wereessentially similar, with the wedgebeing isotropic in one8 and orthotropicin the other.15 However, the anchorwas only partly modeled since thesleeve was not considered.

The radial and longitudinal stressesexisting in the anchor, when the ulti-mate strength of the rod was attained,were the main concern in both investi-gations. The response of the anchorsystem with time was neglected.

Significance of Research

It is evident that more detailed at-tention must be directed towards ex-amining the gripping mechanism ofFRP-wedge anchor systems.

This research strives to provide abetter understanding of the displace-ment behavior in a CFRP rod wedge-type anchor system under tensile loadfor different presetting loads.

In the analytical phase, the completeanchor system (rod, sleeve, wedge,and barrel) was modeled in order to

Fig. 4. Typical slip behavior of anchor components. Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

study the mechanical behavior of theanchor loaded in a continuous manneruntil the ultimate load level of the rodwas reached.16

The performance of the rod-anchorsystem was modeled using the finiteelement analytical technique. It ishoped that the results will provide abasis for future work in refining theanchor system.

Present Anchor SystemSince inconsistent results were re-

ported in the load-carrying capacity of

Fig. 5. Effect of presetting loads on rod displacement. Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

the stainless steel anchor which usedcopper sleeves,11 the present work at-tempted to increase the grip betweenthe rod and sleeve by first insertingfine sand between the two compo-nents. However, no significant im-provement was observed.

The focus then changed to substitut-ing aluminum for the copper sleevewith varied sleeve thicknesses. It wasfound that a 0.64 mm (0.025 in.) thickaluminum sleeve gave optimum re-sults. Failure of the rod consistentlyoccurred outside the anchor. In all

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cases, the maximum design load of therod [104 kN (23.4 kips)] was achievedwith minimum slip.

Fig. 1 shows this optimum designwhich consists of three components: astainless-steel barrel with a conicalsocket; a four-piece stainless steelconical wedge set; and a thin alu-minum sleeve placed between thewedges and the tendon. The mechani-cal properties of the different compo-nents are given in Table 1.8

The barrel was 50.8 mm (2 in.) indiameter and 80 mm (3.15 in.) long,while the larger diameter of thewedges was 25.45 mm (1.00 in.). Thecone angle in the barrel was 1.99 de-grees, 0.1 degree smaller than that ofthe wedges, so that as the wedgeswere inserted into the barrel, theygripped first on the tendon at the rearof the barrel. As the wedges seatedfurther, they gripped the sleeve alongtheir complete length. Since the softmetal sleeve was forced into the gapsbetween the wedges, there was a firmgrip on the tendon.

LABORATORY TESTSDetails of the test specimen and ex-

perimental procedure are presentedbelow and followed by the test results.

Test Specimen and Procedure

The test setup consisted of an an-chor installed at each end of an 800mm (31.50 in.) long CFRP LeadlineTM

rod. One of these was the wedge an-chor (test anchor). Sixteen specimenswere tested to investigate the behaviorof the anchorage with aluminumsleeves under tensile load.

In order to establish a practicalrange for presetting load levels, fourpresetting loads were used: 50, 65, 80,and 100 kN (11.25, 14.61, 18.0, and22.5 kips), respectively, representing48, 63, 77 and 96 percent of the designload capacity of the tendon. Duplicatetests at each presetting load were car-ried out. At the other end, a reusableclamped anchor was used to grip thetendon.

A presetting rig consisted of a hy-draulic jack attached to a steel frame.The jack assembly firmly installed thewedges into the barrel of the test an-chor at the required load. Fig. 2 shows

the presetting load versus displacementof the wedges relative to the barrel.

The equipment used to test the an-chor under static load was an electro-hydraulic servo-controlled universaltesting machine, operated under dis-placement control. A load cell to mon-itor the force was attached to the bot-tom of the actuator.

Two Linear Variable DifferentialTransducers (LVDTs) measured themovement of the rod and sleeve rela-tive to the barrel and their locationsare shown in Fig. 3.

Test Results

Fig. 4 gives a typical load versusdisplacement plot for the rod andsleeve in the anchor. The rod displace-ment showed three distinct regions.

The first started when the loadreached a threshold value of F1. Onlythe rod moved at a load-displacementrate, given by Slope1, until the appliedload reached F2. At this point, thesleeve started to slip. The rate of load-displacement of the rod increased toSlope2. Note that the load continued toincrease until the ultimate design ten-sile load of the rod was reached.

Fig. 4 shows that at 100 kN (22.5kips), the rod had moved by anamount Slip1 [2.37 mm (0.093 in.)]and the sleeve by Slip2 [1.76 mm(0.069 in.)]. The sleeve load-displace-

ment rate (Slope3) was greater thanSlope2. During this stage, the sleeveand wedges were moving together.

Fig. 5 shows the effect of presettingload on rod displacement. Four differ-ent levels of presetting load of 50, 65,80, and 100 kN (11.25, 14.61, 18.0,and 22.5 kips) were tested and the cor-responding load versus rod displace-ment are illustrated in the figure.

As the presetting load increased, therod displacement decreased signifi-cantly due to increased grip at the con-tact surface, which is a function of thecontact area and pressure. By increas-ing the presetting load, the wedgeswere forced into a progressivelysmaller diameter, causing the contactpressure to increase.

The contact area of the wedge-barreland rod-sleeve interfaces increased byincreasing the presetting load due to alarger insert length of the wedges insidethe barrel as shown in Fig 2. The contactsurface between the sleeve and rod in-creased by plastically deforming the softsleeve material and forcing it to flowinto the spiral indentations of the rod.

Fig. 6 illustrates the effect of preset-ting load on the load levels at whichthe rod and sleeve displayed initialdisplacements (F1 and F2, respec-tively). An increase in F1 and F2 wasobserved as the presetting load in-creased. By increasing the presettingload from 50 to 100 kN (11.16 to 22.5

Fig. 6. Presetting load effect on slip initiation of the rod (F1) and sleeve (F2). Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

March-April 2001 93

kips), the threshold load of the rod(F1) increased by 37 kN (8.32 kips).

A similar response for the thresholdfor sleeve movement is shown in Fig.6. As the presetting load increasedfrom 50 to 100 kN (11.16 to 22.5kips), the threshold (F2) increased by38 kN (8.55 kips).

The effect of presetting load on therod displacement at an applied load of100 kN (22.5 kips) is shown in Fig. 7.When the presetting load increasedfrom 50 to 100 kN (11.25 to 22.5kips), the rod displacement (Slip1) de-creased by 1.3 mm (0.051 in.) and thedisplacement of the sleeve (Slip2) de-creased by 0.9 mm (0.035 in.).

This is a general effect. Fig. 4 showsthat the load required to displace therod at the first stage of slip was lessthan that required to move the rod andsleeve together. Also, the sleeve re-quired a higher load than that of therod to move one unit length.

Fig. 8 shows the slipping rates ofthe rod (Slope1, Slope2) and sleeve(Slope3) for different presetting loads.Constant values of 13 and 18 kN/mm(74 and 103 kips/in.) were found forSlope1 and Slope2, respectively, forany presetting load.

However, this is not the case forSlope3. As the presetting load in-creased, the rate of slip of the sleeve(Slope3) increased. In other words, theload required to displace the sleeve

Fig 7. Presetting load effect on displacement of rod (Slip1) and sleeve (Slip2) at 100kN applied load. Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

Model Configuration

In general, there are three types ofcontact elements in finite elementmodeling: gap, slide line, and generalelements.

Gap elements are suitable in finitesliding simulations because the mainrequirement is alignment between theelements of the two contacting bodies.

Slide line contact elements are usu-ally used in simulating large amountsof slip.

General contact elements used inthis study are the simplest. While theyprovide the most realistic contact pres-sure distribution, they are also themost intensive to compute.

A total of 355 axisymmetric linearquadratic elements were employed tomodel the anchor using an ABAQUSfinite element package.

Three contact surfaces were in-cluded to simulate the interaction be-tween any two adjacent parts. Eachsurface possessed a corresponding co-efficient of friction based on the bestdescription of the experimental datagiven in Fig. 5.

The coefficient of friction betweenrod and sleeve varied in a linear man-ner from 0.16 for the first loading stepto 0.3 for the last step. The coefficientof friction of the wedge-barrel inter-face was given a constant value of

one unit length was higher for largepresetting loads than that for lowerpresetting levels.

FINITE ELEMENT MODELThis section considers the finite ele-

ment model configuration and resultsrelative to the radial and longitudinalstress distributions. The results arecompared to the experimental data.

Fig 8. Presetting load effect on displacement rate of rod Slope1, Slope2, and sleeveSlope3. Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

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0.07 due to the nature of the bodiesforming this surface.

The experimental results showedthat the sleeve and wedge moved inunison. Consequently, the coefficientof friction at their interface was high,and defined as a rough surface in ac-cordance with the ABAQUS program.

The boundary conditions duringloading were either constant or vari-able. Note that the constant boundaryconditions included preventing the rodfrom moving in a radial direction byconfining its movement to take placein the longitudinal direction. Con-versely, the barrel was prevented frommoving in the longitudinal direction(see Fig. 9a).

The variable boundary conditionssimulated the loading stages: first, bypresetting while inserting the wedgesinto the barrel (see Fig. 9b); and then, bytensile loading of the rod (see Fig. 9c).

Only one loading step was used inthe presetting process whereas 15

steps were used to simulate tensileloading. The presetting load was de-veloped through displacement of thewedges in accordance with the experi-mental data taken during the anchorset tests presented earlier (see Fig. 2).

Once the rod, sleeve, and wedgeshad been forced into the barrel, thepresetting load was released, leavingthem under pressure. Tensile loadingwas then simulated by progressivelypulling on the rod. The rate of loadingwas 0.25 mm (0.01 in.) for each of the15 steps until the ultimate design load(104 kN) of the rod was reached.

Radial Stress Distribution

It is well known that CFRP is or-thotropic and weak in the transversedirection. Thus, the radial stressshould be at its lowest value in the re-gion of high longitudinal stress to pre-vent undesirable stress concentrationsfrom developing.

Fig. 9. Finite element model: (a) Geometry; (b) Presetting process; (c) Tensile loading.

(a)

(b)

(c)

The distribution of the radial stressfor different presetting displacementswith coefficients of friction of 0.07and 0.16 at wedge-barrel, and rod-sleeve surfaces, respectively, areshown in Figs. 10(a) and (b). Again,these values were chosen based on thebest description of the experimentalresults.

Figs. 10(a) and (b) illustrate that ahigh radial pressure was setup in theregion where the wedges entered thebarrel. Before applying the presettingload, there was only one locationwhere the wedges were in contact withthe barrel due to the interference fit.

The increase in the presetting loadincreased the contact area between thewedges and barrel. This resulted in ahigher radial pressure at the first con-tact point and a lower radial pressureat the far end of the anchor.

The radial pressure decreased to-wards the core of the anchor where therod was located, indicating that the ra-dius of the wedges contributed effec-tively in transferring the radial pres-sure of the rod.

The most affected region was wherethe wedges entered the barrel, thus ex-plaining the indentations at the sur-faces of the wedges and the barrel, asobserved after testing.

Longitudinal Stress Distribution

The distribution of the longitudinalstress along the rod is an importantfactor and is shown in Figs. 11(a) and(b) for an insert distance of 8.5 mm(0.33 in.), which corresponds to a pre-setting load of 65 kN (14.61 kips). Inthis case, the coefficient of friction of0.16 at the rod-sleeve interface in-creased by 0.015 in each of the 15loading steps.

The highest stress level occurred atthe point where the rod entered the an-chor and corresponded to expected lo-cations where the stress was concen-trated. The stress decreased in the rodas the distance increased from theloaded end.

The longitudinal stress decreasedwith increased shear stress that wasgenerated by a gradual increase in thecoefficient of friction and normalstress.

March-April 2001 95

Comparison of FEM andExperimental Results

In Fig. 12(a), the experimentallymeasured rod displacement for a pre-setting load of 65 kN (14.61 kips) iscompared to the FEM description.

For this presetting load, the equiva-lent insert distance of the wedges inthe barrel was 8.5 mm (0.33 in.). Thecoefficient of friction between the rodand sleeve varied from 0.16 for thefirst loading step to 0.3 for the lastloading step, as mentioned earlier.

Also, the coefficient of friction be-tween the wedges and the barrel was0.07 which remained unchanged dur-ing the loading process. It is apparentfrom Fig. 12(a), that there is very goodcorrelation between the experimentaland numerical results.

Fig. 12(b) shows the slip of the rodusing a higher presetting load of 100kN (22.5 kips) caused by 10 mm (0.39in.) insert distance while keeping thecoefficients of friction the same asthose used for the presetting load of 65kN (14.61 kips) above.

The numerical curve remained con-sistently below the experimental plot,underestimating the load for a givendisplacement. However, the discrep-ancy was within 10 percent at most,indicating a reasonable agreement, al-though not as good as that for thelower presetting load.

It is possible that the coefficient offriction at the various presetting loadlevels increased because the amount ofdeformation of the contacting bodiesincreased with presetting load. As theapplied normal pressure on these bod-ies increased, the amount of grip in-creased accordingly due to an increasein the actual area of contact.

PARAMETRIC STUDYUSING FEM

The parameters studied include pre-setting load, coefficient of friction be-tween the wedges and barrel, as wellas that between the rod and sleeve andtheir effect on slippage of the rod.

Presetting Load

It was shown experimentally thatthe displacement of the rod decreasedas the presetting load increased due tohigher contact pressures on the sur-

Fig. 10. Radial stress distribution (MPa) with presetting distance of (a) 3 mm and (b) 9 mm. Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

Fig. 11. Longitudinal stress distribution (MPa) with rod tensile load of (a) 0.0 and (b) 2.75 mm. Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

(a)

(b)

(a)

(b)

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faces. Increasing the contact pressureled to an increase in contact shear fora given coefficient of friction, result-ing in less slip.

Fig. 13 shows the tensile load versusdisplacement of the rod for differentpresetting distances of 7.85, 8.5, 9 and10 mm (0.31, 0.33, 0.35 and 0.39 in.),representing presetting loads of 50, 65,80, and 100 kN (11.25, 14.61, 18.0,and 22.5 kips). As the presetting dis-tance increased, the load versus dis-placement curve shifted upwards. Thisresulted in less slip when the ultimatedesign load (104 kN) of the rod wasreached.

Note that the slopes of the curves, aswell as the initiation loads for slip,were similar to the experimental re-sults, i.e., increasing the presettingload decreased the sliding distance.For presetting distances of 7.85 mmand 9 mm (0.31 and 0.35 in.), numeri-cal instability occurred in the analysisbefore the load level of the other pre-setting distances was reached. Thiscaused non-convergence in the model.That is why dotted trend lines areshown in Fig.13.

Coefficient of Friction Between Wedges and Barrel

The effect of varying the wedge-bar-rel coefficient of friction between 0.03and 0.13 while fixing the presettingdistance at 8.5 mm or 0.33 in. (65 kNor 14.61 kips) and maintaining therange for the rod-sleeve coefficient offriction at 0.16 to 0.3, is shown in Fig.14. As the coefficient of friction in-creased, the load versus displacementcurve shifted down slightly.

This effect is considered less signifi-cant than that of presetting load. Theslight differences in displacement dueto the effect of different coefficients offriction resulted from inserting thewedges at different lengths into thebarrel during the loading stage. For alower coefficient of friction, less shearoccurred, which resulted in a slightlylarger displacement for a given tensileload.

Coefficient of Friction Between Rod and Sleeve

Due to deformation of the rod andparticularly the sleeve, the coefficientof friction was not constant during the

Fig. 12. Displacement of the rod with presetting load of (a) 65 kN and (b) 100 kN.Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

Fig. 13. Effect of presetting load on rod displacement Note: 1 in.= 25.4 mm, 1 kip= 4.448 kN.

(a)

(b)

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various loading stages. Incrementalchanges of the coefficient of frictionmay vary from one step to another dueto the interaction between the preset-ting distance and the contact pressureversus the coefficient of friction.However, this change was not largeenough to affect the resistance of therod to slip.

As mentioned earlier, the slippingresistance of the rod was generally afunction of the normal stress and coef-ficient of friction. Increasing the coef-ficient of friction increased the shear

resistance. Therefore, less rod dis-placement occurred as the applied ten-sile force and corresponding coeffi-cient of friction at a particular contactsurface increased, as shown in Fig. 15.

The values of the coefficient of fric-tion were chosen to accurately describethe experimental values. Accordingly,the initial values for the coefficient offriction increased progressively in fourinstances, starting from 0.1, 0.16, 0.2and 0.25, respectively, to a commonfinal value of 0.3 at the end of theloading process. It is apparent that

Fig. 14. Effect of coefficient of friction at wedge-barrel surface on rod displacement.Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

Fig. 15. Effect of coefficient of friction at rod-sleeve surface on rod displacement.Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

varying the friction at the rod-sleeveinterface had a significant effect on theload-slip mechanism.

ANALYTICAL MODEL An analytical model based on the

force fitting principle used in thickcylinder analysis was developed.

For a hollow cylinder with inner andouter diameters of (a) and (b), respec-tively, and subjected to an inner pres-sure of (pi) and outer pressure (po), theradial displacement (u) at any distance(r) can be determined using the fol-lowing equation proposed by Wang:17

In order to apply Eq. (1) to deter-mine the pressure on the particularsurface, as well as to overcome thevaried thicknesses of the wedges andbarrel, the anchor was divided intonine sections along its length.

Each section is a disk consisting offour cylinders (CFRP rod as shaft,sleeve, wedges, and barrel) as shownin Fig. 16. The contact pressure is de-termined according to the radial dis-placements of each cylinder.

The radial displacement of each an-chor component can be found usingEq. (1) as follows:

ur = f (Er, νr, p1, r)where 0 ≤ r ≤ ror (2)

us = f (Es, νs, p1, p2, r)where ris ≤ r ≤ ros (3)

uw = f (Ew, νw, p2, p3, r)where riw ≤ r ≤ row (4)

ub = f (Eb, νb, p3, p4, r)where rib ≤ r ≤ rob (5)

Four boundary conditions were ap-plied to solve these displacementequations:

ur (r = ror) = us (r = ris) (6)

us (r = ros) = uw (r = riw) (7)

uw (r = row) – ub (r = rib) = δ (8)

Eup a p b

b av r

a b p p

b av

r

i o

o i

= −−

− −

−−

+

2 2

2 2

2 2

2 2

1

11

(1)

( )

( )( )

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p4 = 0 in case of no constrainton outer face of barrel (9a)

or

ub (r = rob) = 0 when outer faceof barrel is constrained (9b)

The Maple V5 program was used tosolve Eqs. (2) to (5), allowing the con-tact pressure on the various anchorcomponents to be determined.

Comparison of Analytical andFinite Element Models

Figs. 17(a) and (b) compare the con-tact pressure distribution on the rod-sleeve interface for presetting insertsof 8.5 and 10 mm or 0.33 and 0.39 in.(65 and 100 kN or 14.61 and 22.5kips) using the analytical and finite el-ement models. It is apparent that themodels give a similar variation of con-tact pressure along the anchor.

The contact pressure increasedalong the longitudinal axis, movingfrom the loaded end to the free end ofthe anchor. This was due to the 0.1 de-gree difference between the two tapersof the wedge and barrel.

At the loaded end of the anchorwhere the rod entered the anchor, thedifference between the outer diameterof the wedges and the inner diameterof the barrel was at its lowest value.This was intended to avoid a high nor-mal pressure in the region of high lon-gitudinal tensile stress, thus avoidingstress concentrations. This can be seenin both the analytical and finite ele-ment models.

Nonetheless, there is a slight differ-ence in values between the results ofthe analytical and numerical methods.The higher contact pressures given bythe analytical method result from theuse of elastic material properties in thetheoretical model, upon which all ofthe equations were based; whereasplastic properties of the sleeve wereused in the FEM.

The theoretical model was not onlyused to validate the FEM results. Italso gave an efficient closed-form so-lution for the magnitude of the radialpressure between the CFRP rod andanchor system. This knowledge willassist the designer of an anchor inquantifying the pressure distribution

Fig 16. Analytical model.

Fig. 17. Contact pressure on rod with presetting load of (a) 65 kN, (b) 100 kN. Note: 1 in. = 25.4 mm, 1 kip = 4.448 kN.

(a)

(b)

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before a more detailed and time-con-suming analysis is carried out.

CONCLUDING REMARKS Based on the results of this investi-

gation, the following conclusions canbe drawn:

1. Using the four-wedge stainlesssteel anchor system modified by theauthors, it is possible to prestressCFRP tendons up to their maximumacceptable design load without fail-ure.

2. The test system allows the amountof slip in all anchor components, in-cluding the CFRP tendon, to be moni-tored for any given presetting load.

3. With progressively higher preset-ting loads, the amount of slip in thetendon and its sleeve decreased due toincreased contact pressure and grip atthe contact surfaces. Minimal slip oc-curred at the other interfaces. This be-havior was modeled using finite ele-ment analysis, giving good agreementwith the experimental data.

4. A parametric study showed a sim-

ilar effect. The amount of slip in thetendon decreased with presetting loadand increase in coefficient of frictionbetween the tendon and sleeve, result-ing from an increase in shear resis-tance at its interface.

5. By applying an analytical modelusing the thick cylinder approach, thecontact pressures on the surfaces weredetermined and found to be in goodagreement with the finite elementanalysis.

RECOMMENDATIONS Use of FRP composites by the pre-

stressed concrete industry in NorthAmerica has been limited partly due tothe lack of corrosion-resistant anchor-age systems.

Physical testing and numerical mod-eling show that, based on the well-established prestressing technologies,a stainless steel wedge-type anchorcan be used successfully with CFRPtendons. Such an anchor, unlike thesteel strand anchor, requires preseatingwedges to fully grip the CFRP tendon.

It is recommended that a preset-ting load in the range of 60 to 80percent of the ultimate strength ofthe tendon be applied. This loadshould not be confused with the al-lowable stresses in the tendon whichare typically 40 to 60 percent oftheir ultimate strength.

The tendon slip data presented in thepaper allow quantification of the an-chorage seating loss in post-tensionedprestressed concrete applications.

ACKNOWLEDGMENTThis work was supported by the

University of Waterloo Interdisci-plinary Grants Program.

Partial funding for the stainless steelanchors was provided by the Networkof Centres of Excellence on IntelligentSensing for Innovative Structures(ISIS Canada). This support is grate-fully acknowledged.

The authors wish to express theirgratitude to the PCI JOURNAL re-viewers for their suggestions and con-structive comments.

100 PCI JOURNAL

APPENDIX – NOTATIONur, us, = radial displacements of rod, sleeve, wedges,uw, ub and barrel, respectivelyE = modulus of elasticityEr, Es, = modulus of elasticity of rod, sleeve, wedges, Ew, Eb and barrel, respectivelyνr, νs, = Poisson’s ratio of rod, sleeve, wedges, and νw, νb barrel, respectivelyp1 = radial pressure on outer surface of rod and

inner surface of sleevep2 = radial pressure on outer surface of sleeve and

inner surface of wedges

p3 = radial pressure on outer face of wedges and inner surface of barrel

p4 = radial pressure on outer face of barrel ror = outer radius of rodris, ros = inner and outer radius of sleeveriw, row = inner and outer radius of wedgesrib, rob = inner and outer radius of barrelδ = difference between original outer radius of

wedges and matching inner radius of barrel at a specific location

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