transfer and development lengths of frp prestressing tendons - … journal... · 2018. 11. 1. ·...
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Transfer and Development Lengthsof FRP Prestressing Tendons
Zhen LuStructural DesignerCUH2APrinceton, New Jersey
Thomas E. Boothby, Ph.D., RE.Associate Professor
Department of Architectural EngineeringThe Pennsylvania State University
University Park, Pennsylvania A
Charles E. Bakis, Ph.D.Associate ProfessorDepartment of Engineering Science andMechanicsThe Pennsylvania State UniversityUniversity Park, Pennsylvania
Antonio Nanni, Ph.D., P.E.V & M Jones Professor
Department of Civil EngineeringUniversity of Missouri
Rolla, Missouri
An experimental investigation was conducted todetermine the transfer length, development length,and flexural behavior of fiber-reinforced polymer(FRP) tendons in prestressed concrete beams. Threetypes of nominally /16 in. (8 mm) diameter FRPtendons were included in the study: CarbonLeadline, Aramid Technora, and a carbon fiberreference material. Thirty beams were pretensionedusing a single FRP tendon. In addition, twelvecontrol beams were pretensioned with a seven-wiresteel strand (ST). The transfer length for FRP tendonswas reasonably well predicted by the AC! designequation, with the modification in AASHTOproviding for a minimum transfer length. The AC!equation predicts the development length veryconservatively provided the tendon rupture stress isused in place of the tendon stress at nominalcapacity. Therefore, it is proposed to modify theAC! equation to account for the larger bond stressdeveloped by the FRP tendons.
In pretensioned concrete members, transfer length is thedistance required to transmit the effective prestressingforce from the prestressing tendon to the concrete. When
a member is loaded to its ultimate flexural strength, an additional bond length beyond the transfer length is requiredto develop the tendon stress from the effective prestress tostress at nominal flexural strength. This additional bondlength is called flexural bond length, and the developmentlength is defined as the sum of the transfer length and theflexural bond length.
With the exception of cantilevers and short span members, strand transfer and development length seldom governthe design of pretensioned concrete members; however,
PCI JOURNAL84
knowledge of transfer and development lengths is essential in preventingbond slip failure of the member.
OBJECTIVES AND SCOPEOF RESEARCH
The objectives of this study are toexperimentally determine the transferand development lengths of threetypes of fiber reinforced polymer(FRP) tendons in precast, prestressedconcrete beams, and to compare theexperimental results to existing models from the literature.
In this study, 30 transfer lengthtests, 24 development length tests andnine flexure tests were done on beamsprestressed with three types of FRPtendons along with control specimensconstructed with steel strands.
The primary variable studied in thisinvestigation is the type of FRP material. Three different FRP materialswere used in the study, and are fullydescribed in the section on the experimental program.
lITERATURE REVIEWBond between reinforcement and
concrete in a structural member is theresult of three mechanisms, namely,adhesion, Hoyer’ s effect, or the wedgeaction due to transverse relaxation ofthe strand in the transfer zone, andmechanical interlocking. These distinctly different mechanisms havebeen investigated by Janney,’ Hansonand Kaar2 and by Russell and Burns,3among other researchers.
A summary of the recommended expressions for transfer and developmentlength for twisted, seven-wire steelstrand is presented in Tables 1 and 2.The nomenclature in these tables follows ACT 3l8-99, with the exceptionsgiven below.
The parameters U, and B in Tables 1and 2 are empirically determined coefficients of nominal bond stress andbond-stress/slip modulus, respectively.The quantity a, also in Table 1 and 2,is an empirically determined coefficient, which varies among tendontypes and manufacturers. The quantity
is used by several authors to represent the initial prestressing.
The quantity Kb1ave in Table 2varies for different types of beams: for
the slender beams used in this study,the denominator of this formula isunity, resulting in no change from theACT equation. Also in Table 2, thevalue of 2. increases from unity fortendons with large strains (over 1 percent) at the nominal capacity of themember.
Abdelrahman5reported transferlength data for fi in. (8 mm) diameterCFRP Leadline rods. The transferlength was estimated to be 14.2 in.(360 mm) or 46 bar diameters whentendon stress after release was 137 ksi(950 MPa) and 19.7 in. (500 mm) or64 bar diameters when the stress afterrelease was 190 ksi (1310 MPa).
Domenico6 investigated the transferlength of seven-wire carbon fibercomposite cable (CFCC). The CFCCdiameter varied from 0.5 to 0.625 in.(12.5 to 15.2 mm). The measuredtransfer length was proportional to thediameter of the CFCC strand and theprestress level, and varied from 5.5 to16.0 in. (140 to 400 mm) or 9 to 32bar diameters.
Mahmoud and Rizkalla7 studied thebond characteristics of CFRP tendonsin pretensioned concrete beams.
Table 1.Proposed equations for transferlength.
Three diameters [/16, 1/2 and 5/ in.(10.5, 12.5 and 15.2 mm)1 were considered for the CFCC strands and /L6
in. (8 mm) diameter was used forLeadline. The measured transferlength varied from 21.0 to 25.5 in.(450 to 650 mm), or 56 to 81 bar diameters for Leadline rods and from 12to 16.5 in. (300 to 425 mm), that is, 20to 40 bar diameters, for CFCC strands.in a further elaboration of this work,Mahmoud, Rizkalla and Zaghloul8present formulas for estimating thetransfer and development lengths forthese two types of FRP tendons.
Soudki, Green and Clapp9 studiedthe transfer length of /i in. (8 mm)spirally indented CFRP Leadline rods.The results were determined by measuring the strain in both the prestressing tendons and the concrete. Themeasured transfer lengths for theCFRP tendons were 26.5 to 28.5 in.(650 to 725 mm), or 80 to 90 tendondiameters.
The authors also concluded that theexisting models for steel may give unconservative transfer lengths for theCFRP tendon and that the long-termtransfer length of Leadline is similar
85
Source Equationiv
—- —
Current ACI-
AASHTO22 L, = .fseb
(AASHTO minimum 50 db)
,Zia and Mostaf&7 L = 1.3
(fct)db — 2.3
(U\ fseApsCousins, Johnston and Zi&9 L, 0.5j) +
dU
Ld5Shahawy, Issa and Batchelor2’ L =
f dRussell and Burns20 L =
f. - db ITMitchell, Cook, Khan and Tham° L =
—--—---
fMahmoud, Rizkalla and Zaghloul5 L, =
March-April 2000
Table 2. Proposed equations for development length.
to the instantaneous transfer lengthmeasured at release. In these results,only slight differences in transferlength for different prestressing levelscan be noted, and no differences werenoted between the transfer length inthe stem of a T-beam with four tendons, and in a rectangular beam with asingle tendon.
Nanni, Utsunomiya, Yonekura andTanigaki’° used concrete strain measurements and static flexural tests todetermine transfer lengths of braidedFiBRA AFRP tendons of nominal/2, and 9/ in. (8, 12, and 16 mm) diameters. The reported transfer lengthfor the tendons are approximately15.7, 17.7, and 21.6 in. (400, 450, and550 mm). Some increase in transferlength for increased prestressing forceand some decrease for multiple strandapplications can be noted. Nanni andTanigaki” reported developmentlengths of less than 33.4 in. (850mm), greater than 39.4 in. (1000 mm),
and 40.9 in. (1040 mm) for the samematerial.
Taerwe and Pallemans’2used 0.3and 0.2 in. (7.5 and 5.3 mm) diameterArapree aramid fiber rods in theirtransfer length study. They suggesteda transfer length of 16 times the nominal diameter of the rods for all of theseArapree rods.
Ehsani, Saadatmanesh and Nelson13conducted tests on three kinds ofaramid FRP tendons: Arapree 0.4 in.(10 mm), FiBRA 0.4 in. (10.4 mm)and Technora /16 in. (7.4 mm). Thetransfer and development lengths werefound to be 33 and 83 bar diametersfor FiBRA, 43 and 117 bar diametersfor Technora, and 50 and 102 bar diameters for Arapree, respectively.
Issa, Sen and Amer’4 conducted acomparative study of the transferlengths of fiberglass and twisted,seven-wire steel pretensioned members. S-2 glass epoxy tendons with /8
in. (9.5 mm) and steel strands with 1/2
in. (12.7 mm) diameter were tested.The transfer length of the fiberglasswas determined to range from 10 to 11in. (254 to 279 mm), or 28 times thenominal diameter of the tendon. Theauthors concluded that fiberglass hadbetter bond characteristics than steel,in this case, due to better adhesion andinterlock at transfer.
Based on previous studies for transfer length and development length ofFRP materials, several conclusionscan be established:
1. Transfer and development lengthsincrease in some nonlinear mannerwith tendon diameter.
2. Transfer length does not varysubstantially with time.
3. Concrete strength, in the range of5000 to 7000 psi (35 to 50 MPa), hasonly a moderate effect on the transferlength of FRP tendons.
4. Higher prestressing force resultsin slightly larger transfer and development lengths.
Source
Current Ad4AASHTO”
Equation
La = Ledi, + (fr. — ise) db
Deatherage, Burdette and Chew”
Cousins. Johnston and Zia’
L1 = + I.5(f,— Le)db
3
Shahawy. Issa and Batchelor”
(u’ ;Jfl f ,A ( ALa = 0.51 ‘ ‘
I+ ‘
± (j — .i. ) I “ —
B rd5U,:Jse
LaLdb /3 + (f5 — Le)db
Buckner’4
h #ave
Mitchell. Cook. Kahn and Tham”
L1 c/= +
(2 — Le)db3
Mahmoud, Rizkalla and Zaghloul5
L1 = O.33Jd— ( —L)d
L,d5 (i — L)dh+ ‘1) 67La
a1J°67 cxffCl
86 PCI JOURNAL
5. Surface finish greatly influencesthe bond between FRP tendons andthe concrete.
6. FRP tendons develop higher bondstresses before undergoing slip thansteel tendons.
EXPERIMENTAL PROGRAM
The experiments involved casting atotal of 42 specimens, ten for each ofthe three FRP tendon materials andtwelve for the seven-wire steel strand.All specimens contained a single tendon. Two specimens with a single tendon concentrically placed were usedto measure transfer length only (seeFig. la).
Forty rectangular specimens werecast with the tendon placed eccentrically (see Fig. lb). All specimenswere fabricated by a PCI-certified producer. The specimens in this studycontained no shear reinforcement orother confinement.
MaterialsThe concrete mix used in this pro
ject contained 750 lbs per cu yd (445kg/rn3) of Type III portland cement,131 lbs per cii yd (78 kg/rn3) of flyash, for a total water-cernentitious materials ratio of 0.36. The concrete wasdesigned for 7.4 percent entrained air,by volume. The average compressivestrength was:
•At release: 5570 psi (38.4 MPa)•At 28 days: 6420 psi (44.3 MPa)At 90 days: 6550 psi (45.2 MPa)
Prestressing
A photograph illustrating the FRPtendons used in this study is shown inFig. 2. The Leadline tendons, designated CL, are made commercially byMitsubishi Chemical, Tokyo, Japan,using the pultnusion process with carbon fibers and an epoxy resin. TheLeadline tendon surface is indentedwith a helical impression in the surface that spirals along the length of thetendon.
Technora tendons, designated AT,are made commercially by TeijinCompany, Osaka, Japan, by the pultrusion process where straight, bundled aramid fibers are impregnatedwith a vinylester resin. Technora
aramid yarns are wound spirallyaround the bundle of straight fibers toprovide a rough surface capable ofachieving adequate bond strength.
A non-commercial tendon developed especially for this investigationis designated CS. This tendon is notintended to achieve optimal resultscompared to the other materials usedin the research; however, it is ageneric, non-proprietary type of tendon that could be produced by anymanufacturer and represents a reference specimen for comparison in thisand any further studies.
As opposed to the commercial tendons used in this and other studies, theexact composition of the CS tendonhas been disclosed by the manufacturer. The tendon consists of a nominalvolume fraction of 65 percent T650carbon fibers, with a tensile strength of650 ksi (4480 MPa), and a tensilemodulus of 34,000 ksi (234 GPa).
The matrix material consists of 100parts Shell 9405 resin, 28 parts Shell9470 curing agent, five parts ASP400P filler, 0.65 parts Axel 1846 moldrelease, and 1.5 to 2 percent by weightShell 537 curing agent accelerator.
The matrix has a tensile strength of9.3 ksi (64 MPa), and a tensile modulus of 396 ksi (2.73 GPa).
The surface of this tendon is roughened by applying a cloth-like peel plyduring processing that, when removed,results in indentations to the tendon.Tendon properties are given in Table3. Manufacturer’s data given in Table3 are guaranteed values — all otherdata are mean values of three tests.
A grouted FRP single-tendon anchorage system was developed andtested.’5 The system consists of a hollow steel tube filled with expansivegrout, into which the end of the tendon is embedded. The volume expansion is delayed until after the groutpartially sets.
The resulting grip minimizes axialand shear stress concentrations. Coupling devices with thread on the outerdiameter were used to couple an FRPtendon to a conventional steel strand,which was then anchored to the hydraulic jacking system with a conventional steel wedge chuck. In this way,the same jacking system that is usedfor a conventional steel tendon canalso be used for FRP tendons.
8 feet
r3.5 in.
iE1
3.5 in.
(a) Concentric strand specimen
10 feet / 9 feet / 8 feetI
(b) Eccentric strand specimen
Fig. 1. Test specimen configuration.
Fig. 2. FRP tendons used in this study. (From top to bottom: CL, AT, CS.)
March-April 2000 87
The tendons were coiled andshipped in requested lengths. The diameters of the coils were around 7 ft(2.1 m) to avoid overstressing the tendons. Before prestressing, the tendonswere precut to required lengths[around 50 ft (17 m)] and were coiledusing cable ties to diameters that wereno smaller than the original coils.
Two grouted anchors were then castand cured for at least three days at twoends of each tendon. The tendon coils,together with the grout anchors, weretransported together to the site for prestressing. All FRP tendons werewrapped with bubble wrap and handled carefully to protect them fromscraping, kinking, notching or crushing during handling.
The three days required for the expansive grout to cure can result in inefficient use of the prestressing bedfor FRP materials; however, these anchors were applied in advance to theFRP prestressing, with the assemblyof the coupler only done in the prestressing bed. Since the couplers arelocated within the prestressing area,their use resulted in the loss of up to 5ft (1.52 m) of prestressing bed.
The jacking force at the live end ofthe bed was monitored with a pressurecell connected to the hydraulic jack.An electronic load cell was used at thedead end of one of the two prestressing lines to verify the applied force.Load at full prestress was locked
Table 3. Tendon material properties.
Note: I in. = 25.4 mn; 1 sq in. = 645 mm’; 1 ksi = 6.89 MPa.* Manufacturer’s values are guaranteed values.t Experimental values are mean values of three tests.t All specimens slipped in grips before rupture.§ Tendon is linearly elastic to rupture.
down using a steel chuck at the liveend anchor plate.
In addition to monitoring of loadduring tensioning, elongation of theFRP tendon plus steel strand and anchorages at the live end were recordedat the face of the hydraulic jack. Target load and target elongation criteriawere established for each tendon. Tensioning was stopped at the target loadcriterion. The FRP tendons werejacked to 62 to 64 percent of thestrength using the same type of anchor, determined by laboratory testing
as part of this study. Tendons were detensioned gradually by releasing thehydraulic jack.
Characteristics, including concretestrength and prestress force at variousload stages are given in Table 4. Further details of the experimental procedure are available in Lu’s thesis.’6
Transfer Length Measurement
Demec gauge readings [a mechanical measurement using metal targetsispaced on 4 in. (102 mm) centers were
Table 4. Characteristics of specimens.
Note: 1 in. = 25.4 mm; 1 ft = 305 mm; 1 psi = 6.89 kPa; 1 ksi = 6.89 MPa.
Tendon type
Nominal Manufacturer”diameter
(in.) Experiment’
CL AT CSLeadline Teclinora Reference
H-
5/16
STSteel
5/16 5/16
Manufacturer-’Area(sq in.)
Experiment
5/16
- 0.078 T0.073 0.078 0.078 —
7700Young’s Manufacturer* 21,300modulus — -—--• —
(ksi) Experiment’ 24.800
ITensile Manufacturer” 327strength
(ksi) Experiment’ 4351
29.00023.300
23.3006500
248
N/At
266 250
2741 4:,
Specimen materialCL AT
Leadline Technora
10(10)
CS
Length, ft(number of beams)
Cross section, in. x in.
Concentric (C) or Eccentric (E)(Eccentricity, in.)
Concrete strength, psiAt release (1 day)At 28 daysAt 90 days
Reference
10(8)8(2)
ST
3.5x7 3.5x7
10(10)
Steel
E
9 (9)8(1)
(1.75)
8 (2)
Prestress
E E(1.75) (1.75)
3.5 x 7 3.5 x 7 ‘ 3.5 x 3.5
580065006580
E(1.75)
625067006830
f,1 (jacking Stress) (ksi)
f, (initial prestress) (ksi)fIf, (percent)f,1/f,, (percent)
C(0)
515061006400
19818062
510063506420
153132
9162
170146
8764
190169
867689
88 PCI JOURNAL
taken for each specimen prior to release of the tendon. Considering thatthese initial readings are especiallyimportant, these measurements wererepeated at least six times by the sameoperator.
Subsequent readings were taken forall specimens at 50 percent release,100 percent release, 28 days after release (CL, AT, CS), and also 90 daysafter release (AT). The measurementsduring and after release were repeatedat least twice by the same operator.
Transfer length observations resulting from this study are based on concrete strain measured on both sides ofthe specimen at the level of the tendons. Release of the prestressingforce, which was accomplished byslow release of pressure on the jack,occurred in two stages for all specimens, 50 and 100 percent release. Thespecimens remained on the prestressing bed while concrete strains weremeasured at these two stages. At 100percent release, the tendons were cutcompletely.
The average values of measuredconcrete strain were plotted versusdistance along the length of each specimen to generate a strain profile foreach specimen at each time interval.To further reduce anomalies in thedata, the raw strain profiles weresmoothed by averaging the data overthree gauge lengths. The smoothingtechnique can be summarized by thefollowing equation:
(Strain)1 =
(Strain)11 + (Strain) + (Strain)11
3(1)
where the i, i-i, and i+ 1 measurementsproceed from one pair of Demecpoints to the next, in sequence.
Transfer lengths for each specimenwere determined by evaluating theconcrete strain profiles. The methodused in this study is as follows:
1. Plot the smoothed strain profileversus longitudinal position in thebeam.
2. Determine the average maximumstrain for the specimen by computingthe numerical average of all the strainscontained within the strain plateau.The plateau is determined by visualinspection. Calculate 95 percent of the
average maximum strain and constructa horizontal line through the data corresponding to this value.
3. The transfer length at each end ofthe beam is determined by the intersection of the 95 percent line with thesmoothed strain profile. Reported values of transfer length are the averagevalues from the two ends of the beam.The average maximum strain is computed by averaging all the strains contained on the plateau of the fully effective prestressing force. This procedureis identical to that employed byEhsani, Saadatmanesh, and Nelson13and similar to that employed by Mahmoud, Rizkalla, and Zaghloul,8whochose to use 100 percent of the average strain.
Development LengthMeasurement
The development length test is athree-point flexural test. A hydraulicjack and a hand pump were used toapply a point load at the designatedembedment length, which varied foreach test. In addition to increments ofapplied load measured using a loadcell, the end slip of the prestressingtendon was determined by measuringthe distance from a metal bracket,which is fixed on the tendon, to theend surface of the concrete specimenusing LVDTs (Linear Variable Differential Transformer). The metal bracketcan hold three LVDTs, evenly dis
tributed around a circle 120 degreesapart.
Different embedment lengths wereattained by applying load at varyingdistances from one of the supports.The test apparatus is shown in Fig. 3.
TEST RESULTSDiscussed below are the results
from the experimental determinationof transfer and development lengths.
Transfer Length Results
Five CL beams, three AT and threeCS beams were tested for transferlength. The results are summarized inTable 5. In Table 6, based on concretestrain data, the measured transfer lengthfrom the end of the beam required toachieve maximum effective prestressing force (i.e., distance to the strainplateau) is compared to the predictedtransfer lengths, which are determinedusing the equations listed in Table 1.
Transfer length values in this studywere based on the 95 percent averageplateau strain method determinedusing concrete strain results. Thetransfer length results for the CL andthe AT tendons were verified to beclose to values reported by Ehsani,Saadatmanesh, and Nelson,13 who obtained values of 17 in. (430 mm) forthe CL tendon and 12.3 in. (312 mm)for the AT tendon, using the samemeasurement method.
Fig. 3. Development length test apparatus.
March-April 2000 89
The following observations can bemade based on Table 6:• There is little change in transfer
length with time for all four materials, although it should be noted thatthe test was conducted over a relatively short time period.
• The ACI design equation is adequate in predicting transfer lengthfor the /l6 in. (8 mm) CL tendon;however, the calculated transferlength from the ACT equation isvery close to the measured transferlengths, barely leaving any safetymargin. The ACT design equation isunconservative in predicting thetransfer length for the /16 in. (8 mm)AT tendon. The measured transferlengths are 20 to 25 percent largerthan that predicted by the ACICode. The ACT design equation isunconservative in predicting thetransfer length for the /,6 in. (8 mm)CS tendon, simply because the initial prestress is smaller than that ofthe CL tendon. The measured trans
fer lengths are 25 to 28 percentlarger than that predicted by theACT Code.The equation suggested by Zia andMostafa’7 and the equation byMitchell et al.18 give smaller transferlengths than the measured values forall four materials. The equation byCousins et al.19 over-predicts transfer length for the three materials.The equation by Russell and Burns20gives larger values for all three materials. The equation by Shahawy,Issa, and Batchelor2’gives a closeprediction of transfer length for allthree materials.When applying the models to thethree tendons tested, the only variable is the prestressing force. For agiven model, the differences in predicted transfer lengths for the threematerials are only a reflection of thedifferences in prestressing forces.The lack of variation in transferlength among the materials, and theunconservative predictions of trans
fer length for some of the materialsappears to be resolved by the adoption of a minimum value of transferlength, such as in the AASHTOSpecifications.22
Development Length Results
Based on the usual assumption thatplane cross sections of a beam remainplane as bending moment is applied,the concrete strains at any loadingstage vary linearly. Using strain compatibility from the appropriate linearstrain distribution and force equilibrium from the appropriate stress distribution, flexural analysis can be donefor any loading stage.
For each of the embedment lengthsinvestigated in this study, the force inthe tendon was estimated using a simple flexural model of a prestressedconcrete beam.
Details of this procedure are givenby Lu.’6 In the cases where tendonslip was recorded, the nominal bondstress (tendon force divided bybonded surface area) decreases withincreasing embedment length, and isof maximum magnitude of 300 to 600psi (2 to 4 MPa) for fully developedtendons.
In Table 7, the measured development lengths are compared to the predicted development lengths, which aredetermined using the equations inTable 2. The further equations ofDeatherage et al.23 and Buckner24 arealso compared to the experimental results. Measured development lengthsof 58 in. (1473 mm) for the CL tendonand 34 in. (865 mm) for the AT tendon were previously reported byEhsani, Saadatmanesh, and Nelson.’3
The Cousins, Johnston, and Zia19model, and the Mahmoud, Rizkalla,and Zaghloul8models explicitly incorporate material properties, while theBuckner24 model, in increasing the development length for higher strain atnominal flexural strength implicitlyincorporates material properties.
Two values of the measured development length are reported in Table 7for each material. The first value ofdevelopment length reported is the development length determined in thetesting program. A value of calculated from the flexural model at failureis inserted into the formulas for the
Table 5. Strand transfer length results of specimens.
At 50 percent release At 100 percent release,* i fl fL — B g
Tendon type (in.) (in.) (sr) (in.) (in.) (pr)
CL — — — 10 166 091 276(Leadline)
AT 6 14.1 0.75 105 6 14.5 1.0 197(Technora)
CS 6 16.6 0.51 118 6 16.1 0.79 218(Reference)
ST 12 18.1 1.6 111 12 19.1 1.1 189(Steel)
At 28 days At 90 days
fl* I9ag P i
Tendon type (in.) (in.) (pr) (in.) (in.) (pr)
CL 10 16.1 0.75 609 — — — —
(Leadline)
T
AT 6 14.8 1.1 503 6 14.8 1.3 816(Technora) I
CS 6 16.3 0.51 446 — — — —
(Reference)
ST — — .— — — — — —
(Steel)
Note: I in. = 25.4 mm.* Number of repetitions.t Mean.
Standard deviation.
PCI JOURNAL
Table 6. Comparison of measured strand transfer length with predicted strand transfer length.
Note; 1 in. = 25.4 mm.* Published values of material parameters for steel used in calculations.
least embedment length at which aflexural failure occurred.
For the embedment lengths attainedin this study, all of the specimensfailed by tendon slip, or concretecrushing. Hence, a linear trend line
was used to predict the required development length at tendon rupture. Embedment length versus tendon force atfailure are plotted for each material,based on which the maximum development length of the material was de
termined, as shown in Figs. 4a through4d. This is reported as a maximum development length in Table 7.
Discrepancies between the measured and maximum developmentlength appear because the maximum
Table 7. Comparison of measured and predicted strand development lengths.
CL AT I cs STModel (Leadline) (Technora) (Reference) (Steel)
Measured development length (in.) 42.1 37.4 45.1 51.0
Nominal bond stress at failure (psi) 585 454 465 287
Maximum development length (in.) 43.0 44.2 45.9 46.2
Current ACT4/AASHTO22(in.) 68.5 35.6 62.1 48.5
CurrentACI4/AASHTO22(in.), using 68.5 54.6 62.1 48.5rupture strength in place off.
Proposed modifiedACI4/AASHTO22(in.) 57.6 43.9 48.4 —
Model by Cousins, Johnston and Zia’9 (in.)* 153 73.6 140 77.8
Model by Deatherage et al.23 (in.) 99.4 47.5 86.7 65.2
Model by Shahawy, Issa and Batchelorn (in.)* 68.5 35.6 62.1 48.5
Model by Buckner34 (in.) 77.7 75.4 65.7 . 58.0
Model by Mitchell, Cook, Khan and Tham (in.) 59.6 29.1 54.2 39.5
Model by Mahmoud, Rizkalla and Zaghlouls (in.) 42.7 — — —
Note: 1 in. = 25.4 mm; 1 psi = 6.89 kPa.* Published values of material parameters for steel used in calculations.
Model (units in in.)CL
(Leadline)
50 percent
Measured transfer length 100 percent
28 days
AT(Technora)
166
Cs(Reference)
14.2
ST(Steel)
16.6
14.5
90 days
16.1
Current ACI4/AASHTO22
18.2
16.0
14.8
Model by Zia and Mostafa’7
19.1
16.3
16.4/18.8
14.8
Model by Cousins, Johnston and Zia’9 *
11.8/18.8
10.7
Model by Shahawy, Issa and Batchelor2*
12.9/18.8
6.4
23.6
Model by Russell and Bums2°
15.0/18.8
9.2
18.1
19.3
Model by Mitchell. Cook and Khan’5
11.2
Model by Mahmoud, Rizkalla and ZaghlouP
24.6
13.9
21.4 18.8
15.2
17.7
13.7
17.6
19.4
17.6
9.6
_______
22.4
19.4 224
13.3
March-April 2000 91
development length is based on guaranteed values of rupture strength, orthe nominal value of the yieldstrength in the case of the ST tendons,which can be exceeded by individualspecimens.
Calculated values of the development length, using the formulas inTable 2, are also provided in Table 7.All of the models predict the development length of the AT tendon very
poorly. This is due to the exceptionally low longitudinal modulus of elasticity of this material, which results ina very slight difference between thestress at the nominal strength of themember, f, and the effective prestress f.
The approach used by Mahmoud,Rizkalla, and Zaghloul,8 of using therupture strength of the tendon inplace of addresses this issue, al
though it results in conservative estimates of the development length forFRP tendons. The developmentlength calculated by the ACT formula,with this substitution, is also shownin Table 7.
It can be noted that the nominalbond stress of the FRP tendons is considerably higher than that of the steel.The result is that the developmentlength for the FRP material is consid
Fig. 4(a). Development length test results for Leadline tendons (CL).
Fig. 4(b). Development length test results for Technora tendons (AT).
92
P=104kN
..
Embedment Length (in)
0 10 20 30 40 50120
25000
100
20000
1500060 .. —.-—---.,
10000•• 40 ——-—--
o 0I-,
20 . 5000
0 . 00 250 500 750 1000 1092 1250 1500
Embedment Length (mm)
• failed by end slip• failed in flexure
— linear (test data)
.———.---
0100
10 20
Embedment Length (in)
30 40
80
50
600
0000
a0
40
20000
•P=86kN
• failed by end slip• failed in flexure
linear (test data)
20
0
15000
10000 •
a0
0 250
5000
500 750 1000 1122 1250
Embedment Length (mm)
01500
PCI JOURNAL
erably lower than predicted by anyformula developed for steel tendons,when the rupture strength is substituted forf.
The development length can be conservatively calculated for FRP tendonsby modifying the ACI formula to reflect the larger nominal bond stress.Based on a nominal bond stress of 333psi (2.30 MPa), the ACI formula canbe modified to:
Ld = fsedb + (fr - fse)db(2)
for FRP tendons only, in which:db diameter of tendon
fr = rupture strength of tendonLe = effective prestress of tendonThis modified formula, which is also
applied in Table 7, results in closer butconservative predictions for all testsnoted in the literature review and this
study, including Ehsani, Saadatmanesh,and Nelson’s’3 finding of a development length of 58 in. (1473 mm) forin. (8 mm) diameter Leadline.
CONCLUSIONS ANDRECOMMENDATIONS
Based on the results of this investigation, the following conclusions andrecommendations can be made:
• failedbyendslip. failed in flexure
— linear (test data)
Fig. 4(c). Development length test results for non-commercial carbon/epoxy tendons (CS).
Fig. 4(d). Development length test results for steel strand (ST).
P9l.7kN
Embedment Length (in)
0 10 20 30 40 50120
25000
100
20000
8O
1500060 :
10000• 40 .
o 0
20 5000
01167’
00 250 500 750 1000 1250 1500
Embedment Length (mm)
Embedment Length (in)
0 10 20 30 40 50100
20000
80
15000
600 0
0 0o 010000 •
‘ 40
0 0
20 5000
0. 0
0 250 500 750 1000 1174 1250 1500
Embedment Length (mm)
PDsO7kN
• failedbyendslip• failed in flexure
— linear (test data)
March-April 2000 93
1. Transfer length values in thisstudy were based on the 95 percent average plateau strain method determined using concrete strain results.The transfer length results for the CLand AT tendons used in this studywere verified to be close to values reported by Ehsani, Saadatmanesh, andNelson’3 and Mahmoud, Rizkalla, andZaghloul8 using the similar measurement methods.
2. Despite differences in tendon material properties and prestressingforces, the measured transfer lengthswere virtually identical for all threeFRP materials. The steel strand had aslightly longer transfer length than theFRP tendons.
3. The transfer length predicted bythe ACT formula is in direct proportionto the effective prestress fse in the tendon; however, the results of this studyindicate that the transfer length forFRP tendons is only slightly influenced by the prestress level. Since the
fse was lower for AT and CS tendonsin this study, the transfer lengths ofthese two materials were poorly predicted by the ACI equation. Use of aformula that is solely based on tendondiameter may give better predictions,especially for materials with lower initial prestressing levels. The adoptionof a minimum value of transfer length,as given in the AASHTO Specifications,22 improves this result.
4. Despite differences in tendon material properties and prestressingforces, the maximum measured development lengths were almost equal forall three FRP materials and the steelstrand tested in this study.
5. The FRP materials consistentlyhad a nominal bond stress (pull-outforce divided by nominal surface area)over 450 psi (3.10 MPa) at their development length, considerably higherthan the nominal bond stress of steeltendons.
6. The development lengths of thethree FRP tendons were very conservatively predicted by the ACI designequation, provided that the strand nipture strength is substituted for f, thestrand stress at nominal strength.
7. A number of other models, in-eluding models developed specificallyfor FRP tendons, give wide-rangingdevelopment length results, most ofwhich are over-estimations comparedto the ACI equation. While it may appear obvious that formulas developedfor steel tendons do not give good predictions for FRP tendons, it is worthconsidering the reasons for this,namely, that the higher bond stress ofthe FRP tendons results in shorter development lengths.
8. It is recommended that a transferlength of at least 50 tendon diametersbe used for FRP tendons.
9. The interest in calculating thedevelopment length conservativelymay account for the large overestimation produced by many of the existing models, for steel as well asFRP strands; however, the existingcode philosophy appears to suggestthat an average value of the transferand development length should becalculated.
10. It is recommended that therupture strength of FRP tendons beused, rather than the stress at the
nominal flexural strength of thecross section f, in calculating theflexural bond length of FRP tendons.It is further recommended that thedevelopment length formula takeinto account the higher bond stressdeveloped by FRP tendons, so thatdevelopment length is not calculatedexcessively conservatively.
11. The experience of fabricatingthe specimens has indicated that theanchorage of the prestressing tendon is a key issue to be resolved before widespread implementation ofFRP prestressing is possible.Whereas an anchor based on the useof expansive grout will develop thestrength of the tendon effectively,the long time period required forthe grout to cure results in an inefficient use of the prestressing beds.The methods of coupling anchorsused in this study would allow theprecasting beds to be turned overquickly, and less than 2 to 3 percentof the bed would be lost due to thecoupling.
ACKNOWLEDGMENTSThis research was funded by the
Federal Highway Administrationunder Contract Number DTFH6 1-96-C-00019, monitored by Eric Munley.The assistance of New EnterpriseStone and Lime in the preparation ofthe test specimens is gratefully acknowledged. The authors also expresstheir gratitude to the five reviewersand especially to George Nasser fortheir extraordinarily careful review ofthis paper.
94 PCI JOURNAL
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17. Zia, P., and Mostafa, T., “Development Length of PrestressingStrands,” PCI JOURNAL, V. 22, No. 5, September-October,1997, pp. 54-65.
18. Mitchell, D., Cook, W. D., Khan, A. A., and Tham, T., “Influence of High Strength Concrete on Transfer and DevelopmentLength of Pretensioning Strand,” PCI JOURNAL, V. 38, No.3, May-June, 1993, pp. 52-66.
19. Cousins, T. E., Johnston, D. W., and Zia, P., “Transfer and Development Length of Epoxy Coated and Uncoated PrestressingStrands,” PCI JOURNAL, V. 35, No. 4, July-August 1990, pp.92-103.
20. Russell, B. W., and Burns, N. H., “Measured Transfer Lengthsof 0.5 and 0.6 in. Strands in Pretensioned Concrete,” PCIJOURNAL, V. 41, No. 5, September-October, 1996, pp. 44-65.
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