measured transfer lengths of 0.5 and 0.6 in. strands in ... · 3 ubp) transfer leng_ se fully...

Measured Transfer Lengths of0.5 and 0.6 in. Strands inPretensioned Concrete

__

—I

Bruce W. Russell, Ph.D., P.E.Assistant ProfessorSchool of Civil Engineering andEnvironmental ScienceUniversity of OklahomaNorman, Oklahoma

Ned H. Burns, Ph.D., P.E.Zarrow Centennial Professorof EngineeringDirector, Ferguson StructuralEngineering LaboratoryThe University of Texas at AustinAustin, Texas

In pretensioned concrete, transferlength is the distance required totransmit the fully effective pre

stressing force from the strand to theconcrete. Stated another way, transferlength is the length of bond from thefree end of the strand to the pointwhere the prestressing force is fullyeffective. The transfer zone is definedas the region of concrete spanned bythe transfer length.

An idealization of steel stresses is

shown in Fig. 1. Stresses in the pretensioned steel vary from zero at the freeend of the strand, and increasethroughout the transfer zone until theprestress force is fully effective. Increases in strand tension come aboutby bond stresses that restrain, or holdback, the strand. At the point of fulltransfer, the stress in the steel remainsconstant over the length. This is represented by the horizontal portion of thecurve.

Transfer lengths were measured for both 0.5 and 0.6 in. (12.7 and15.2 mm) diameter strands for a wide variety of research variablesthat included strand spacing, debonding strand, confiningreinforcement, number of strands per specimen and size and shape ofthe cross section. Overall, the test results indicate that the transferbond characteristics for 0.6 in. (15.2 mm) strands are very similar tothe bond behavior for 0.5 in. (12.7 mm) strands. Furthermore,average measured transfer lengths for both sizes of strand aremarginally predicted by current AASHTO and ACI Code provisions.These results clearly demonstrate that 0.6 in. (15.2 mm) strands canbe safely employed in pretensioned concrete members with spacingsof 2 in. (50.8 mm). However, the ranges of measured transfer lengthsclearly indicate that a significant proportion of actual measuredtransfer lengths exceed the current design recommendations of either50db or fsedb/3. Therefore, to incorporate a more consistent level ofsafety, transfer lengths should be approximated by the expression

‘se db/2.

44 PCI JOURNAL

Concrete and steel forces must be inequilibrium at every point along thelength. Tension in the steel is alwaysbalanced by equivalent compression inthe concrete. Therefore, the variationof steel strain is mirrored by the variation in concrete strain. The idealization of Fig. I is confirmed by actualstrain measurements from SpecimenFCT35O-3, shown in Fig. 2.

The increase in concrete strain ateach end of the specimen demonstrates the transfer of prestress forceinto the concrete. A transfer zone isfound at each end of every pretensioned element, evidenced by the increasing strains in the concrete. Thestrain plateau in the interior of thespecimen distinguishes the regionwhere the prestress force is fullyeffective.

CURRENT CODEPROVISIONS

Neither the “ACT Building Code Requirements for Structural Concrete(AC! 318-95)” nor the AASHTO Standard Specifications for HighwayBridges2 compel a transfer length requirement. However, both codes suggest a transfer length of 50 strand diameters, or SOdb (ACT Section 11.4.4and AASHTO Article 9.20.2.4).

This recommendation is located inthe shear provisions of each code. Section 12.9 of the ACT Commentary tothe Building Code provides a formulafor transfer length based on the effective prestressing force and strand diameter, derived from the expressionfor development length. The suggestedtransfer length is given by:

(1)

Fig. 3 shows the ACT Commentaryassumption for transfer and development of stress in the strand. Steelstress is plotted vs. the “distance fromthe free end of strand.” The transferlength is represented in the first andsteeper portion of the curve.

Variations in steel stress are represented in two sections, the “transferlength” and the “flexural bondlength.” In the flexural bond zone, thesteel stress is shown to increase be-

yond fse as strand tension increases inresponse to external loads. The term“flexural bond length” shown in Fig. 3is defined as the additional bondlength required to develop the strandtension necessary to resist externalloads. Summing the transfer lengthwith the flexural bond length gives theACI 318, Section 12.9.1 requirementsfor development length:

Ld fsedb +(f. _fse)1b

=(f2 fse}1b

Current ACI and AASHTO Codeprovisions for both the transfer lengthand development length are based on

assumed values for bond stresses.These values for bond stress are empirical and are based on transfer lengthtesting performed by Janney,3 andHanson and Kaar.4 The assumed average transfer bond stress per ACI 318can be calculated by solving equilibrium on the strand where the totalbond force must equal the effectiveprestress force:

LtubPPS =fseAps (3)

Substituting the ACT Commentary(2) expression for transfer length gives the

following expression:

(4)3 UbP)

Transfer Leng_

se

Fully Effective Prestress

Cl)0

Cl)ci)a)

C’) A.Constant strainsindicate fullyeffective prestressforce.

Increasing strains IIndicate transfer ofprestress from steel toconcrete.I

0 Lt

Fig. 1. Idealized steel stress vs. length for pretensioned strand.

Distance from freeend of strand

Lz;. 480

0

‘ 320

0

160

: :

....1 *.f Concrete Strain vs. Specimen Length

24 48 72 96 120 144 168

Specimen Length (in.)

1 J2

Fig. 2. Typical strain profile for pretensioned concrete, Specimen FCT35O-3.

September-October 1996 45

Fig. 3. Strand stress vs. length, ACI Commentary Section 1 2.9.

F I144 in.

-

LiFE- 144 in. —

Fig. 4. Details of single-strand transfer length specimens.

that is used in the ACT developmentlength expression is:

146 psi 305 lbs per in. (6)

The average flexural bond stress isless than transfer bond stresses largely

because flexural cracking occurswithin the flexural bond length anddisturbs bonding between steel andconcrete, thereby reducing bondstrength.

The ACI Commentary acknowledges other factors that may affecttransfer length, such as low slumpconcrete and the strand’s surface condition. Low slump concrete may causelonger transfer lengths if the concreteis not properly consolidated. Additionally, the importance of surface condition is recognized. Strands that areslightly rusted have been shown tohave shorter transfer lengths.”4’567’8

Conversely, strands that are lubricated demonstrate significantly longertransfer lengths. In fact, surface condition of the strand has been shown to bethe single biggest variable in estimating the transfer length of pretensionedstrand.7’9As such, the strand surfacecondition should be of primary concern for designs when transfer length iscritical to structural performance.

Concrete strength is reported as anon-factor in transfer length undercurrent design codes. Tests performedby Kaar, LaFraugh and Mass6 indicated that concrete strength did not affect the transfer length. However,more recent research suggests thatconcrete strengths do affect transferlengths.’°’’ These tests indicate thatstronger concrete results in shortertransfer lengths.

If A,,3 = 7I36rd and P = 4/3rdh,then the equation can be solved directly to obtain the average transferbond stress, Ub.

Ub = 438 psi 916 lbs per in.for 0.5 in. strand

[Authors’ Note: The authors suggestthat bond stresses be expressed interms offorce per unit length to avoidconfusion that is caused by expressing

bond stress as force per unit area. Because of the irregular geometry’ of aseven-wire strand, one is never surewhether reported bond stress is takenover a perimeter of jrd,, or4/3lrdb.]

The code treats flexural bond in asimilar manner, but its assumed aver-

(5) age value is lower by a factor of three.Average flexural bond stresses werederived empirically from flexuralbond tests.4 Using the same methoddescribed above, the empirical valuefor the average flexural bond stress, uf,

TRANSFER LENGTH: ITSIMPORTANCE AND USE

Transfer length is a structural requirement only in that the transfer ofprestressing force is essential to maintain the integrity of the structure.However, small variations in transferlength will not normally control thedesign or alter the performance of pretensioned concrete structures. Consequently, an exact value for transferlength may not be necessary to designand build safe concrete structures.

AASHTO and ACT suggest a trans

Transfer Flexural Bond Length — (fps - fse)d bLength00

L= seti --

Cl,

.

0

/ PS

Distance from freeend of strand

Ld, Development Length = (f5— fse)db

A

ElevationFC15O-11 and 12FC16O-11 and 12

r Debonding A

181fl Section A

Elevation

DC15O-l3andl4DC16O-l3andl4

46 PCI JOURNAL

Fzzd1921n.

Fig. 5. Details of fully bonded three-strand transfer lengthspecimens.

A

288in. ‘I

288 In.

Fig. 6. Details of debonded three-strand transfer lengthspecimens.

cause anchorage failure of the strand.Flexural tests demonstrate that whenanchorage failure occurs, not only isthe concrete contribution to shearstrength lost, but the tension requiredfrom prestressing strand is also lost. Asimple truss model for shear demonstrates that loss of the bottom tensionchord will result in a shear failure ofthe structure. Consequently, currentcode provisions for shear may not preclude bond/shear failures in some pretensioned members. This behavior isdiscussed in greater detail in Ref. 12.

Tests performed at the University ofTexas at Austin’2 and at the Universityof Oklahoma’3demonstrate that transfer length is very important in accurately predicting strand developmentfailures. In the ultimate limit state forhighway girders, both the flexural capacity and shear capacity of pretensioned beams are affected by thetransfer length.

Testing consistently demonstratesthat if a crack propagates through ornear the transfer zone of a pretensioned strand, then that crack can beexpected to generate general bondslip. Because either flexural crackingor shear cracking can occur in thetransfer zone of a strand, it is important to predict and/or prevent bothtypes of cracks within the transferzone. Therefore, to prevent crackingwithin the transfer zone, a reliabletransfer length is important to accurately predict cracking loads and thelocation of cracking.

In summary, transfer length hasbeen shown to significantly affectstructural behavior in many designcases, indicated by testing where theinteraction between cracking throughor near the transfer zone caused failureof strand anchorage. Therefore, it isimportant to understand the designcases where transfer length can controlbehavior, and to adjust structural design and detailing accordingly.

fer length of 50 strand diameters(SOdb). They also recommend the assumption that the effective prestressforce varies linearly from zero at thefree end of the strand to the maximumprestress force over the transferlength. These suggestions are provided

so that the designer can calculate theconcrete’s contribution to shearstrength, l/, which is, in current design, either the web cracking shear(V,) or inclined cracking shear (Vs).

One problem with this approach isthat shear cracking has been shown to

TRANSFER LENGTH TESTSTransfer lengths were measured on

a wide variety of research variablesand on different sizes and types ofcross sections. The variables included:

1. Number of strands (1, 3, 4, 5,and 8)

A

Plan

Section A

P0350. 1 and 2FCT35O -3 4P0360 -1 and 2FCT36O -3 and 4

Section A

FC362-11FOT 362- 12PC 362 -13

6[f3

Transverse ReInforcement#3 bars @4 In C-C.FCT series spedmens

—zp---Elevation00360-5 and 600360-5 and 6007360-7

Elevation00360-SOCT 360-10

Section A

Details:

Transverse Reinforcement#3 bars @ 4 In C-C.DOT series specimens


Table 1. Key to specimen numberingsystem (Example FCT36O-4).

were constructed with concentric prestressing in rectangular transfer lengthprisms. The remaining 12 specimenswere built as scale model AASHTOtype beams with four, five, or eightstrands.

Figs. 4 through 8 show the designdetails of the test specimens. Fig. 4 illustrates the single-strand specimens,Figs. 5 and 6 depict the three-strandspecimens, Fig. 7 shows the five-strand specimens and Fig. 8 illustratesthe details of the AASHTO-Typebeam specimens. Each specimen isnumbered by a code that identifies theresearch variables and design characteristics of each specimen. The specimen numbering system is explainedby the example given in Table 1.

Instrumentation

Fig. 8. Details of AASHTO-type beams.

2. Size of strand [0.5 and 0.6 in.(12.7 and 15.2 mm) diameter]

3. Debonding (fully bonded ordebonded strands)

4. Confining reinforcement (with orwithout)

5. Size and shape of the cross section

The number of specimens and thevariables included in the testing represent one of the largest bodies of transfer length data taken from a single research project. Altogether, transferlengths were measured on each end of44 specimens. Of these specimens, 32

Primarily, transfer lengths were determined by measuring concrete surface strains along the length of eachspecimen. The transfer length is defined as the distance from the end of amember to the point where the prestress force is fully effective. By measuring the concrete strains and plottingthe strains with respect to length,transfer length can be determined fromthe resulting strain profile. These datawere collected:

1. Strains on the outside surface ofthe concrete

2. End slips3. Electrical Resistance Strain Gauges

(ERSGs) attached to the strand wires

A

— 192in.

F = Fully bonded (D = Some strands are

debonded)

C = Rectangular cross sectionA = 22 in. deep AASHTO-type beam

B 23.5 in. deep AASHTO-type beam

T = Transverse reinforcement is included

(if transverse reinforcement is not

included, T does not appear)

3 = Number of prestressing strands

6 = 0.6 in. diameter strands (5 = 0.5 in.

diameter strands)

0 2 in. strand spacing (2 = 2.25 in. strand

spacing)

4 = Number of the specimen in a particular

series

ElevationFC 550-1 and 3FCT 550 -2FC 560- 1 and 3FCT 560-2

TransverseReinforcement inFCT specimens#3 Bars @ 4” O.C.

Note: tin. = 25.4 mm.

Section A

Fig. 7. Details of five-strand transfer length specimens.

FULLY BONDED GIRDERS

FA 550 -1 thru 4FA460-1 thru6

DEBONDED GIRDERS

DB 850-5 and 6

48 PCI JOURNAL

4. Visual inspection of the specimens

Concrete strains were measuredwith detachable mechanical straingauges (DEMEC° gauges), used inconjunction with DEMEC© targetpoints. Essentially, this gauge measures the change in length betweentargets. The gauge and targets areshown in Fig. 9. The gauges used inthis research were manufactured byHayes Manufacturing Company in theUnited Kingdom. The gauges provedto be accurate within 20 to 30 micro-strains (±20 to ±30 x 106 in./in.). Thegauge length was 200 mm (7.87 in.).

Electrical Resistance Strain Gauges(ERSGs) were mounted on the prestressing strands before the concretewas cast. Ideally, the change in strainover the strand’s length would measuretransfer length. However, the ERSGsproved to be unreliable for several reasons. First, each wire of the seven-wirestrand experiences a slightly differentstrain condition.1°As the strand is detensioned and relative displacementsbetween the strand and concrete takeplace, relative displacements betweenwires are also probable.

Secondly, a large percentage of thegauges in the transfer zone were destroyed at transfer. Either the changesin strain exceeded the capacity of theERSG or the relative displacement between the steel and concrete destroyedthe gauge. Thirdly, the ERSG’s presence on the strand may interfere withbond, at least locally. The adverse effect of too many ERSGs mounted on astrand would prejudice the test result.

Lastly, the gauges proved difficultto protect during casting because theyare susceptible to damage from vibration and/or moisture while casting theconcrete. All of these factors compound to render ERSGs ineffective inmeasuring transfer length of pretensioned strand.

Strand end slips were also measured. In earlier tests on single-strandspecimens, a dial gauge was clampedto the strand at the end of the specimen to measure the amount of strandthat slipped into the concrete upon release of the pretensioning force. However, release of the strands proved tobe too violent and several dial gaugeswere damaged. End slips were then

measured by placing a tape marker onthe strand, and measuring the distancethe tape slipped toward the concreteupon release of the strand. These measurements were made with a steel rule.Measurements with this method wereaccurate to about ±1/32 in. (±0.8 mm).

Test Procedure

Test procedures were adopted toduplicate actual pretensioned concrete plant construction as much aspossible. Accordingly, procedures forthe fabrication of the specimens followed industry standards for plantconstruction.

The procedures for fabrication andtesting can be summarized by a fewsimple steps:

1. Stress the prestressing steel to 75percent about 202.5 ksi (1396MPa)

2. Place the mild steel reinforcement

3. Set the forms4. Cast the concrete5. Cure the concrete (approximately

48 hours)6. Remove the formwork7. Take initial measurements8. Detension the strands (by flame

cutting)9. Take final measurements (The

difference between initial and finalgauge measurements produced theconcrete strains that are plotted along

the length of each specimen. Fromthese strain plots, the transfer lengthsare determined.)

Strands were tensioned using an hydraulic actuator and an electric hydraulic pump. Hydraulic pressure wascontinuously monitored as a measureof strand tension. Strands were initially tensioned to approximately1600 lbs (7.11 kN) of tension, andERSGs were attached to the strands intheir proper locations. Strands werethen tensioned incrementally until thecorrect initial prestress was reached.

Strand elongations were also measured on all strands as a check againstthe hydraulic pressure. Strand elongations and pretension stresses are listedin Tables 2 and 3. Elongations weremeasured over a gauge length of about71.5 ft (21.8 m). Some small variations in initial strand tension are noted.However, the variation in the transferlength data exceeds the differencesthat possibly result from variation inpretension stress. The differences instrand tension do not significantly affect the test results.

After the strands were tensioned, themild steel reinforcement was tied inplace. Debonding material, if required,was placed on the strands. Concretewas cast into wooden forms. Duringcasting, the concrete was internally vibrated to ensure proper consolidation.

Strand tension was released approximately 48 hours after casting, with


Table 2. Transfer length data for 0.5 in. diameter, fully bonded strands.

Strand stress Concrete strengths Transfer lengths End slips-

- F ---- - —

Elongation fqtM f f’ North end South end North end South endSpecimen (in.) (ksi) (psi) (psi) (in.) (in.) (in.) (in.)

FCI5O-I! - 5.933 195 671027.0 34.0 0.125 0.125

FCI5O-12 5.933 195 4480 6710 28.5 28.0 0.125 0.125

FC350-l 6.026 198 4320 6630 32.5 27.5 — —

FC350-2 6.026 198 4320 1 6630 — 27.5 — 27.5 — —

FCT35O-3 - 6.026 198 — 4320 6630 — 30.5 30.0 — —

FCT35O-4 6.026 198 4320 6630 29.0 32.0 — —

DC350-5 5.941 195_— 4200L 6250 26.5 28.0 0.063 0.063

DC350-6 5.941 195 4200 6250 28.5 30.5 0.063 0.063

FC550-l 5.929 195 3850 5400 39.5 36.5 0.031 0.031

-----FCT55O-2 5.929 195 3850 - - 5400 36.0 39.5 — —

FC550-3 5.929 195 3850 5400 33.0 44.0 — —

FA550- * 5.976 196 4640 51 10 18.0 16.0 0.075 —

FA550-2’ 5.976 196 4640 5110 20.5 21.0 0.088 — -

FA5503* 5.976 196 f 4040 5280 21.5 22.0 0.056 0.063

FA5504* 5.976 196 4040 5280 21.0 21.0 0.0811 0.069

DB8505* 5.761 193 5580 7220 30.5 44.0 0.125 0.176

DB8506* 5.865 196 5150 6880 36.5 33.5 0.250 0.125

Average 195 28.6 30.3

Note 1 in. = 25.4 mm; 1000 psi = 6.895 MPa.* AASHTO-type beams.t f, strand tensile stress prior to release.

E = 28,200 ksi for Specimens FC15O, FC350, DC350, FC550 and FA550.E = 28,700 ksi for Specimens FA550 and 08850.

§ Elongations were measured over 71.5 ft gauge length.

few exceptions. Factors such as student work schedules precluded the release of prestressing within 24 hours.In only one casting series, release wasperformed on the third day because oflow concrete strength. The timing ofthe release was held as an importantparameter because of its importance inthe pretensioned concrete industry. Intypical precast concrete plants, quickturnarounds are driven by an extremely competitive marketplace.Therefore, the most important concrete parameter is the strength at release. Conversely, concrete strengthsat 28 days are not usually critical.Concrete strengths at release and at 28days are listed in Tables 2 and 3.

Two different release methods wereused to detension the strands. Usingone method, the strands were flame cutat full tension in order to create a worstcase for release of the prestressingforce. Several past researchers hadnoted that transfer lengths on the “cut”end were much longer than transferlengths on the “dead” end.56’5However,

when the initial single-strand specimens (not reported in this paper) wereflame cut at full tension, moderatedamage was inflicted on some of thespecimens. Additionally, the datashowed relatively wide variation, raising doubts about the release procedure.

With the testing of the multiplestrand rectangular specimens, a moderated flame cutting release procedurewas adopted. Instead of flame cuttingat full tension, the strands were detensioned gradually to about 70 percentof their full pretension, and then flamecut. The moderated flame cuttingmethod was employed on the FC1,FC3, DC3 and FC5 series specimens.

The larger AASHTO-type beamcross sections were flame cut at 100percent tension without any detensioning beforehand. The specimens thatwere flame cut at 100 percent tensioninclude the FA550, FA460 and theDB850 series specimens. Interestingly,the moderated method resulted intransfer lengths that closely matchedthe transfer lengths that were measured

on larger specimens where strandswere cut at 100 percent tension.

The moderated flame cuttingmethod is justified when consideringthe damage caused at strand release toa small cross section when comparedto the damage caused to a large crosssection. Because of their larger massand multiple strands, large cross sections possess greater ability to absorband distribute the energy at releasethan small cross sections. Furthermore, larger cross sections usuallycontain a greater number of strandsthat are flame cut one at a time.

The progressive release of each additional strand increases the overallprecompression of the pretensionedmember, and the effect imprOves therelease conditions for members withmultiple strands over smaller crosssections with only a few strands. Theconclusion from this argument is thatlarger specimens with multiple strandsshould suffer less cumulative damageat release than smaller specimens(with fewer strands). As a result,

50 PCI JOURNAL

Table 3. Transfer length data for 0.6 in. diameter, fully bonded strands.

Strand stress [ Concrete strengths Transfer lengths End slips

Elongation f’ North end South end I North end South endSpecimen (in.) (ksi) (psi) (psi) (in.) (in.) (in.) (in.)

FCl60-11 5.882 195 50 5400.—

— I—

FC16O-12 5.882 195 3850 5400 48.0 46.0 0.031 0.063

FC360-1 5.880 195 4200 6250 42.0 40.5 0.094 0.135

FC360-2 5.880 195 4200 6250 37.0 48.0 0.094 0.156

FCT36O-3 — 5.880 195 4200 6250 39.5 45.5 0.073 0.135

FCT36O-4 5.818 193 4790 7300 50.5 42.0 0.146 0.115

DC360-5 5.901 196 4790 7300 42.0 36.0 0.094 0.125

DC360 6 5901 1964790 7300 345 410 0125 0 125

DCT36O-7 5.818 193 4790 7300 40.5 34.5 0.156 0.109

DC3609** 5.943 197 4760 7530 —. — — —

-3-- —-DCT36010** 5.943 1974760 7530— j_— — —

FC362-11 5.464 182 4760 7530 46.0 44.0 0.125 0.146

FCT362-12 5.464 182 4760 7530 44.0 42.0 0.125 0.146- —---------- -------- -------- —

FC362-13 5.464 182 4760 7530 44.0 40.0 0.135 0.146

FC560-1 5.865 195 4480 6600 45.5 47.0 0.163 0.156

FCT56O-2 5.865 - 195 4480 6600 48.0 51.5 0.169 0.144 —

FC560-3 5.865 195 4480 6600 48.0 48.0 0.169 0.150

FA4601* 5.867 195 4880 6360 29.5 37.0 0.102 0.094

FA460-25 5.945 198 4460 6570 34.0 37.0 — . —

FA4603* 5.945 198 4460 6570 33.0 32.5 — —

FA460-45 5.995 199 4840 6460 27.5 28.5 0.125 0.133

FA4605* 6.219 207 4660 7020 31.5 31.0 0.125 0.117

FA4606* 6.219 207 4660 7440 31.5 31.0 0.117 0.086

Average 195 39.8 40.2

Note: 1 in. = 25.4 mm; 1000 psi = 6.895 MPa.* AASHTO-type beams.t f’,j = strand tensile stress prior to release.

E = 28,500 ksi for all 0.6 in. strands.§ Elongations were measured over 71.5 ft gauge length.

Specimens contained two debonded strands with a debond length of 50 in. (1.27 m) and one fully bonded strand; the transfer lengths of fully bonded strands were notdiscernible from the data.

shorter transfer lengths could be expected for larger cross sections.

Before release, initial measurementswere taken. The initial measurementsincluded electrical resistance straingauges, initial strain readings on theexternal faces of the concrete, and theinitial end slip readings. After release,these measurements were repeated.Strains in the concrete and steel aregiven by the difference between initialand final readings from the strain data.Strand end slip is also given by thedifference between the initial and finalreadings.

To minimize strain reading errors, aspecific procedure for obtaining strainmeasurements was adopted. All strainreadings were taken by teams of two

persons. Each person would take measurements independently of the other.Once the measurements were taken,readings were compared. If the readings from the two individuals differedby more than 0.000032 in./in., measurements were retaken until the difference was resolved. Strain measurements from the two individuals werethen averaged together with the average measurements from the oppositeside of each specimen. In effect, the“bare” strain measurements are actually the average of four sets of readings, collected by two individualsfrom both sides of each specimen.

Measurement of concrete strainswith the strain gauges proved to be aneffective and reliable method to mea

sure transfer length. Strain measurements were taken on the outside surface of the concrete along both sidesof the specimen. By averaging strainreadings from both sides of the specimen, the effects from eccentric prestressing were negated. The repeatability and reliability of the strainmeasurements was proven over manydifferent trials with several differentstudent researchers.

DATA ANAlYSISThe strain profile taken from Speci

men FCT35O-3 is illustrated in Fig. 2where measured concrete strains areplotted vs. the length of the specimen.These strains are labeled “bare strains”


although each strain profile is constructed from the average readings offour sets of strain measurements: tworesearch assistants by two sides of eachspecimen. To further reduce anomaliesin the data, the “bare” strain profileswere smoothed by averaging the dataover three gauge lengths. Fig. 10 illustrates the same strain profile of Fig. 2,but with smoothed values. Thesmoothing technique can be summarized by the following equation:

(Strain) +(Strain) +(Strain)(Strain) =

Determination of Transfer Length:The 95 Percent Average MaximumStrain Method (95 percent AMS)

Transfer lengths for each specimenwere determined by evaluating theconcrete strain profiles. The methodused has been labeled the “95 PercentAverage Maximum Strain” methodand was conceived by personnel fromthis research project.1214 Its executionis very simple:

1. Plot the “smoothed” strain profile.

2. Determine the “Average MaximumStrain” for the specimen by computing

(7) the numerical average of all the strains

contained within the strain plateau of thefully effective prestress force.

3. Calculate 95 percent of the “Average Maximum Strain” and constructa line corresponding to this value.

4. Transfer length is determined bythe intersection of the 95 percent linewith the “smoothed” strain profile.

This procedure is illustrated inFig. 11 for Specimen FC350-2. Theaverage maximum strain is computedby averaging all the strains containedon or near the plateau of the fully effective prestress force. The averagemay include all of the points above the95 percent line, but generally, only thepoints clearly within the strain plateauare included in the average.

The method gives a transfer lengthvalue that is free from arbitrary interpretation because the “Average Maximum Strain” will not change significantly if one or two data points areeither included or excluded from theaverage. Current variations in analysismethods leave data open to arbitraryinterpretation. Its “inherent objectivity” is the major advantage derived byusing the “95 percent AMS” method.

On the other hand, this method hasdrawn criticism because it does notuse the fully effective concrete strainto determine the transfer length.Precedent does exist for using 95 percent of the maximum stress or strain.Kaar and Hanson used 95 percent ofthe maximum strain in their transferand development length study for pretensioned concrete railroad ties.8

Overall, the 95 Percent AverageMaximum Strain (95 percent AMS)method represents an accurate valuefor determining the transfer length. Ifon the one hand, the reported transferlengths are too short because only 95percent of the maximum strain is usedto define transfer length, then it mustalso be recognized that the use of mechanical strain gauges combined withthe technique of “smoothing” the dataartificially lengthens the measuredtransfer lengths. Additionally, if 100percent of the average maximum strain(100 percent AMS) is employed, itcould prove difficult to determine anexact intersection between the strainprofile and the 100 percent AMS because the strain profile can approachthe 100 percent AMS asymptotically.

Fig. 10. Strain profile of “smoothed” strains, Specimen FCT35O-3.

480

Lt 27.5 in.1 Lt= 27.5 in

C

.90

c

320

160

“T.[_:;;;E .

• Max. Strain

Concrete Strain vs. Specimen Length

U — ——

24 48 72 96 120

Spedmen Length (in.)

Fig. 11. 95 percent average maximum strain method.

1

3

52 PCI JOURNAL

MEASURED STRANDTRANSFER LENGTHS

All reported measured transferlengths were obtained using the “95percent AMS” method. Fig. 12 illustrates the strain profile for SpecimenFCT350-3, containing three 0.5 in.(12.7 mm) diameter strands that wereenclosed within confining reinforcement. The transfer lengths on bothends of Specimen FCT35O-3 weremeasured at about 30 in. (762 mm).For specimens with fully bondedstrands, the transfer length at each endof the specimen is evidenced by theascending and descending portions ofthe strain profile. Strain profiles for allof the specimens are included in Appendix A of Ref. 12.

Fig. 13 depicts the strain profile forSpecimen FC362-13. This specimencontained three 0.6 in. (15.2 mm)strands spaced at 2.25 in. (57 mm).The transfer lengths measured onSpecimen FC362-13 were 44 and 40in. (1.118 and 1.016 m). TypicaLly, 0.6in. (15.2 mm) strands required longertransfer lengths than 0.5 in. (12.7 mm)strands.

Fig. 14 illustrates concrete strainstaken from Specimen DC350-5, wherethe middle of three strands wasdebonded for a distance of 70 in. (1.78m). The strain profile clearly depictsfour separate and distinct transferzones, two at each end. Transfer of thetwo fully bonded strands are represented by the initial transfer zone ateach end. An intermediate plateau occurs between the transfer zone of thetwo fully bonded strands and thetransfer zone of the single debondedstrand. This clearly demonstrates thatblanketing effectively eliminated bondbetween the prestressing strand andthe concrete. Also, note that the slopein the fully bonded transfer zone issteeper than the slope of the debondedstrand, corroborating two fully bondedstrands vs. a single debonded strand.

Measured transfer lengths are reported in Tables 2 through 6. Table2 lists the measured transfer length for0.5 in. (12.7 mm) diameter strands,fully bonded from the end of the specimen. Table 2 also includes data fromthe FA550 and DB850 AASHTO-typebeams whose strands were flame cut

at 100 percent tension. For specimenslabeled “DC”, these data refer to measured transfer lengths on the fullybonded strands, even though the specimen may have contained one or moredebonded strands.

Measured transfer lengths on specimens containing 0.6 in. (15.2 mm)strands, fully bonded from the end ofthe member, are listed in Table 3.Transfer lengths are also reportedfor the specimens in the FA460,AASHTO-type beam series that wereflame cut at 100 percent tension.

Table 4 lists the transfer lengthsmeasured for strands that weredebonded, or blanketed. These strandswere debonded a distance of 8 in. (203mm) in the DC 150 and DC 160 series,70 or 50 in. (1.78 or 1.27 m) in theDC350/DC360 series, and 78 in. (1.98m) in the DB850 series.

Strand end slips were also measuredat each end of each transfer lengthspecimen. End slips are also reportedin Tables 2 and 3. The reported endslip values are derived from the average value of end slip measured for all


Fig. 12. Strain profile and transfer length for Specimen FCT35O-3.

C

C

0

C

CI


Fig. 13. Strain profile and transfer length for Specimen FC362-1 3.


fully bonded strands. End slips on0.5 in. (12.7 mm) diameter strandsranged from 0.031 to 0.25 in. (0.8 to6.4 mm), although end slips greaterthan 0.125 in. (3.2 mm) were uncommon. For 0.6 in. (15.2 mm) diameterstrands, measured end slips rangedfrom 0.03 1 to 0.25 in. (0.8 to 6.4mm), but most of the end slip valueswere in the range of 0.09 to 0.16 in.(2.3 to 4.1 mm).

Strand end slips were also measuredon debonded strands, and generally,these strand slips were much greater

than end slips measured on fullybonded strands. The larger end slipson debonded strand suggest that theprestressing strand was unrestrainedover the length of debonding.

DISCUSSION OFTEST RESULTS

Discussed below are the effects ofstrand diameter, cross section size andstrand spacing on strand transferlength. Also discussed are transferlengths for debonded strands, confin

ing reinforcement, strand surface condition, strand end slip and comparisons with other research data.

Transfer Length vs.

Strand Diameter

The measured transfer lengths forfully bonded 0.5 in. (12.7 mm) diameter strands are summarized by the histogram in Fig. 15. The histogramcharts the incidence of measuredtransfer lengths by plotting the transferlength vs. the number of ends measured for specific transfer length values. Measured transfer lengths aregrouped in ranges of 4 in. (102 mm).For example, the histogram in Fig. 15illustrates that 11 specimen ends hadmeasured transfer lengths of 28.0 ±2.0in. (711 ±51 mm), and the incidenceof measured transfer lengths between30.0 and 34.0 in. (762 and 864 mm)was eight.

For fully bonded 0.5 in. (12.7 mm)diameter strands, the average measured transfer length was 29.5 in. (749mm) with a standard deviation of 6.85in. (174 mm), or 24.0 percent. The average transfer length and the standarddeviation are indicated on the plot.Transfer lengths were measured on atotal of 34 ends of specimens containing fully bonded 0.5 in. (12.7 mm)strands.

The histogram in Fig. 16 illustratesthe incidence of measured transferlengths for fully bonded, 0.6 in. (15.2mm) diameter strands. These data include transfer lengths measured oneach end of 19 specimens for 38 measurements. The average transfer lengthfor 0.6 in. (15.2 mm) strands was 40.0in. (1.02 m) with a standard deviationof 6.80 in. (171 mm), or 17.0 percent.

Clearly, the measured transferlengths for 0.6 in. (15.2 mm) diameterstrand are longer than those for 0.5 in.(12.7 mm) strand. These data reinforcetransfer length as a function of stranddiameter.

The current expressions of eitherSOdb or fsedb/ 3 suggest that transferlength varies proportionately withstrand diameter. The linear relationship between the transfer length andstrand diameter is also supported bythe simplified bond model wheretransfer length is proportional to the

0

Ici

640 11111111 -- ii I II

Lt=22in. Lt=20.51fl.

480 ‘‘‘‘ - -I

Lt=26.5in. iT’ —95%Ave. L=28 ifl.

320 : : ...

7 DC350-5:)‘ Middle Strand Debonded

160-—--—-___Debonded

nj—————— 111111111124 48 72 96 120144168192

Specimen Length (in.)2 6 240 2 2 8

Fig. 14. Strain profile and transfer length for DC350-5, with debonded strand.

Table 4. Transfer lengths for debonded strands.

Strand size Specimen North end (in.) South end (in.)

DC15O-13 23.0 23.5

DC15O-14 27.0 17.0

DC350-5 22.0 20.50.5 in. strand ——

DC350-6 30.0 26.5

DB850-5 35.5 30.0

DB850-6 25.5 29.0

._______ Average transfer length: debonded 0.5 in. diameter strands = 25.8 in. —

DC16013 31.5

DC16014 375 375

DC3605 315 200

0.6in.strand DC360-6 28.0 21.0

DCT36O-7 29.5 26.5

DC360-9 32.0 26.5

DCT36O 10 31 5 410

Average transfer length: debonded 0.6 in. diameter strands = 32.7 in.

Note: 1 in. = 25.4 mm.

54 PCI JOURNAL

ratio of strand area to strand perimeter,Ap/Ppc. This ratio is a linear functionof db.

The histogram in Fig. 17 normalizesand plots all 74 transfer lengths by thestrand diameter. By normalizing 0.5and 0.6 in. (12.7 and 15.2 mm) stranddiameter data, 74 transfer length measurements are compared on the samehistogram. The transfer lengths of0.5 in. (12.7 mm) strand are shownwith the solid bars and the transferlengths of 0.6 in. (15.2 mm) strand areindicated by the hatched bars. For alldata, the average transfer length isgiven by 63.ldb with a standard deviation ofl3.ldb, or 20.8 percent.

However, when the transfer lengthsof 0.5 in. (12.7 mm) strand are compared to the transfer lengths of 0.6 in.(15.2 mm) strands, the data indicatethat the transfer lengths cannot be normalized by the strand diameter. Inother words, these data demonstratethat the measured transfer length ofpretensioned strands is not directlyproportional to the strand diameter.Whereas the ratio of the strand diameters would predict only a 20 percentincrease in transfer lengths for 0.6 in.(15.2 mm) strands compared to 0.5 in.(12.7 mm) strands, these data indicatethat the ratio of measured transferlengths is greater than 1.2. The actualratio of the average transfer lengthsfor 0.6 in. (15.2 mm) strands compared to 0.5 in. (12.7 mm) strandsis 1.36.

By their unmatched transfer lengthdistributions, Fig. 17 shows that 0.6in. (15.2 mm) diameter strands requiremore strand diameters to transfer prestressing forces when compared to 0.5in. (12.7 mm) strands. Transferlengths for 0.6 in. (15.2 mm) strandsaverage almost 67db whereas thetransfer lengths for 0.5 in. (12.7 mm)strands average about 59db.

Considering these data, the transferlength distributions indicate the transfer lengths cannot be normalized bythe strand diameter. Instead, the datasuggest the following form for the relationship between transfer length andstrand diameter:

L=Kd

where K equals a constant and aequals 1.68 for these data.

16

(8) The histogram in Fig. 18 shows all shows that data from the 0.6 in. (15.2of the transfer length data normalized mm) transfer lengths closely match theagainst the bar diameter raised to the data from the 0.5 in. (12.7 mm) strands1.68 power, db’68. This histogram and their pattern of distribution, when

Table 5. Average transfer lengths vs. strand size and specimen series.

Tests series(cross section dimensions)

Single strand specimens(5 x4 in.)

Three strand specimens(5 x9 in.)

Five strand specimens(5x 13 in.)

Average transfer lengths (in.)(number of ends tested) Ratio

0.5 in. strands 0.6 in. strands L,11,IL,{0.6

29.4 47.01 60

(4) (2)

29.1(12)

38.1(6)

41.61.43

(20)

AASHTO-type beams 25.5(I-beams) (12)

Average 29.5

Standard deviation I 6.9

48.01.26

(6)

32.0(12)

1.25

40.0 1.36

6.8

Note: I in: = 25.4 mm.

Table 6. Transfer lengths vs. strand spacing; 0.6 in. strands spaced at 2.0 and 2.25 in.

______________ Transfer lengths (in.)

- Specimen - North end—

South end

FC362-11 46 44

212

JZAverage transfer lengths: Specimens with strands at 2.25 in. spacings = 43.3 in.

Standard deviation = 2.0 in.

Average transfer lengths: All specimens with 0.6 in. strands = 40.0 in.Standard deviation = 6.8 in.

Note: I in. = 25.4 mm.

C”

C

.

0C0E

ITransfer Length (÷1- 2 In.)

Fig. 15. Histogram of transfer lengths for 0.5 in. (12.7 mm) fully bonded strands.


Fig. 17. Histogram of transfer lengths for allstrand diameter, db.

the transfer lengths are normalized bydb raised to the 1.68 power.

Overall, the comparison of thetransfer length data by strand sizeshows that 0.6 in. (15.2 mm) strandsrequire longer transfer lengths than 0.5in. (12.7 mm) strands. Furthermore,these data indicate that the relationshipbetween transfer length is not linear,but rather the transfer length is an exponential function of strand diameter.

However, these data, taken by them-

selves, do not represent justification toalter the currently accepted linear relationship between transfer length andstrand diameter, and the authors arenot recommending a change based onthese data. On the other hand, this isan interesting result and other researchers should continue to investigate the possibility that strand transferlength and/or flexural bond lengthmay not be linear functions of stranddiameter.

Effects of the Cross Section’s Sizeon Measured Transfer Iength

Much of the earlier transfer lengthresearch was performed on smallrectangular prisms with a singlestrand.3’5’6’78”°Fewer transfer lengthmeasurements have been taken onmulti-strand specimens such as thethree- and five-strand specimenstested as part of this research program.Even fewer transfer length studieshave been performed on beams withcross sections as large as theAASHTO-type beams in this research.Intuitively, data from larger test specimens should match more closely thetransfer lengths of real pretensionedconcrete members, particularly testspecimens with multiple strands.

Figs. 19 and 20 compare the transferlengths from each series of transferlength specimens. The range of transfer lengths are portrayed separately foreach type of cross section, depictingthe high, low and average values ofmeasured transfer lengths. The dataare grouped according to cross sectiondimensions and numbers of strands.For both 0.5 and 0.6 in. (12.7 and 15.2mm) strands, the figures illustrate thatlarger specimens tend to possessshorter transfer lengths.

Considering specimens with 0.5 in.(12.7 mm) strands and illustrated inFig. 19, the transfer lengths for theAASHTO-type beams are almost 40percent less than transfer lengths fromthe FC3 series. (The FC5 series resultscould be slightly skewed because oflow concrete strength.) This result ismade more remarkable by the cuttingtechniques. The FC 1, FC3, DC3, andthe FC5 series were flame cut afterslight detensioning whereas theAASHTO-type beams were flame cutat 100 percent of tension.

The same trend is demonstratedwith 0.6 in. (15.2 mm) strands inFig. 20 where the transfer lengths forAASHTO-type beams were 28 percentshorter than other cross sections. Thistrend is also described numerically inTable 5 where average transfer lengthvalues are reported for each specimenseries. For both 0.5 and 0.6 in. (12.7and 15.2 mm) strands, the transferlengths for AASHTO-type beamswere markedly shorter than the trans

C

ITransfer Length (I- 2 In.)

Fig. 16. Histogram of transfer lengths for 0.6 in. (15.2 mm) fully bonded strands.

InC,

I56 63

Transfer Lengths (db)

fully bonded strands, normalized by

56 PCI JOURNAL

fer lengths of the other test specimens.These data indicate that test speci

mens with larger cross sections andmultiple strands possess significantlyshorter transfer lengths. Transferlength measurements on the differentcross sections were performed withconsistent procedures using the sameprestressing strand and under similarlaboratory conditions. The results alsoindicate that transfer lengths measuredon relatively small, single-strand specimens may not simulate transferlengths of real pretensioned concretemembers.

Perhaps the most striking illustration of this effect is found in Fig. 15,the histogram of transfer lengths for0.5 in. (12.7 mm) strands. In this histogram, the data fall into two distinctregions separated by a significant gapin the data. Eight data points are indicated with transfer lengths less than 22in. (0.56 m). All of these points weregenerated from the tests on the larger,AASHTO-type beams whereas thelonger transfer lengths were measuredon rectangular prisms.

Several factors can explain theshorter transfer lengths measured inlarger cross sections. First, if flamecutting is the method of release, thenstrands are cut one at a time. As eachstrand is detensioned, the largermasses of concrete will be less affected by the sudden release of eachindividual strand because the largermass has more capacity to withstandlocalized damage from sudden release.

Secondly, in larger cross sectionswith multiple strands, the release ofeach individual strand acts to furtherprecompress the cross section. Consequently, a cross section becomes increasingly precompressed as tensionfrom each successive strand is released.Lastly, multiple strands also act as reinforcement to the cross section, helpingto distribute the energy and stress fromthe release of a single strand.

Typical pretensioned beams, withlarger cross sections and multiplestrands, could be expected to registershorter transfer lengths when compared to many of the typical researchspecimens. Researchers should also becautioned that small rectangularprisms may not represent “real” pretensioned structures.

Effects of Strand Spacing onPretensioned Transfer

Current practice dictates that center-to-center spacing of strands should beat least four times the strand diameter.Although this “rule of thumb” is basedon very little experimental data, it hasserved the industry well, primarily because the industry standard used 0.5in. (12.7 mm) strands at 2.0 in. (51mm) spacings. Now, with the approved use of 0.6 in. (15.2 mm) strandfor pretensioned applications, the stan-

dard spacing should be investigated todetermine if the “rule of thumb”should be maintained as a standard.Strong economic impetus for thesestudies exists because the structural efficiency of 0.6 in. (15.2 mm) strands isnullified if 2.4 in. (61 mm) spacingsare required. Therefore, tests were performed to determine what effects, ifany, strand spacing would have onpretensioned transfer.

The data for transfer lengths of 0.6in. (15.2 mm) strand with 2.0 and 2.25in. (51 and 57 mm) spacings are corn-

InU)

a,E

I77 88 99 110

Transfer Length I (d .68

Fig. 18. Histogram of transfer lengths for all fully bonded strands, normalized bystrand diameter raised to the 1 .68 power, d-68.

2

IDC3

Specimen Senes

Fig. 19. Summary of transfer lengths by specimen series, 0.5 in. (12.7 mm) fullybonded strands.


pared in Table 6. The table lists thetransfer lengths from each end of threespecimens where 0.6 in. (15.2 mm)strands were spaced at 2.25 in. (57mm). The average transfer length forthese six measurements was 43.3 in.(1100 mm). This value is slightlylonger than 40.1 in. (1019 mm), theaverage transfer length for all 0.6 in.(15.2 mm) strands. These data indicatethat strands with 2.25 in. (57 mm)spacings have longer transfer lengthsthan strands with 2 in. (51 mm) spacings, and the need for wider spacingsto accommodate 0.6 in. (15.2 mm)strands is not demonstrated for thesespecimens.

In a related issue, 0.6 in. (15.2 mm)diameter strands could be more likelyto cause splitting upon pretensioningrelease because the larger size cancause larger bursting stresses aroundthe strand. Current standard box girdershapes in the State of Texas are madewith 5 in. (127 mm) thick bottomflanges and 6 in. (152 mm) wide webs.Tests were performed to study the reliability of transferring fully bonded 0.6in. (15.2 mm) strands on 2.0 in. (51mm) spacings in a 5 in. (127 mm)wide concrete member. Three specimens were fabricated 5 in. (127 mm)wide and 13 in. (330 mm) deep withfive 0.6 in. (15.2 mm) strands each,FC(T)560-1, 2, and 3.

After pretensioned transfer, thesespecimens were inspected for splitting

cracks and measured for transferlength. No signs of splitting were detected. Furthermore, transfer lengthsfor these specimens were within normal ranges. These tests confirm that a2.0 in. (51 mm) spacing was sufficientfor 0.6 in. (15.2 mm) strands for thesecross sections.

Transfer Lengths forDebonded Strands

Table 4 compares the measuredtransfer lengths for debonded strandsagainst the transfer lengths of fullybonded strands. Overall, the datademonstrate that measured transferlengths of debonded strands are consistently shorter than those of fullybonded strands. Debonded 0.5 in.(12.7 mm) strands were transferred inan average of 25.8 in. (655 mm)length while their fully bonded counterparts were transferred in 29.5 in.(749 mm) length.

Differences were even greater for0.6 in. (15.2 mm) diameter strands.Measured transfer lengths ofdebonded strands were 32.2 in. (818mm) compared to 40.1 in. (1.02 m) forfully bonded, 0.6 in. (15.2 mm)strands. While it has been argued thatthe bond of debonded strands could beadversely affected because their anchorage is not aided by confiningstresses developed at the support,these data indicate that the transfer

bond stresses of debonded strands exceed the bond stresses for fullybonded strands.

The transfer zone of a debondedstrand is positioned in regions of thespecimen that are subject to precompression from strands that are fullybonded. While the difference in transfer lengths is significant, the differences do not appear large enough towarrant special provisions for thetransfer length of debonded strands.Again, variations in transfer length between debonded strands and fullybonded strands do not greatly exceedthe general variation observedthroughout the transfer length testing.

Confining Reinforcement

Confining reinforcement is analogous to hoop ties in a column. In acolumn, the hoop ties prevent the longitudinal reinforcement from bucklingoutward. The ties also help to confinethe concrete within the core by resisting lateral deformations. In the pretensioned transfer zone, the transfer ofpretensioned strands causes burstingstresses in the surrounding concrete.Presumably, confining reinforcementsurrounding the concrete and pretensioned strand would improve strandanchorage and shorten the transferlength. However, these data do notsupport this theory.

Transfer lengths measured on specimens containing confining reinforcement are presented in Table 7. Thetable reports that the average transferlengths for specimens made with confining reinforcement are 32.8 in. (833mm) for 0.5 in. (12.7 mm) strands and45.4 in. (1.15 m) for 0.6 in. (15.2 mm)strands. Also listed in the table are theaverage transfer lengths for all strands.In comparison, specimens containingconfining reinforcement possessedslightly longer transfer lengths thanspecimens where confining reinforcement was omitted. These tests demonstrate that confining reinforcement didnot contribute significantly to prestress transfer for these tests.

It is postulated that the confining reinforcement remained largely ineffective because the concrete remainedrelatively free from cracking throughout the transfer zone. Even though

0

C

IDC3

Specimen Series

bonded strands.

FC5 FM (AASHTO)

Fig. 20. Summary of transfer lengths by specimen series, 0.6 in. (15.2 mm) fully

58 PCI JOURNAL

confining reinforcement necessarilymust increase each member’s elasticstiffness in the circumferential direction, this effect is apparently smallcompared to the elastic stiffness ofconcrete. Indeed, fundamental mechanics prove that small radial cracking must occur locally at the interfaceof strand and concrete.3 However,these cracks do not usually becomelarge enough to activate confiningforces in the reinforcement hoops.Therefore, the confining reinforcement exerts little or no influence onthe prestress transfer.

On the other hand, for the generaldesign case, pretensioned concretemembers must be detailed to preventpropagation of splitting cracks that canoccur at transfer. In cases where splitting does occur at transfer, confiningand/or transverse reinforcements arethe only elements that maintain integrity of the concrete if splittingcracks should occur. Therefore, transverse reinforcement should not beeliminated from standard detailing.

Strand Surface Condition

The impact of strand surface condition on transfer length has been established by many researchers.’3’4’5’67’8Strands that are rusted or weathered,even in limited amounts, generallypossess measurably shorter transferlengths compared to bare, brightstrand. A coating of light rust improves the frictional restraint betweenconcrete and strand. Conversely,transfer lengths can become very longif the strand is lubricated or otherwisecontaminated with oil.

The strand used in this study wasfurnished with a bright, mill conditionsurface. During testing, the strand wasprotected from contamination and corrosion by storing it in a dry warehouse. Throughout specimen fabrication, the strands were handledcarefully to avoid contaminating thestrand surface. Additionally, no formrelease oils nor lubricants of any kindwere allowed near the bare strand atany stage of fabrication.

Efforts were made to eliminate thestrand surface condition as a variable,yet the data demonstrate significantvariations in measured transfer lengths

with standard deviations on the orderof 20 percent of the average values.None of the research variables can account for this variation in data, leavingthe unknown variations in surface condition as a possible cause. Other research studies noted similar variationsin transfer lengths in their studies.However, no quality assurance orquality control procedures currentlyexist to monitor or control the surfacecondition of strands.

To summarize, the strand surfacecondition is probably the most important variable affecting transfer lengthof strand, yet it is the least predictable.Large degrees of scatter in the dataexist not only from researcher to researcher, but within an individual research project, as exhibited here.

Strand End Slips vs.Transfer Lengths

At prestress release, at the ends of apretensioned member, the pretensioned strands slip into the surrounding concrete and relative displacementoccurs throughout the transfer zone.At the ends of the pretensioned members, the relative slip between the concrete and the strand can be measured;it is generally referred to as “strandend slip” and the designation Le. S

used in this paper.\Vhere prestress transfer is fully ac

complished, no slip occurs betweensteel and concrete and concrete strains

Table 7. Effects of confining reinforcement on measured transfer lengths.

Measured transfer length (in.)

Specimen end

FCT35O-3 30.5

FCT35O-4 29.0

0.5 in. strands-F

North Southend

30.0

0.6 in. strands

North Southend end

32.0 —

_______

FCT55O-2 36.0 39.5 — —

FCT36O-3 — — 39.5 45.5

FCT36O-4 — — 50.5

FCT362-I2 — -

— L 44.0 42.0

FCT56O-2 — — 48.0 51.5

Average transfer lengths: 32.8 45.4Strands confined by hoops (Standard deviation = 4.1 in.) (Standard deviation = 4.3 in.)

Average transfer lengths: 29.5 40.0All test specimens (Standard deviation = 6.9 in.) (Standard deviation = 6.8 in.)

Note: I in. = 25.4 mm.

are compatible with strand strain. Inother words, in regions not includingthe transfer zone, steel strains arecompatible with the concrete strainand no relative displacement occursbetween the concrete and the steel.

A theoretical relationship has beendeveloped that relates the transferlength as a function of strand slip.’2”5”6The equation is derived from a mechanistic relationship integrating steelstrains over the transfer length andsubtracting the concrete strains overthat same length. Assuming linearvariation of steel and concrete strainswithin the transfer zone yields theexpression:

Lt=•3±(Les) (9)

where is the elastic modulus of thesteel strand, f is the strand stress immediately before release, and Les is themeasured end slip. Note that this theoretical relationship is independent ofstrand size. For these tests, the equation is simplified to the following:

L1 = 29OLes (10)

Strand end slips were measured onevery strand at each end of all transferlength specimens. End slips were averaged for each end of each specimen andlisted in Tables 2 and 3. In some cases,the end slip measuring devices weredisturbed during detensioning and accurate measurements were not available.


In Fig. 21, strand end slips are plotted vs. the measured transfer lengths.Each data point represents one end ofone transfer length specimen. Thereare a total of 54 data points for strandend slips vs. transfer lengths. Fig. 21combines and depicts data from0.5 and 0.6 in. (12.7 and 15.2 mm)strands.

The figure shows that the data arearrayed around the theoretical relationship, L5 290Les, indicating thatthe data tend to corroborate the theoretical, mechanistic relationship between transfer length and strand endslips. A regression analysis was performed to determine the line that represented the data with the least error.This line, constrained through the origin, is given by L = 294.9Lgs. The reported correlation of r = 0.717 indicates that a statistical correlation does

exist between transfer length andstrand end slips, and suggests that endslips may reliably predict transferlength.

Comparison With Other Research

Some recent transfer length research is summarized in Table 8. Thetest results from Cousins et al. werefirst reported in 1986,18 spurring theFederal Highway Administration(FHWA) to restrict the use of 0.6 in.(15.2 mm) diameter strands from pretensioned application, and to increasethe development length provisions forother sizes of strand. Cousins et al.found the transfer lengths of uncoated0.5 in. (12.7 mm) strands to exceedcurrent code recommendations fortransfer lengths by over 100 percent,with average transfer lengths mea

sured at 49.7 in. (1.26 rn).’5’92°The transfer lengths reported by

Deatherage et a!. from the Universityof Tennessee at Knoxville (UTK)were performed under research sponsored by PCI in response to theFHWA moratorium.6’7Shahawy et al.also conducted transfer length research at the Florida Department ofTransportation (FDOT).222

The UTK and FDOT tests are particularly related to this research because AASHTO girders were used astransfer length specimens. UTK measured transfer lengths on AASHTOType I girders and FDOT measuredtransfer lengths on AASHTO Type IIgirders. The tests performed by FDOTwere conducted at a prestressing plant.

It should be mentioned that resultsfrom these other researchers shouldbe tempered because their analysistechniques differed from the technique reported here. In some cases,analysis techniques are susceptible toarbitrary interpretation that can significantly influence the research results. The data reported in Table 8summarize the data as it is reported inthe literature.

Researchers at FDOT employed aplateau intercept method that is subject to arbitrary interpretation. Inusing the plateau intercept method,transfer lengths are defined by the intersection of the parabolic portion ofthe concrete strain with the strainplateau. The transfer length is poorlydefined using this technique becausethe parabolic portion of the strain profile approaches the strain plateauasymptotically. UTK utilized a bilinear intersection method that requirestwo arbitrary lines be drawn from thetransfer length data.

Table 8. Results of concurrent transfer length research.

0.5 in. strands 0.6 in. strands

Number Measured transfer lengths (in.)Number Measured transfer lengths (in.)

of ends Standard of ends StandardSpecimen tested Maximum Average Minimum deviation tested Maximum Average Minimum deviation

NCSU* 20 74 49.7 32 10.7 10 68 56.5 44 8.0

FDOT 12 32 30.1 29.5 0.7 7 36 34.7 32 1.5

UTK 8 36 27.9 22 5.6 8 30 24.4 21 2.9

50Lt294.9(Les

‘r v DataPoints

;O)vv °EE20 v’/ j meoreticai:

15 .//‘ 1.]: L2Les(EpsIfsi) [10

Correlation vs. RegressIon:5 //7 r—0.717

0o. o.b8 0.12 0.16 0.2 0.24 0.i8

End Sup (In.)

Fig. 21. Measured transfer lengths vs. measured end slips for all strands.

Note: 1 in. = 25.4 mm.* Method for data analysis is not reported.

t Transfer length data were analyzed using a plateau intercept method that may allow arbitrary interpretation of results.Transfer length data were analyzed using a bilinear intersection method that may allow arbitrary interpretation of results.

60 PCI JOURNAL

DEVELOPMENT OFDESIGN GUIDELINES FOR

TRANSFER LENGTH

In reviewing the transfer length datacollected in this and other researchprojects, the data are most remarkablefor their relatively wide variation. Certainly, if one includes data from otherresearch projects, the transfer lengthdata do not converge to a single value.Cousins et al. report a maximum transfer length for 0.5 in. (12.7 mm) diameter strands of 74 in. (1.88 m) with anaverage value of 49.7 in. (1.26 m). Onthe other hand, Shahawy reports transfer lengths for 0.5 in. (12.7 mm)strand to be tightly grouped around 30in. (762 mm).

Transfer lengths measured in this research appear to distribute somewhatnormally around an average value.The average transfer length for 0.5 in.(12.7 mm) diameter strands is 29.5 in.(749 mm) and the average transferlength for 0.6 in. (15.2 mm) strands is40.0 in. (1.02 m). The only significant,identifiable variable that affectedtransfer lengths measured in this research was strand diameter. All othervariables, i.e., confining reinforcement, debonded strands and strandspacing affected transfer lengths to asmaller degree. Concrete strength wasnot a research variable in this testingprogram and no recommendations canbe made in that regard.

Figs. 15 and 16 present the data inhistograms based upon the measuredtransfer lengths from this research project. The histograms are helpful in thatthey illustrate the distribution of measured transfer lengths by plotting thenumber of specimen ends vs. theirmeasured transfer lengths. The transfer lengths are grouped in ranges of±2 in. (±51 mm).

Shahawy et al. suggested that thetransfer length could be predicted byfsidb/3. This expression yields transferlengths of approximately 32.5 in. (826mm) for 0.5 in. (12.7 mm) diameterstrands and 39 in. (991 mm) for 0.6 in.(15.2 mm) strands. This expressionhas also been recommended by Buckner in his recent summary of strandbond research.23 However, this recommended expression predicts a shortertransfer length rather than a large per-

centage of the measured transferlengths that are reported in this andother literature.

On the histograms in Figs. 15through 18, the transfer lengths corresponding tofs1db/3 are shown. Thedata indicate that the expressionfsidb/3 roughly predicts the averagevalues of transfer lengths measured inthis research. However, the recommended expression would be unconservative to much of the transferlength data. For transfer lengths measured on 0.5 in. (12.7 mm) diameterstrands, 10 transfer lengths of 34 measured exceed 32.5 in. (826 mm). Considering 0.6 in. (15.2 mm) strands, 21transfer lengths out of 40 measuredtransfer lengths exceed 39 in. (991mm). Overall, the recommended expression, fsjdb/3, predicts shortertransfer lengths than 43 percent of thedata (shown in Fig. 17).

Considering the sudden and violentnature of failures that can result fromstrand anchorage failure, it seems inappropriate to recommend an expression that predicts the average value fortransfer length. Because flexural testshave shown that strand development isdirectly related to the transferlength,7’8’2”324 the expression predictingtransfer length must be conservativelychosen. Accordingly, it would seemmore appropriate to select a value oran expression that provides an upperlimit for a greater percentage of thetest results. By choosing a more conservative expression for transferlength, the expression could be usedconfidently in a wide variety of applications. The following expression issuggested by the data and recommended for use in design applications:

Lt=1db (11)

This expression would predict transfer lengths of 40 in. (1.02 m) for0.5 in. (12.7 mm) diameter strands and48 in. (1.22 m) for 0.6 in. (15.2 mm)strands, assuming an effective prestress of 160 ksi (1100 MPa). Corresponding values for fsedbl2 are shownon each of the histograms (see Figs. 15through 18). Alternatively, transferlengths could be predicted by settingtransfer length equal to 80 strand diameters, or 8Odb (as long as Grade 270,

low relaxation strands are employed).There are two primary advantages in

using fsedb/2First, this expression exceeds the

measured transfer length from most ofthe data, which is important as transferlength relates to strand development.As development length testing hasconsistently shown, successful strandanchorage depends upon the prevention of cracking through or near thetransfer zone. Therefore, an undisturbed transfer zone is essential tostrand development.

Secondly, the expression relatestransfer length to both strand diameterand to the prestressing force, using thesame variables currently employed inthe expression from the ACI Commentary. This expression would allowevolution to new strand sizes andhigher strand strengths. However,transfer lengths do not appear to be directly proportional to strand diameter.Introduction of strand sizes larger than0.6 in. (15.2 mm) will require additional testing.]

In developing an expression fortransfer length, one must consider theimportance of transfer length and themanner in which transfer length isused for design. For some designers,transfer length will be important onlyas it relates to predicting the elasticproperties in the end regions of a pretensioned member. Primarily, thisconcern focuses most specifically incalculating the shear strength of concrete, ‘l’.

In the early and mid 1980s, manytesting programs focused on developing reliable design guidelines for theshear design of pretensioned concrete.Tests performed in these research programs consistently demonstrated a direct interaction between shear failuresand bond failures. In fact, the failuremodes are difficult to distinguish andfailures were labeled shear/bond failures. Significantly, these shear/bondfailures were sudden, violent andwould represent catastrophic failuresin real structures.

Similarly, in the late 1980s and intothe l990s, strand bond issues of transfer length and development length became the focus of new testing programs. In the development lengthresearch that followed, research pro-


grams at Tennessee (UTK), FDOT,and Austin tested I-shaped beams forstrand development. In many of thosetests, violent and catastrophic failureswere observed that resulted directlyfrom bond failure precipitated by webshear cracking. These failures werelabeled bond/shear failures andclosely matched the shear/bond failures that were observed in shear testing. A brief summary of the test resuits is included in a recent issue ofthe PCI JOURNAL.25

From the development length testing, it is imperative to recognize thatthe transfer length can directly and adversely affect the strength and ductility of a pretensioned member. Typicalshear/bond failures have not only beenrecorded in research laboratories, butalso during the Northridge earthquake.26 These failures highlight theneed for the industry to collectivelyacknowledge the importance of transfer length in the safe design of pretensioned beams.

Accordingly, the expression fortransfer length must be conservativelychosen, and must encompass a largepercentage of the data to prevent unexpected and non-ductile failures. (Also,acceptance criteria should be established to control and limit the extremevalues for transfer length.) Therefore,the more conservative expression fortransfer length is recommended:

L = fsedb

2

[Authors’ note: The essential criteriathat control strand anchorage failuresare the interaction between the anchorage failure and cracking thatpropagates through or near the transfer zone of a pretensioned strand,thereby causing anchorage failure.Failure to recognize the importance ofthe interaction between cracking andbond failures has led to ultra-conservative recommendations for the development length equation by Shahawy etal. and by Buckner. By conservativelychoosing a transfer length provision(and by requiring acceptance criterialimiting the maximum strand transferlength), pretensioned strand anchorage should be assuredfor a wide variety of applications without resorting toextremely conservative equations for

development length. It is imperative tonote that the longer design transferlength given in Eq. (11) directly reflects the wide variation in measuredtransfer lengths and the need for a design value to exceed a large percentage of the possible transfer lengths. Atsome point in the future, if a standardized bond performance test is implemented that significantly reduces thedegree of scatter in pretensionedbond, then a less conservative designexpression for transfer length could beadopted without reservation.]

CONCLUSIONSBased on the results of this investi

gation, the following conclusions canbe made:

1. The average measured transferlength for 0.5 in. (12.7 mm) diameterstrands was 29.5 in. (749 mm) with astandard deviation of 6.9 in. (175mm), or 23 percent. Transfer lengthswere measured on 34 ends of pretensioned specimens.

2. The average measured transferlength for 0.6 in. (15.2 mm) strandswas 40.0 in. (1.02 m) with a standarddeviation of 6.8 in. (170 mm), or 17percent. Transfer lengths were measured on 40 ends of pretensionedspecimens.

3. The transfer lengths for debonded strands were measurablyshorter than those of the fully bonded

(12) strands. Transfer lengths for debondedstrands were, on average, 16 percentshorter than transfer lengths for fullybonded strands. For 0.5 in. (12.7 mm)debonded strands, the average transferlength was 25.8 in. (655 mm). For 0.6in. (15.2 mm) debonded strands, theaverage transfer length was 32.7 in.(831 mm).

4. Overall, confining reinforcementhad little or no effect in improving thetransfer lengths of 0.5 or 0.6 in. (12.7or 15.2 mm) diameter strands. In fact,the measured transfer lengths forstrands confined by mild steel reinforcement were marginally longerthan strands where confining reinforcement was not provided. Forstrands enclosed by confining reinforcement, the average transfer lengthwas about 12 percent longer than forstrands without confining reinforce-

ment. These results indicate that confining, or transverse, reinforcement isnot activated until splitting cracksoccur at prestress transfer. The authorsrecommend that standard detailingcontinue to include transverse reinforcement to prevent loss of anchoragedue to the splitting cracks that canoccur at release of pretensioning.

5. The 0.6 in. (15.2 mm) diameterstrands were found to adequately andreliably transfer prestressing forcesinto the concrete. Therefore, the 0.6in. (15.2 mm) strands should be allowed for regular use in pretensionedconcrete. Furthermore, although the0.6 in. (15.2 mm) strands requiredlonger transfer lengths than 0.5 in.(12.7 mm) strands, the transfer offorces from 0.6 in. (15.2 mm) strandswas similar to the transfer of forcesfrom 0.5 in. (12.7 mm) strands.

6. The 0.6 in. (15.2 mm) diameterstrands required measurably longertransfer lengths than 0.5 in. (12.7 mm)strands. On average, the 0.6 in. (15.2mm) strands required 36 percentlonger transfer lengths to adequatelytransfer prestressing forces into theconcrete when compared to 0.5 in.(12.7 mm) strands. Therefore, stranddiameter, db, should continue to bepart of the transfer length expression.

7. Results from these transfer lengthtests indicate that the transfer lengthmay not vary linearly with strand diameter, db. Instead, these data indicatethat the expression, L5 = Kd, wouldbe more accurate (for these data, a =

1.68). However, the authors do notsuggest that these data alone providesufficient evidence to recommendadoption of an exponential equation.Therefore, additional research is required to evaluate the transfer lengthas a nonlinear function of the stranddiameter, db.

8. The anchorage of 0.6 in. (15.2mm) diameter strands was adequately and reliably accomplished byspacing strands at 2.0 in. (51 mm)center-to-center spacings. Narrowspecimens with 0.6 in. (15.2 mm)strands spaced at 2.0 in. (51 mm)centers reliably transferred prestressing forces, without evidence of splitting cracks or other adverse effects.Furthermore, specimens with 0.6 in.(15.2 mm) strands spaced at 2.0 in.

62 PCI JOURNAL

(51 mm) spacings had essentiallyidentical transfer lengths. Therefore,0.6 in. (15.2 mm) strands should beallowed for use in pretensioned concrete on 2.0 in. (51 mm) center-to-center spacings.

9. Larger cross sections containingmultiple strands had measurablyshorter transfer lengths than thesmaller transfer length specimens. Thelarger AASHTO-type beam specimenshad measured transfer lengths thatwere 25 percent shorter than thesmaller rectangular transfer lengthprisms, on average.

10. The data indicate that correlationdoes exist between transfer length andstrand end slips. Linear regression ofthe data, transfer length vs. end slip,generated a “best fit” line described byL, = 294.9Les, with a coefficient ofcorrelation, r = 0.717. This “best fit”line is nearly identical to the theoretical relationship, L = 2Les(EpsILj) =

29OLes. Significantly, the relationshipbetween end slip, Les, and transferlength is independent of strand size,concrete strength and all other variables that are recognized to affectstrand transfer length.11. From the data, a rational and

safe expression for transfer length

is determined:

L = fs/tb

2

It should be emphsized that the conservative nature of this recommendeddesign equation is a direct reflectionof the wide variation in measuredtransfer lengths.

RECOMMENDATIONS

1. The expression for transfer lengthshould be changed to protect againstthe potentially dangerous failures iftransfer length is underestimated. Therecommended expression is:

2

2. The transfer length for debondedstrands should be assumed to matchthe transfer length for fully bondedstrands, and is also given by the expression above.

3. The 0.6 in. (15.2 mm) diameterstrands should be allowed for use inpretensioned concrete at an allowablecenter-to-center spacing of 2.0 in. or50 mm. Designers of pretensionedconcrete must also be aware that 0.6in. (15.2 mm) strands require longer

transfer lengths and adjust designsaccordingly.

AUTHORS’ POSTSCRIPTIn recent testing conducted at the Uni

versity of Oklahoma begirming in 1994,at the University of Texas at Austin andat Stresscon Corporation in ColoradoSprings, Colorado, it is becoming increasingly clear that transfer lengths forsome strands can be quite shorter thanthe transfer lengths measured in the research described in this paper. Additionally, the authors recognize ongoing efforts to implement quality controlprocedures that should help control thebond properties of prestressing strands.

If the transfer lengths of strands aremeasurably shortened from these efforts, or if the variations in measuredtransfer lengths are significantly reduced, then a less conservative designexpression for transfer length may bemore appropriate. Therefore, if appropriate quality assurance can be enactedto ensure the reliability of bond ofstrands used in pretensioned applications, then it may be possible for theseauthors to acknowledge that transferlengths could remain at the current expression, L fse4”3.


REFERENCES

1. ACI Committee 318, “Building CodeRequirements for Structural Concrete(ACT 3 18-95),” American ConcreteInstitute, Farmington Hills, MI, 1995.

2. AASHTO, Standard Specifications forHighway Bridges, 15th Edition, American Association of State Highway andTransportation Officials, Washington,D.C., 1992.

3. Janney, Jack R., “Nature of Bond inPre-Tensioned Prestressed Concrete,”ACI Journal, V. 50, No. 9, May 1954,

pp. 717-736.

4. Hanson, Norman W., and Kaar, PaulH., “Flexural Bond Tests of Pretensioned Prestressed Beams,” ACJ Journal, V. 55, No. 7, January 1959,

pp. 783-802.

5. Janney, Jack R., “Report of StressTransfer Length Studies on 270K Prestressing Strand,” PCI JOURNAL,V. 8, No. 1, February 1963, pp. 41-45.

6. Kaar, Paul H., LaFraugh, Robert W.,and Mass, Mark A., “Influence ofConcrete Strength on Strand TransferLength,” PCI JOURNAL, V. 8, No. 5,October 1963, pp. 47-67.

7. Hanson, Norman W., “Influence ofSurface Roughness of PrestressingStrand in Bond Performance,” PCIJOURNAL, V. 14, No. 1, February1969, pp. 32-45.

8. Kaar, Paul H., and Hanson, NormanW., “Bond Fatigue Tests of BeamsSimulating Pretensioned ConcreteCrossties,” PCI JOURNAL, V. 20,No. 5, September-October 1975,

pp. 65-80.

9. Rose, D. R., and Russell, B. W., “Investigation of Standardized Tests toMeasure the Bond Performance ofPrestressing Strands,” Research Report (Preliminary), Fears StructuralEngineering Laboratory, School ofCivil Engineering and EnvironmentalScience, University of Oklahoma,Norman, OK, July 1996, 212 pp.

10. Castrodale, R. W., Kreger, M. E., andBurns, N. H., “A Study of Pretensioned High Strength Concrete Girders in Composite Highway Bridges—Laboratory Tests,” Research Report

381-3, Center for Transportation Research, University of Texas at Austin,Austin, TX, January 1988.

11. Mitchell, D., Cook, W. D., Khan,A. A., and Tham, T., “Influenceof High Strength Concrete on Transfer and Development Length ofPretensioning Strand,” PCI JOURNAL, V. 38, No. 3, May-June 1993,

pp. 52-66.

12. Russell, B. W., and Burns, N. H.,“Design Guidelines for Transfer, Development and Debonding of Large Diameter Seven Wire Strands in Pretensioned Concrete Girders,” ResearchReport 1210-5F, Center for Transportation Research, University of Texas atAustin, Austin, TX, January 1993.

13. Paulsgrove, G. A., and Russell, B. W.,“Development Length Guidelines forPretensioned Strands,” Research Report, University of Oklahoma, Norman, OK, July 1996, 262 pp.

14. Unay, I. 0., Russell, B. W., Burns,N. H., and Kreger, M. E., “Measurement of Transfer Length on Prestressing Strands in Prestressed ConcreteSpecimens,” Research Report 1210-1,Center for Transportation Research,University of Texas at Austin, Austin,TX, March 1991.

15. Anderson, Arthur R., and Anderson,Richard G., “An Assurance Criterion for Flexural Bond in Pretensioned Hollow Core Units,” ACIJournal, V. 73, No. 8, August 1976,

pp. 457-464.

16. Deatherage, Harold J., and Burdette,Edwin, G., “Development Length andLateral Spacing Requirements of Prestressing Strand for Prestressed Concrete Bridge Products,” TransportationCenter, University of Tennessee,Knoxville, TN, February 1991.

17. Deatherage, Harold J., Burdette,Edwin G., and Chew, Chong Key,“Development Length and LateralSpacing Requirements of PrestressingStrand for Prestressed ConcreteBridge Girders,” PCI JOURNAL,V. 39, No. 1, January-February 1994,

pp. 70-83.

18. Cousins, Thomas E., Johnston, DavidW., and Zia, Paul, “Bond of EpoxyCoated Prestressing Strand,” Centerfor Transportation Engineering Studies, Department of Civil Engineering,North Carolina State University,Durham, NC, December 1986.

19. Cousins, Thomas E., Johnston, DavidW., and Zia, Paul, “DevelopmentLength of Epoxy-Coated PrestressingStrand,” ACI Materials Journal, V. 87,No. 4, July-August 1990, pp. 309-3 18.

20. Cousins, T. E., Johnson, D. W., andZia, Paul, “Transfer and DevelopmentLength of Epoxy Coated and Un-coated Prestressing Strand,” PCIJOURNAL, V. 35, No. 4, July-August1990, pp. 92-103.

21. Shahawy, M., and Batchelor, B. DeV,“Bond and Shear Behavior of Prestressed AASHTO Type II Beams,”Progress Report No. 1, Structural Research Center, Florida Department ofTransportation, Tallahassee, FL,February 1991.

22. Shahawy, Mohsen A., Issa, Moussa,and Batchelor, Barrington deV,“Strand Transfer Lengths in Full ScaleAASHTO Prestressed Concrete Girders,” PCI JOURNAL, V. 37, No. 3,May-June 1992, pp. 84-96.

23. Buckner, C. Dale, “A Review ofStrand Development Length for Pretensioned Concrete Members,” PCIJOURNAL, V. 40, No.2, March-April1995, pp. 85-105.

24. Brooks, M. D., Gerstle, K. H., andLogan, D. R., “Effect of Initial StrandSlip on the Strength of Hollow-CoreSlabs,” PCI JOURNAL, V. 33, No. 1,January-February 1988, pp. 90-111.

25. Russell, B. W., and Burns, N. H.,Comments on “A Review of StrandDevelopment Length for PretensionedConcrete Members” by C. Dale Buckner, PCI JOURNAL, V. 41, No. 2,March-April 1996, pp. 112-127.

26. Englekirk, R. E., and Beres, A., “TheNeed to Develop Shear Ductility inPrestressed Members,” Concrete International, V. 16, No. 10, October1994, pp. 49-56.

64 PCI JOURNAL

APPENDIX — NOTATION

= area of prestressing strand, for all prestress losses) U,, = average transfer bond stress7/36rd

= stress in prestressed reinforce- Uf = average flexural bond stressdb = diameter of prestressing strand ment before release and transfer

= nominal shear strength promodulus of elasticity of pre- Lb = length of debonding, or length vided by concretestressing strand of blanketing

= nominal shear strength prof’ concrete compressive strength Ld = development length vided by concrete when diagoat 28 days (ASTM C 39)nal cracking results from cornLes = amount of strand slip into conbined shear and momentf = concrete compressive strength

crete on release of prestressingat release of prestressingstrands = nominal shear strength pro

f5 = stress in prestressed reinforce- vided by concrete when diagoment at nominal strength L = transfer length

nal cracking results from exfse = effective stress in prestressed P,, = perimeter of prestressing cessive principal tensile stress

reinforcement (after allowance strand, 4/37rd, in web


measured transfer lengths of 0.5 and 0.6 in. strands in ... · 3 ubp) transfer leng_ se fully...

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