Download - Evaluation of Code Requirement for 0.6 in. (15 mm) prestressing strands

422 ACI Structural Journal/May-June 2005

ACI Structural Journal, V. 102, No. 3, May-June 2005.MS No. 04-036 received March 1, 2004, and reviewed under Institute publication

policies. Copyright © 2005, American Concrete Institute. All rights reserved, includingthe making of copies unless permission is obtained from the copyright proprietors.Pertinent discussion including author’s closure, if any, will be published in the March-April 2006 ACI Structural Journal if the discussion is received by November 1, 2005.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

This study investigated the effects of concrete strength and strandsurface condition on the transfer and development lengths of fullybonded and various combinations of bonded and debonded strandsin AASHTO Type I I-beams. Furthermore, the effect of H-bars onthe transfer length and end-slip of the strand was investigated. Sixbeams with lower-strength concrete and rusty strand were tested.The results were used to evaluate the requirements of ACI andAASHTO and equations by Buckner and Lane. Transfer lengthresults showed that ACI, AASHTO, and Buckner equations areconservative but the Lane equation is very conservative. Developmentlength results showed that ACI and AASHTO requirements areconservative for fully bonded strand and are overly conservative fordebonded strand. Buckner and Lane equations are very conservativefor fully bonded strand and decreasingly conservative for debondedstrand. H-bars were effective in decreasing strand end slip andshear crack widths within the H-bar region.

Keywords: development length; prestressed concrete; transfer length.

INTRODUCTIONThe use of newer and improved materials in construction

(such as low-relaxation prestressing strand, 0.6 in.-diameter[15 mm] prestressing strand, and high-strength concrete)calls into question several code requirements that weredeveloped from research conducted using older materials,properties, and sizes. The efficient use of high-strengthconcrete requires a much larger prestressing force to fullyprecompress the service load tension zone of the member.This, in turn, requires a much larger area of prestressingstrand if the strand is pretensioned to its typical value of 75%of guaranteed ultimate tensile strength. The number ofstrands, however, that can be placed in any given I-beamsection on a 2 in. (50 mm) grid spacing is limited. Thisnecessitates the use of a 0.6 in. (15 mm) diameter strand toobtain the required increase in strand area and prestressingforce. The cross-sectional area of a 0.6 in. (15 mm) diameterstrand is over 40% greater than that of a 0.5 in. (13 mm)diameter strand, which is the more common previously usedsize, thus providing over a 40% increase in the prestressingforce with the same number of strands and at the same levelof prestress.

The Federal Highway Administration (FHWA) placed amoratorium1 on the use of 0.6 in. (15 mm) diameterprestressing strands at a 2 in. (50 mm) grid spacing forpretensioned bridge applications in October 1988. Theresearch conducted at Texas Tech University (TTU) in 1996and the results reported herein are an integral part of a largerjoint research project conducted with The University of Texasat Austin (UT) for the Texas Department of Transportation(TxDOT) that was designed to provide additional test datafor consideration toward lifting the FHWA moratorium.Prohibition of the use of 0.6 in. (15 mm) diameter prestressing

strands at a 2 in. (50 mm) grid spacing in pretensionedconcrete beams was lifted by another FHWA memorandum2

in May of 1996 due to numerous experimental studies thathave been conducted using 0.6 in. (15 mm) diameterprestressing strands. The other 1988 FHWA restrictionsremain in effect.

In a pretensioned concrete beam, the tension force in theprestressing strand is transferred as a compression force intothe concrete via two primary bond mechanisms: wedge/friction action and mechanical interlock. The length of beamrequired to fully transfer the force in the strand into theconcrete is defined as the transfer length. The efficienttransfer of the prestress force from the steel strand to theconcrete is very important to the composite action of thematerials. Also, sufficient embedment of the strand in theconcrete beyond the point of maximum service load momentmust be available to provide adequate anchorage of thestrand. As flexural moments increase, internal forces in thestrand increase, requiring additional embedment length ofthe strand in the concrete for proper anchorage. The lengthof embedment required to fully develop the maximumtension force in the strand is defined as the developmentlength, which is also very important to the composite actionof the materials. The overall joint project was developed andexecuted to provide additional full-scale test data on thetransfer and development lengths of 0.6 in. (15 mm) diameterprestressing strands for two key variables: concrete strengthand strand surface condition. The effects of the two keyvariables were investigated for fully bonded and variouscombinations of bonded and debonded strands when used instandard AASHTO I-beams. Beams tested by TTU werelimited to the lowest of the three concrete strengths used inthe joint project and were limited to strands with rustysurface conditions. Transfer and development lengthsdetermined in TTU’s portion of this experimental study arecompared with the values predicted by the current codes(ACI 318,3 AASHTO-Standard,4 and AASHTO-LFRD5) andtwo proposed equations: one by Lane6 and one by Buckner.7

RESEARCH SIGNIFICANCEThe main significance of this research is to investigate the

bond performance of 0.6 in.-diameter (50 mm) prestressingstrands in fully bonded and partially debonded pretensionedconcrete beams. Moreover, results obtained from thisresearch will increase the current available database of

Title no. 102-S42

Evaluation of Code Requirement for 0.6 in. (15 mm) Prestressing Strandby Mehmet M. Kose and William R. Burkett

423ACI Structural Journal/May-June 2005

experimental data for the bond characteristics of 0.6 in.-diameter (15 mm) prestressing strands. Consequently, theexpanded database could be used to modify the currentspecifications or to set new specifications concerning thetransfer and development lengths of 0.6 in.-diameter (15 mm)prestressing strands. Furthermore, the effect of horizontalweb reinforcement (H-bar) on transfer and developmentlengths was investigated.

PROJECT OVERVIEWThe joint project was designed using standard AASHTO

Type I I-beams with cast-in-place concrete deck slabs toprovide additional full-scale test data on the transfer anddevelopment lengths of 0.6 in.-diameter (15 mm) prestressingstrands. A total of 36 beams were fabricated and testedduring the entire project. The beams were cast in pairs withvariations between the pairs in concrete strength, strandsurface condition, and the percentage of bonded/debondedstrands used. Table 1 provides the test matrix and targetmaterial values used in the overall project as well as thoseassigned to the beams tested by TTU. Each end of each beamwas tested separately resulting in the four tests per pair ofbeams as shown in Table 1. It should be noted that each beamend was tested separately for both transfer length and devel-opment length. Thus, six beams (three pairs) resulted in12 tests for transfer length and 12 tests for developmentlength. The test results were compared with ACI 318,AASHTO-Standard, and AASHTO-LRFD code requirementsand to requirements proposed by Buckner and by Lane.

FABRICATIONMaterial properties

The prestressing steel used in this project was a 0.6 in.-diam-eter (15 mm), seven-wire, low-relaxation strand with a specifiedultimate tensile strength of 270 ksi (1860.3 MPa) and a nominalcross-sectional area of 0.217 in.2 (140 mm2).8,9 A rusty strandsurface condition was used in all the beams tested duringTTU’s portion of this study, whereas bright and rusty strandsurface conditions were used in UT’s portion of the study.

The rusty strand had a light, somewhat uniform coating ofrust on the strand. The corrosion, however, was not severeand had not significantly affected the cross-sectional area ofthe strand. Three concrete strength ranges were used duringthe project as identified in Table 1. Beams tested by TTUused the lowest concrete strength range. Actual concretestrength and modulus of elasticity values were determinedfor each I-beam and deck slab at the time of flexural testing.These values are reported in Table 2.

Beam fabricationAll specimens tested by TTU were fabricated using a

target beam concrete strength in the 5000 to 7000 psi (34.5to 48.2 MPa) range and a prestressing strand with a rustysurface condition. With these conditions, three pairs ofbeams were fabricated with varying levels of bonded/debonded strands: fully bonded, 50% debonded, and 60%debonded. The specific identification codes assigned to thesix beams tested by TTU were L0R0, L0R1, L4R0, L4R1,L6R0, and L6R1. The first code character (L) indicates alower-strength concrete range in the test specimen. Thesecond code character (0, 4, or 6) indicates the total numberof debonded strands used in the specimen and representsfully bonded, 50% debonded, and 60% debonded, respectively.The third code character (R) indicates a rusty surface conditionon the strand used in the test specimen. The fourth codecharacter (0 or 1) was an identifier used to distinguishbetween the two beams in the like pair. Specific details as tothe number and location of strands, levels of initial prestress,and lengths of debonding are provided for the three-beamSeries L0RX, L4RX, and L6RX in Fig. 1, 2, and 3, respec-tively. In Specimens L0RX and L4RX, two strands were placedin the upper region of the beams and stressed to only 92 ksi

Mehmet M. Kose is an assistant professor at K. Sutcu Imam University, Kahraman-maras, Turkey. He received his BS from Middle East Technical University, Ankara,Turkey, and his MS and PhD from Texas Tech University, Lubbock, Tex. His researchinterests include reinforced and prestressed concrete design, finite element analysis,and structural dynamics.

ACI member William R. Burkett is an associate professor at Texas Tech University.He received his BS from Lamar University, Beaumont, Tex; his Master of Engineeringfrom Texas A&M University, College Station, Tex.; and his PhD from The Universityof Texas at Austin, Austin, Tex. His research interests include reinforced and prestressedconcrete design, finite element analysis, and full-scale experimental testing.

Table 1—Test matrix and material target values

Concrete strength, psi

Steel strand

Bright Rusty

Fully bonded

Debonded Fully bonded

Debonded

50% 60% 75% 50% 60% 75%

5000 to 7000 4/UT 4/UT 4/UT — 4/TTU 4/TTU 4/TTU —

9500 to 11,500 4/UT 4/UT — 4/UT 4/UT 4/UT — 4/UT

13,000 to 15,000 4/UT 4/UT — 4/UT 4/UT 4/UT — 4/UT

Table 2—Concrete material properties

Beam series

Precast beam Deck slab

f ′ci , psi f ′c , psi Ec, 106 psi f ′c , psi Ec, 106 psi

L0R0-1 4540 5440 4.20 6500 4.42

L0R0-2 4540 5440 4.20 6500 4.42

L0R1-3 4540 5440 4.20 6120 4.32

L0R1-4 4540 5440 4.20 6120 4.35

L4R0-1 3790 5050 3.80 5835 4.29

L4R0-2 3790 5050 3.80 5700 4.29

L4R1-3 3790 5050 3.80 6070 4.31

L4R1-4 3790 5050 3.80 5700 4.32

L6R0-1 4630 7480 5.45 6850 4.69

L6R0-2 4630 7480 5.45 5360 4.12

L6R1-3 4630 7480 5.45 6360 4.48

L6R1-4 4630 7480 5.45 6360 4.48Fig. 1—Beam cross section of L0RX series.


(634 MPa), as shown in Fig. 1 and 2, to help control tensilestresses in the top extreme fiber of the beams at release.

The specimen cross sections were developed through aniterative process that sought to optimize the concrete deck sizeand the number and location of the prestressing strands.Specimen configurations were controlled by project specifi-cations that required that the bottom row of prestressingstrand should reach a minimum ultimate tensile strain of0.035 during flexural testing, that the levels of stress in theconcrete at release remained within code allowable limits,and six strands should be contained in the bottom row ofstrands. Also, in the L6RX series, debonded strands wereplaced in the web of the beam to address concerns about webshear cracking. The split sheathing method of debondingwas used to prevent a bond from developing between theconcrete and the prestressing strand where specified.

Deck slab fabricationA 6.5 in. (165 mm) thick by 60 in. (1524 mm) wide

(1524 mm) reinforced concrete deck slab was cast-in-placeto provide composite action with the I-beam. The deck slabdetails were selected to model an in-place bridge deck and toprovide a compression flange adequate to fully develop theprestressing strands and strain them to a total strain greaterthan 3.5% at ultimate, well beyond their yield strain. Specificdeck slab details are shown in Fig. 4.

TRANSFER LENGTH TESTSPrior to the release of the prestress force, Demec points

were epoxied to each side of the lower beam flange on bothends of the beams at the height of the centroid of theprestressing strands in the bottom flange. They were placedon an approximate 2 in.-center-to-center (50 mm) spacing

over a distance greater than the estimated transfer length.Measurements were then taken using a Demec mechanicalstrain gauge device to determine the actual distance betweenthe Demec points, shown in Fig. 5. These measurementswere taken twice along each series of Demec points,resulting in two sets of measurements along each series ofDemec points. If a significant variation occurred betweenthe two sets of measurements was observed, additionalmeasurements were taken until the discrepancy wasresolved. This general procedure was used every timeDemec point measurements were taken.

Immediately after release, Demec point measurementswere taken again using the same general procedure describedpreviously. Knowing the distance between any pair of Demecpoints prior to and after release, the compressive strainbetween the points caused by the release of the prestressforce was determined. Using this data, a concrete compressionstrain profile along each end of each beam was developedand was used to evaluate the transfer length of the strand ineach beam. In addition, Demec point measurements were taken4 to 6 weeks after release to investigate long-term effects ontransfer lengths. Concrete compression strain profiles were alsodeveloped from the delayed Demec point measurements.

DEVELOPMENT LENGTH TESTSA typical configuration of the test geometry used during

this portion of the project is shown in Fig. 6. After completionof the first flexural test (as shown in Fig. 6) on the left-handend of the member, the supports and load-spreader beamwere moved to the opposite end of the specimen using anapproximate mirror image, and a second similar flexural testwas conducted on the undamaged right-hand end of themember. The distance from the end of the member to the firstload point is equal to the sum of unbonded length and theembedment length of the prestressing strand and is shown asLub + Le. The beam span Ls was selected large enough toprevent a shear failure from occurring and to allow two tests

Fig. 2—Beam cross section of L4RX series.

Fig. 3—Beam cross section of L6RX series.

Fig. 4—Concrete deck slab details.

Fig. 5—Demec point measurements.

ACI Structural Journal/May-June 2005 425

to be conducted on each beam (one on each end). Ls,however, was selected small enough to prevent significantdamage from occurring to the beam near the midlengthsupport. Any damage to the beam near the midlength supportor at the far end would affect the bond between theprestressing strand and the concrete in that region and wouldhave the potential to impact the results of the far end test. Thedimension a was selected to provide a constant momentregion between the two spreader beam load points.

The last test of each series always tested the end of thebeam in each pair that contained extra hairpin H-bars in thelower web end region. The embedment length for the last testin each series was set equal to the shortest embedment lengthof that series in which a flexural failure mode occurred. Thiswas done to determine whether or not the H-bars had anyimpact on the response of the beam.

Prior to loading, instrumentation was installed for test datacollection. Test data included applied load, beam deflectionat the load center point, concrete strain in the top fiber of thedeck slab in the constant moment region, and prestressingstrand end-slip. The load was applied incrementally to thebeam by a 400 ton (3560 N) hydraulic ram. Test data valueswere recorded at each load increment.

TEST RESULTSTransfer length

Short-term and long-term transfer lengths were determinedfor each beam using the beam’s concrete compression strainprofile. To reduce variations in the strain data, the data wassmoothed by averaging the strain at a point over three pointsalong the length of the beam. The following equation wasused to smooth the strain data

εi,smoothed = (1)εi 1– εi εi 1++ +

3-------------------------------------

Typical smoothed strain profiles for beams with fullybonded, 50% debonded, and 60% debonded strands areshown in Fig. 7, 8, and 9, respectively. While only onetransfer region exists at each end of the beam with only afully bonded strand, it should be noted that there are threeand four transfer regions on each end of each beamcontaining 50% and 60% debonded strands, respectively. Atransfer region exists at each location where debonding stopsand bonding between the strand and concrete starts.

The 95% average maximum strain (AMS) method wasapplied to the smoothed concrete compression strain data todetermine the transfer length in each transfer region of eachbeam. This method is described in detail in Russell andBurns.10 In this method, the AMS for the specimen wasdetermined by computing the numerical average of all of thecompressive strains contained within the plateau region ofthe strain profile at the end of the beam. A line correspondingto 95% of the AMS was drawn. For fully bonded strand, thetransfer length was selected as the distance from the end ofthe beam to the intersection of the 95% AMS line and thebeam’s strain profile. For the partially debonded strand, thetransfer length was selected as the distance from thedebonding point of that strand to the intersection of the 95%AMS line and the beam’s strain profile. The correspondingcalculated values for the experimental short-term andlong-term transfer lengths are provided in Table 3.

Effect of time and debonding on transfer lengthsThe effect that time and debonding of strands has on the

transfer length was also considered. Because of the variabilityor scatter of data typically associated with experimentalwork, average or mean values were used to look at the effectof time and debonding. As seen from Table 3, transfer

Fig. 6—Test geometry.

Fig. 7—Typical smoothed strain profile for fully bondedstrands.

Fig. 8—Typical smoothed strain profile for 50% debondedstrands.

Fig. 9—Typical smoothed strain profile for 60% debondedstrands.


lengths increased with time as well as with increases inlevels of debonding. Increases in transfer length with timerange from 8 to 12%. Also, as seen from Table 3, the transferlength is longer in beams with debonded strands. Short-termtransfer lengths for fully bonded strands increased by 12%when 60% of the strands were debonded. Long-term transferlengths for fully bonded strands increased by 8% when 60%of the strands were debonded.

Development lengthThe development length was determined for each given

beam series (L0RX, L4RX, and L6RX) by testing each of thefour beam ends from each series with incrementally shortenedstrand embedment lengths. When the failure mode changedfrom a flexural mode to a hybrid or a bond slip mode, thedevelopment length was bracketed. The development lengthfor each beam series was taken as the shortest strandembedment length at which a flexural failure mode occurred.From this definition, the development length for each of thethree beam series was determined to be 54, 96, and 114 in.(1372, 2438, and 2896 mm) from tests L0R1-3, L4R1-3, andL6R0-1, respectively. Only one bond slip failure modeoccurred: Beam Test L4R0-2. Three beams (L6R0-2, L6R1-3,and L6R1-4) failed in a hybrid mode. The hybrid mode wascharacterized by an end-slip of approximately 0.1 in. (0.25 mm)when the theoretical moment capacity of the section was

reached. It should be noted again that the strand embedmentlength for the fourth beam end tested in each series was arepeated value from a previous test in an effort to determineH-bar effects on the strand development length.

Effect of H-barsTwo identical tests were done on each of the three beam

series to evaluate the effect of the H-bars on end-slippage ofthe prestressing strands. Because the second beam in each ofthe three series (L0RX, L4RX, and L6RX) had the H-barsinstalled at only one end, these beams were tested with thesame embedment length on each end of the beam.

In the L0RX series, the length of the H-bars extendedbeyond the critical section. Because the H-bars were insidethe maximum moment region and had enough flexural bondlength beyond the critical section, they increased the beammoment capacity. Because there was no end-slip in either ofthe identical tests of this series, the effect of the H-bars onend-slip for the fully bonded strands could not be determined.

In the L4RX and L6RX series, the H-bars did not extendinto the critical section as in the L0RX series. Therefore, theH-bars were outside of the maximum moment region and didnot affect the beams’ moment capacities. The maximumend-slip reduced from 0.028 in. (0.71 mm) in Beam TestL4R1-3 to 0.005 in. (0.127 mm) in Beam Test L4R1-4 thathad the H-bars. No significant end-slip effect was observedin the L6RX series between Beam Tests L6R1-3 and L6R1-4.Another effect of the H-bars that was observed in all threeseries was that of reduced crack widths in the H-bar regions.

COMPARISON WITH CODE AND PROPOSED EQUATIONS

Transfer lengthsThe values of the short-term and long-term transfer

lengths that were experimentally determined in this projectare compared with three code values (ACI 318, AASHTO-Standard, and AASHTO-LRFD) and to two proposed equations:one by Buckner and one by Lane. All of the comparativeequations are provided in Table 4. The transfer length valuesfrom Table 3 were normalized by dividing by db, 0.6 in.(15 mm), for use in Fig. 10, 11, and 12.

Table 3—Short- and long-term transfer lengths

Beam series

First, in. Second, in. Third, in. Fourth, in. Beam end average, in.

ST LT ST LT ST LT ST LT ST LT

L0R0-1 16.0 16.5 — — — — — — 16.0 16.5

L0R0-2 18.0 22.0 — — — — — — 18.0 22.0

L0R1-3 16.5 18.5 — — — — — — 16.5 18.5

L0R1-4 15.5 18.5 — — — — — — 15.5 18.5

Mean 16.5 19.0 — — — — — — 16.5 19.0

L4R0-1 14.0 12.5 16.0 19.5 14.5 18.0 — — 15.0 16.5

L4R0-2 15.0 16.0 16.5 26.5 27.5 29.5 — — 20.0 24.0

L4R1-3 13.5 15.0 20.0 19.5 30.5 28.5 — — 21.5 21.0

L4R1-4 17.0 16.5 * * * * — — 17.0 16.5

Mean 15.0 15.0 17.5 22.0 24.0 25.5 — — 18.5 20.0

L6R0-1 16.5 15.0 17.5 18.5 27.5 30.0 19.5 18.5 20.5 20.5

L6R0-2 19.5 18.5 24.0 24.0 21.5 20.5 16.0 21.0 20.5 21.0

L6R1-3 17.5 14.5 23.5 23.5 16.0 19.5 14.5 22.0 18.0 20.0

L6R1-4 14.0 16.5 21.0 23.0 24.5 22.0 20.0 20.0 20.0 20.5

Mean 17.0 15.0 21.5 21.0 22.5 23.0 17.5 20.0 19.5 20.5*Transfer length could not be calculated because of erratic strain profile.

Fig. 10—Comparison of short- and long-term transferlengths with code values.

ACI Structural Journal/May-June 2005 427

Short-term and long-term experimentally determinedtransfer lengths for each beam series are compared with codevalues in Fig. 10. It can be seen that only one short-termtransfer length exceeds the current ACI and AASHTO-Standard code values of 50db. This occurred in the thirdtransfer region of Beam L4R1-3 where the transfer length of30.5 in. (775 mm) exceeds the code requirement by 1.6%.There were two other transfer lengths—one short-term andone long-term—that had values of 30 in. (762 mm), exactlymatching the code requirement of 50db. It can also be seen inFig. 10 that no transfer length values, short-term or long-term,reached or exceeded the AASHTO-LRFD code requirementof 60db. Short-term and long-term experimentally determinedtransfer length values are compared with values predicted byBuckner’s equation in Fig. 11. No experimentally determinedtransfer lengths exceed Buckner’s predicted values. Also,short-term and long-term experimentally determinedtransfer length values are compared with values predicted byLane’s equation in Fig. 12. It can be seen that no experi-mentally determined transfer lengths exceed Lane’spredicted values. It should be noted that Lane’s equationyielded very conservative results.

Development lengthsThe development lengths were selected for Beam Series

L0RX, L4RX, and L6RX as 54, 96, and 114 in. (1372, 2438,and 2896 mm), respectively, as discussed previously. Theexperimentally determined and equation-predicted values ofthe development length for each beam series are provided inTable 5.

The development lengths for Beam Series L0RX aspredicted by the three equations are significantly longer thanthe value experimentally determined, as seen in Table 5.This shows that all three equations yield fairly conservativepredictions with regard to development length for fullybonded strands. The development lengths for the BeamSeries L4RX and L6RX as predicted by the three equationshave mixed results when compared with the values experi-mentally determined in this project. The code equations forfully bonded strand overpredict the development lengthsdetermined in this portion of the project. The limited data inthis portion of the project indicates that debonding some ofthe strands increases the development length of the strand. Itappears, however, that the current code factor of 2 is overlyconservative. With respect to Beam Series L4RX and L6RX,both the Buckner and the Lane equations again yieldconservative development length values for beams withsome percentage of debonded strands. Both the Buckner andthe Lane equations yield less conservative results as thepercentage of debonded strands increases.

CONCLUSIONSAverage short-term transfer lengths increased by 15, 8,

and 5% over time for Beam Series L0RX, L4RX, and L6RX,respectively. Also, average values of both short- and long-termtransfer lengths for each beam series increased as the numberof debonded strands increased. Average values of short-termtransfer lengths for fully bonded strands increased by 12 and18% as 50 and 60% of the strands were debonded, respectively.Average values of long-term transfer lengths for fullybonded strands increased by 5 and 8% as 50 and 60% of thestrands were debonded, respectively.

All individual short- and long-term transfer length valuesthat were experimentally determined were compared with

Fig. 11—Comparison of short- and long-term transferlength with Buckner equation.

Fig. 12—Comparison of short- and long-term transferlengths with Lane equation.

Table 4—Equations used to compare with measured data

Author Transfer length Development length

ACI 318AASHTO Standard

AASHTO-LRFD

Lt = 60db

Lane

Buckner

Ld = Lt + λ(fps – fse)db 1.0 ≤ λ ≤ 2.0

λ = (0.6 + 40εps) or

(0.72 + 0.102 )

Ltfse

3-----db 50db≈=

Ld Lt fps fse–( )db=

fps23--- fse–

db=

Ld fps23--- fse–

db=

Lt4fpt

f ′c--------db 5–= Ld Lt

6.4 fps fse–( )db

f ′c----------------------------------- 15+=

Lt1250fsi

Ec

-----------------db=

fsi

3----db≈

β1

ωp

------

Table 5—Comparison of development lengths

Beam series

Experimental ld, in.

Code Buckner Lane

ld, in. Ratio* ld, in. Ratio* ld, in. Ratio*

L0RX 54 94 0.57 160 0.34 171 0.32

L4RX 96 94† 1.02 159 0.60 183 0.52

L6RX 114 96† 1.19 164 0.70 129 0.88

*Ratio = ld,exp./ld,predicted.†Code requires equation values to be doubled for debonded strand.


code requirements for ACI-318, AASHTO-Standard, andAASHTO-LRFD. Only one short-term transfer length valueexceeded the 50db requirement. None of the short-termtransfer length values exceeded the 60db requirement. Also,none of the long-term transfer length values exceeded eitherthe 50db or 60db requirements.

All individual short- and long-term transfer length valuesthat were experimentally determined were compared withthose predicted by the Buckner and the Lane equations.None of the short- or long-term transfer length valuesexceeded the value predicted by the Buckner or the Laneequations. The Lane equation, however, was shown to beextremely conservative.

The development lengths from this project were comparedwith the requirements of the three codes (ACI 318,AASHTO-Standard, and AASHTO-LRFD). Beam SeriesL0RX had a development length that was 57% of the coderequirement. This would indicate that the code requirementfor a fully bonded strand is adequate and that the additionalFHWA requirement to increase the code value by 1.6 is notnecessary. The experimentally determined development lengthvalues for Beam Series L4RX and L6RX, which containeddebonded strand, are 51 and 59% of the code requirement,respectively. This indicates that some lengthening of the devel-opment length for debonded strands is necessary, but that thecurrent code requirement of doubling may be too conservative.

The development lengths determined in this project werecompared with values predicted by the Buckner and the Laneequations. The development length values that were experi-mentally determined in this project are 34, 60, and 70% ofthe values predicted by the Buckner equation and 32, 52, and88% of the values predicted by the Lane equation for SeriesL0RX, L4RX, and L6RX, respectively. This indicates thatthe Buckner and the Lane equations are very conservativefor fully bonded strands and decreasingly conservative forbeams containing debonded strands.

Two identical tests were done on each of the three beamseries to evaluate the effect of additional hairpin-shapedreinforcing bars, H-bars, that were installed in only one endof the beam in its lower web region. In all three beam series,smaller crack widths were observed in the H-bar region ofthe beams that contained the H-bars. No strand end-slip wasobserved in the L0RX beam series. The maximum end-slip wasreduced from 0.028 to 0.005 in. (0.71 to 0.127 mm) in the L4RXbeam series, indicating some possible H-bar benefit. No signif-icant end-slip effect was observed in the L6RX beam series.

ACKNOWLEDGMENTSThe authors gratefully acknowledge the support of N. Burns and R. Barnes

from University of Texas-Austin (UT-Austin) for their cooperation and supportin this project. We also thank H. L. Jobson, J. W. Grove, J. H. Kilgore, andU. Tuladar from UT-Austin for their help in reading data at the Texas Con-crete Plant in Victoria, Tex. We also want to thank the people at the TexasConcrete Co. in Victoria, Tex., for their cooperation and contribution to thisproject.

NOTATIONa = distance to provide constant moment region between two loader

beam load pointsdb = diameter of prestressing steel, in.Ec = modulus of elasticity of concrete, ksif ′c = concrete compressive strength at 28 days, ksifps = stress in prestress strand at nominal strength, ksifpt = initial stress in prestressing steel prior to transfer, ksifse = effective stress in prestress strand after all losses, ksifsi = initial stress in prestressing steel, immediately after release, ksiLe = embedment length of prestressing strand Ls = beam spanLub = unbonded length of prestressing strandεi = measured concrete strain data

REFERENCES1. Federal Highway Administration (FWHA), “Memorandum,” FHWA,

Washington, D.C., Oct. 26, 1988.2. Federal Highway Administration (FWHA), “Memorandum,” FHWA,

Washington, D.C., May 8, 1996.3. ACI Committee 318, “”Building Code Requirements for Structural

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