Twenty-two precast, pretensioned concrete beams

Transcription

1 nfluence of Hgh Strength Concrete on Transfer and Development Length of Pretensonng Strand Wllam D. Cook, Ph.D. Research Engneer Department of Cvl Engneerng and Appled Mechancs McGll Unversty Montreal, Quebec, Canada Dens Mtchell, Ph.D., P.Eng. Department of Cvl Engneerng and Appled Mechancs McGll Unversty Montreal, Quebec, Canada Arshad A. Khan Ph.D. Canddate Department of Cvl Engneerng and Appled Mechancs McGll Unversty Montreal, Quebec, Canada Thomas Tham Cvl Engneer Group Consultants Sabah, Malaysa Twenty-two precast, pretensoned concrete beam specmens were fabrcated and tested to determne the nfluence of concrete strength on the transfer length and development length of pretensonng strand. The man varables were the concrete compressve strength, wth f~, at 28 days, varyng from 45 to 12,9 ps (31 to 89 MPa), and the strand dameter, whch ncluded%,!1 and.62 n. (9.5, 12.7 and mm) dameters. Expressons are gven for the nfluence of concrete strength on the transfer length and development length of pretensonng strand. Twenty-two precast, pretensoned concrete beams were fabrcated and tested n order to expermentally determne the nfluence of concrete strength on the transfer length and development length of pretensonng strand. The prme varables were the concrete strength and the strand dameter. The concrete compressve strengths vared from 35 to 725 ps (21 to 5 MPa) at transfer and from 45 to 12,9 ps (31 to 89 MPa) at the tme of testng. The strand dameters nvestgated were %,!1 and.62 n. (9.5, 12.7 and 15.7 mm). Fg. 1 llustrates the varaton n the stress n the strand along the embedment length of the strand as assumed by the AC Buldng Code.' The dstance from the end of the member over whch the stress n the strand bulds up to the effectve stress, f se s called the transfer length, l" of the strand. The transfer length s gven n the AC Code as: 52 PC JOURNAL

2 Usng ks and n. unts: = fse d t 3 b (la) Usng MPa and mm unts: where t=.48fsedb (lb) t = transfer length fse = effectve stress n prestressed renforcement after allowance for all prestress losses db = nomnal dameter of prestressng strand The AC Code permts the desgner to use a smplfed expresson for transfer length when calculatng stress lmts n the concrete near the end of a member and when determnng the nomnal shear strength of a member. For these purposes, t may be assumed that the transfer length s 5 db. Fg. l shows the flexural bond length over whch the stress n the strand bulds up from fse to the stress, fps at nomnal strength of the member. The AC Code 1 uses a flexural bond length, lfb, of: Usng ks and n. unts: Usng MPa and mm unts: where lfb = flexural bond length fps = stress n prestressed renforcement at nomnal strength The development length, ld, s the sum of the transfer and flexural bond length, that s: (3) These formulatons frst appeared n the 1963 AC Code' and were adopted n the 1983 AASHTO Specfcatons. 3 These equatons were based on the transfer length test results of Kaar, LaFraugh and Mass and on the flexural bond studes carred out by Hanson and Kaar. 5 These earler studes used stress-releved strand wth an ultmate strength, fpu of 25 ks (172 MPa) whch was typcally tensoned to about PC JOURNAL (/) (/) ~ fse... (/) Q) Q)... (/) ft Dstance from free end Fg. 1. Development of stress n pretensoned strand.'.7fpu n the bed. These tests had concrete strengths whch are consderably lower than some of the hgher strength concretes used today and few tests were done on strands havng dameters larger than.5 n. (12.7 mm). There s concern that the earler research on transfer and development of strand may not be applcable to current practce. Currently, a great deal of low-relaxaton strand, wth fpu of 27 ks (186 MPa), s used wth a hgher bed stress (up to.8 fpu), and n some cases larger dameter strand s used. An addtonal factor whch would nfluence the transfer and development length of strand s the use of hgh strength concrete. n 1988, the Federal Hghway Admnstraton ssued a memorandum whch dsallowed the use of.6 n. (15.2 mm) dameter strand n pretensoned applcatons and ntroduced a factor of 1.6 on the AC and AASHTO development length expressons. Ths memorandum 6 was ssued due to concern over the lack of expermental results for.6 n. (15.2 mm) dameter strand and because research 7 ndcated that the development length of uncoated, low-relaxaton strand, wth an ultmate strength of 27 ks (186 MPa), was greater than that predcted by the equatons n the AASHTO Specfcatons. 3 Research s needed to nvestgate the nfluence of strand dameter, strand type and concrete strength on the requred transfer and development lengths. PREVOUS RESEARCH A bref summary of prevous research s gven here, hghlghtng some of the mportant parameters and ther nfluence on the transfer and development lengths: 1. An ncrease n strand dameter results n both a longer transfer length and a longer development length. These lengths have typcally been assumed to be proportonal to the strand dameter, db [see Eqs. (1), (2) and (3)]. 2. n 1963, before the advent of very hgh strength concrete, Kaar, LaFraugh, and Mass concluded that concrete strength had lttle nfluence on transfer lengths. n ths seres of tests, the concrete strengths vared from 166 to 5 ps (11.4 to 34.5 MPa). 3. An ncrease n the strand stress, fse after all losses, results n a longer transfer length, 1 1, but a shorter flexural bond length, lfb [see Eqs. (1) and (2)]. 4. The manner n whch the strand s released at transfer s a major factor n determnng the transfer length. Flame-cuttng the strands results n transfer lengths of about 6 to 3 percent greater than that determned for smlar strands released gradually.' Due to long-term effects, the transfer length ncreases wth tme. 53

3 Table 1. Transfer lengths determned from concrete strans on sde face of beam at level of strand. t at release t at 21 days b h db n. n. n. Specmen (mm) (mm) (mm) f~ fpbed fp End A EndB ps ks ks n. n. (MPa) (MPa) (MPa) (mm) (mm) End A n. (mm) EndB n. (mm) 9.5/ /8 (1) (2) (9.5) (21) (1271) (1219) (56) 19.9 (56) - 9.5/ /8 (1) (2) (9.5) 9.5/ /8 (1) (2) (9.5) (27) (1285) (124) (482) (584) (27) (1285) (124) (482) (381) (584) (482) (482) (584) 9.5/ /8 (1) (2) (9.5) /8 (1) (2) (9.5) (48) (1225) (1192) (33) (5) (1264) (123) (34) (46)! (34) (46) 9.5/ /8 (1) (2) (9.5) (5) (1264) (123) (46) (34) (46) (34) 9.5/ /8 (1) (2) (9.5) (5) (1267) (1234) (415) (313) (415) (313) 9.5/ /8 (1) (2) (9.5) (5) (1267) (1234) (419) (317) (419) (419) 13/ l/2 (15) (225) (12.7) 13/ l/2 (1) (2) (12.7) (21) (1442) (1374) (71) (27) (1298) (1217) (584) (584) (811) (584) (584) 13/ l/2 (1) (2) (12.7) (27) (1298) (1217) (584) (584) (584) (685) 13/ l/2 (15) (225) (12.7) (48) (1358) (1315) (56) (56) 13/ l/2 (1) (2) (12.7) (5) (1367) (133) (57) (432) (57) (534) 13/ /2 (1) (2) (12.7) 13/ /2 (125) (175) (12.7) (5) (1367) (133) (33) (45) (5) (1382) (1329) (387) (387) (43) (57) (489) (489) 13/ l/2 (125) (175) (12.7) (5) (1382) (1329) (495) (495) (495) (495) 16/ (2) (25) (15.7) (21) (1286) (122) (735) (872) (836) 16/ (2) (25) (15.7) (21) (1286) (122) (79) (768) (912) (97) 16/ (2) (25) (15.7) (48) (1218) (1176) (528) (427) (528) (427) 16/ (2) (25) (15.7) 16/89-975* (125) (175) (15.7) 16/89-675* (125) (175) (15.7) 3/8 m. (9.5 mm) strand, stress reheved, fpu = 263 ks1 (1813 MPa) 1/2 n. (12.7 mm) strand, low relaxaton, fpu = 276 ks (193 MPa).62 n. (15.7 mm) strand, low relaxaton, fpu = 26 ks (1793 MPa) *The low values of fpbed and fp were due to problems durng stressng., (48) (1218) (1176) (536) (435) (5) (922) (871) (36) (36) (5) (922) (871) (465) (465) j_ (536) (435) (48) (345) 54 PC JOURNAL

4 After a year, the ncrease n transfer length s about 6 percent, 4 1 although ncreases as hgh as 2 percent have been reported n 1977, Za and Mostafa 12 concluded that transfer length s a functon of the ntal stress n the strand and the concrete strength at the tme of transfer. 7. The surface condton of the strand plays a sgnfcant role n determnng the bond characterstcs. Lghtly rusted strand gves shorter transfer lengths than smooth, untreated strand. t3.t4.ts 8. Strand havng epoxy coatng, wthout grt, has lttle or no bond to the concrete. The use of epoxy coatngs mpregnated wth grt mproves the bond characterstcs and, hence, reduces the transfer and development lengthsy 6 More complete lterature revews on the factors nfluencng transfer and development lengths are gven by Cousns et al.9 16 and by Deatherage and Burdette. 17 -e:l ~ ~ ~ ~ ~ ~ ~ ~ ~- ~~" (a) Stran gages on strand 4 n. (1 mm) typ. (b) Stran targets on concrete surface 2 n. b (5 mm) dal gage --'--== , ;:;;wo~ 1/2 ln. (13 mm) ~'- thck x 4 n. (1 mm) long bearng pad (c) Testng setup Fg. 2. Detals of test specmens. TEST PROGRAM Table 1 and Fg. 2 gve the detals of the beam specmens tested. The specmen labels start wth a number ndcatng the metrc sze desgnaton of the strand, followed by a number ndcatng the concrete strength at the tme of testng, n megapascals (MPa), and a number ndcatng the embedment length n mllmeters (mm). For all specmens, the center of the strand was located 2 n. (5 mm) above the bottom face. n 18 of the test specmens, the strand was nstrumented wth electrcal resstance stran gauges to montor the strans n the strand. Concrete targets, glued to the sde faces of the beams, at the level of the strand, enabled the concrete surface stran varaton to be determned, permttng an assessment of the transfer length. The strands were released n a gradual manner by slowly reducng the pressure n the hydraulc stressng rams. Stran measurements were taken before release, just after release and just before testng to determne the transfer lengths. Surface stran measurements were also taken durng the loadng of PC JOURNAL Table 2. Mx desgns for concrete. ~~ Batch No. ps (MPa) Components 1 45 (31) Cement (Type 3) (43) Sand Aggregate (5-2 mm) Water Water reducng admxtures Ar entranng agent Water-cement rato (65) Cement+ slca fume* 4 1,88 (75) Sand Aggregate (5-1 mm) Water Water reducng admxtures Superplastczer Water-cement rato 5 12,9 (89) Cement+ slca fume* Sand Aggregate ( mm) Water Water reducng admxtures Superplastczer Water-cement rato * Blended cement contanng 7 percent slca fume. Quanttes 691 lb/yd' ( 41 kg/m') 1264lb/yd' (75 kg/m') 1719lb/yd' (12 kg/m') 287 lb/yd' (17 kg/m') 2.17 lb/yd' ( lm').43 lb/yd' (.26 lm') lb/yd' (56 kg/m') 1337 lb/yd' (793 kg/m') 1711lb/yd' (115 kg/m') 212lb/yd' (126 kg/m') 2.2 lb/yd' ( 1.35 lm') 12.6lb/yd' (7.5 lm') lb/yd 3 (5 kg/m') b/yd' (69 kg/m') b/yd' (118 kg/m') 199lb/yd' (118 kg/m') 2.521b/yd' (1.5 lm') 17.91b/yd' (1.611m').26 55

5 the specmens to enable the determnaton of curvatures (see Fg. 2b). The testng of each beam was carred out wth ether a sngle-pont load or wth two-pont loads, as shown n Fg. 2c. The embedment length, le, s the dstance from the end of the beam to the locaton of the frst pont load. Each specmen was supported on 4 n. ( 1 mm) long, ~n. (13 mm) thck neoprene bearng pads at each end. Durng the loadng, the deflectons of the beams were measured by lnear voltage dfferental transducers at the loadng ponts and at the supports. Dal gauges at each end of the beam measured the slp of the strand relatve to the end of the beam. At each load stage, the crack wdths at the level of the strand were measured. The mx desgns for the three types of concrete are gven n Tablle 2. Batches 1 and 2 were steam cured for 18 hours, whle Batches 3, 4 and 5 were most-cured for 2 hours. The hgher strength concretes (Batches 3, 4 and 5) dd not requre steam curng to reach the desred 24-hour release strength. The prestressng wa:; released at an age of 24 hours, except for the specmens cast wth concrete from Batch 2; that prestressng was released at 48 hours. The varatons of concrete strength, wth tme for the dfferent batches of concrete,. are shown n Fg. 3. The Ys n. (9.5 mm) dameter stressreleved strand had an ultmate strength of 263 ks (1813 MPa) and the strand was slghtly rusted. The low-relaxaton Yz n. (12. 7 mm) and.62 n. (15.7 mm) dameter strands had ultmate strengths of 276 and 26 ks ( 193 and 1793 MPa), respectvely, and both szes had smooth, untreated surfaces. The load-stran relatonshps for the three types of strands used n ths study are shown n Fg. 4. RESULTS OF TRANSFER TESTS The transfer length was defned as the dstance from the end of the beam to the pont at whch the stran n the concrete becomes essentally unform. n order to determne the transfer length from the stran readngs, a ,9 ps {89 MPa) * 1,88 ps {75 MPa) 12 -* ps (65 MPa) a... 6 () 8 ~ 624 ps {43 MPa) ~ 4 --~---~ ~ ps (31 MPa) Age, days Fg. 3. Varaton of concrete compressve strength wth tme n. (15.7 mm) 2 z ~ ~ / / 1/2 n. (12.7 mm) 15 / 3 "' "' /8 n. (9.5 mm) x1-3 Stran Fg. 4. Measured load-stran relatonshps for strand ~ ~ () Q. slope-ntercept method' 7 was used. The transfer length s determned as the dstance from the end of the beam to the pont of ntersecton of a lne fttng the stran values n the transfer regon wth a horzontal lne representatve of the stran values beyond ths regon. Fg. 5 shows the varaton of measured concrete surface strans, at the level of the strand, for Specmens 9.5/31-12 and 9.5/89-825, both contanng Ys n. (9.5 mm) dameter strand. These specmens have concrete compressve strengths at transfer of 3 and 731 ps (21 and 5 MPa), respectvely. As can be seen from ths fgure, the transfer length at release s reduced from 19.9 to 16.3 n. (56 to 415 mm) as the concrete strength at transfer s ncreased from 3 to 731 ps (21 to 5 MPa). The varaton of measured concrete strans at 25 and 2 days after transfer s also shown n Fg. 5. At the ends of the beams, the concrete strans have ncreased by an amount equal to the shrnkage stran that occurred durng PC JOURNAL

6 n c (/).. (,) ::E -4-2 release Specmen 9.5/ Dstance from free end, mm n c -6.. Specmen 9.5/ (/) 2 days.. (,) -4 ::E -2 release Dstance from free end, mm Fg. 5. Measured concrete surface strans for Specmen 9.5/31-12, /~; = 3 ps (21 MPa) and Specmen 9.5/89-825, /~; = 731 ps (5 MPa). the 25- and 2-day nterval. Away from the ends, the ncrease n stran after release s due to the combned effect of creep, shrnkage and relaxaton of the prestressng strand. An ncrease n the concrete strength gves smaller transfer lengths, as shown n Fg. 5, due to the mproved bond characterstcs. n addton, a hgher strength concrete also has a larger modulus of elastcty, smaller shrnkage strans after release and lower creep strans. These effects gve smaller elastc shortenng losses and smaller long-term losses, whch result PC JOURNAL n larger long-term prestressng stresses. Table summarzes the transfer lengths obtaned at the ends of each specmen, both at release and at 21 days after transfer. For the lower concrete strengths, the average transfer lengths at release were 53 db, 55 db and 49 db for the Ys, Y, and.62 n. (9.5, 12.7 and 15.7 mm) dameter strands, respectvely. To derve an expresson for the transfer length whch accounts for the concrete strength, one must realze that there are some nconsstences n Eq. (1). Za and Mostafa 12 ponted out that the transfer length should be a functon of the concrete strength at the tme of transfer, rather than the 28-day strength and should also be a functon of the stress n the strand mmedately after transfer, fp rather than the stress n the strand after all losses, fse Fg. 6 llustrates the reducton of the average transfer lengths wth ncreasng concrete strength, for the dfferent strand szes nvestgated. n these plots, the transfer length has been dvded by fp; n order to account for the dfferent levels of stress n the prestressng strand. Also shown n Fg. 6 are the values of 1 1 /fp; predcted by the followng expresson: Usng ks and n. unts: Usng MPa and mm unts: (4a) n ths expresson, whch s a modfed form of Eq. (1), fse has been replaced by fp; and the square root functon s a correcton factor to account for the nfluence of concrete strength at transfer. As can be seen from Fg. 6, ths expresson s approprate for the range of concrete strengths and strand dameters nvestgated. t must be noted that, for these tests, the strands were released n a gradual manner. RESULTS OF DEVELOPMENT LENGTH TESTS Table 3 summarzes the results of testng the 22 beams wth 34 dfferent embedment lengths, subjected to ether sngle-pont or two-pont loadng. The strand embedment length, le, s measured from the end of the specmen to the closest pont load. The values of fse correspond to the stress n the prestressng steel at the tme of testng each specmen. Also gven n Table 3 are the observed modes of falure for each specmen. n some cases, a small slp was observed at the end of the strand pror 57

7 to flexural crushng, but ths was not ks consdered to be a bond falure. The 1. specmens whch faled by frst ex- 3/8 n. (9.5 mm) strand D 21 days hbtng sgnfcant strand slp, followed by a premature falure n ether.8 - release a shear or flexure, were classfed as :::!!: bond falures...._.6 -.::1...._ Fg. 7 shows the appearance of three E E c specmens at falure and the change of ' falure modes as the embedment a..4 - Equaton ( 4) -.1 a. length s ncreased. All three spec- '+- '+mens contaned.62 n. (15.7 mm) d- ' = '-... ~ ~ ameter strand and had a concrete com-.2 - pressve strength of 45 ps (31 MPa), but each had a dfferent embed-. J. ment length [59.1, 7.9 and 73.4 n (15, 18 and 1865 mm)]. Concrete st1 ength at transfer, MPa Specmen 16/31-15 faled n shear that was ntated by a bond falure, as can be seen from the nclned 1. shear crack to the left of the loadng ks pont. Specmen 16/31-18 faled at a flexure-shear crack to the rght of one 1/2 n. (12.7 mm) strand D 21 days of the pont loads after strand slp had.8 release occurred on the rght-hand sde of the a...2 beam. Specmen 16/ faled by :::!!:..._ ' ' ' flexural crushng after a small strand.::1. E.6..._ slp of.3 n. (.8 mm) was mea- E Equaton (4) c sured at the rght-hand end of the a..4 specmen..1 a Fg. 8 shows the strans measured ~ '-... by the stran gauges glued to the pre- Q/ ~.2 stressng strand n Specmen 16/ , whch contaned.62 n. (15.7 mm) strand, had a concrete compres sve strength of 45 ps (31 MPa) and had an embedment length of 73.4 n. Concrete strength at transfer, MPa (1865 mm). t can be seen that there s a sgnfcant stran ncrease n the strand n the central regon of the 2 3 ~ ks beam near the appled load. There s 1. also a small ncrease n stran n the.62 n. (15.7 mm) strand D 21 days transfer length porton on the rght- " hand end of the specmen, where a.8 " ' release small strand slp was recorded near a...2 :::!!: falure. The maxmum measured..._.6.::1. strand stran s.187, whch corre- E..._ sponds to a stress n the strand of 249 E c Equaton ( 4) ks ( 1716 MPa). Ths specmen faled a..4.1 a. by flexural crushng at a maxmum '+- '+moment of 34.4 ft-kps (46.6 kn-m). ~ '-... Q/ or Fg. 8 also shows the dstrbuton of.2 steel strans measured n Specmen 16/65-115, whch contaned.62 n... (15.7 mm) strand, had a concrete com pressve strength of 943 ps (65 MPa) Concrete strength at transfer, MPa and had an embedment length of 45.3 n. (115 mm). Ths specmen faled Fg. 6. Average transfer length vs. concrete strength at tme of transfer and at 21 days. by flexural crushng and developed a 58 PC JOURNAL

8 Table 3. Development length tests. db ~~ le b n. ps n. n. Specmen (mm) (MPa) (mm) (mm) 9.5/ / (9.5) (31) (12) (1) 9.5/ / ! 3.9 (9.5) (31) (11) (1) 9.5/ / (9.5) (43) (135) (1) 9.5/43-1 3/ (9.5) (43) (1) 1 (1) 9.5/65-8 3/ (9.5) (65) (8) (1) 9.5/ / (9.5) (65) (725) (1) 9.5/ /8 1, (9.5) (75)! (95) (1) 9.5/75-7 3/8 1, (9.5) (75) (7) (1) 9.5/ /8 12, (9.5) (89) (825) (1) 9.5/ /8 12, ! (9.5) (89) (575) (1) 13/ / (12.7) (31) (125) (!5) 13/ / (12.7) (31) (12) (!5) 13/ / (12.7) (31) (11)! (!5) 13/ / (12.7) (43) (16) (1) 13/ / (12.7) (43) (125) (1) 13/ / (12.7) (65) (85) (15) 13/65-7 1/ (12.7) (65) (7) (!5) 13/ / (12.7) (65) (65) (15) 13/ /2 1, (12.7) (75) (lloo) (1) 13/ /2 1, (12.7) (75) (95) (1) 13/ /2 12, (12.7) (89) (95) (125) 13/ /2 12, (12.7) (89) (65) (125) 16/ (15.7) (31) (1865) (2) 16/ (15.7) (31) (18) (2) 16/ (15.7) (31) (165) (2) 16/ (15.7) (31) (15) (2) 16/ (15.7) (65) (115) (2) 16/ (15.7) (65) (15) (2) 16/ (15.7) (65) (95) (2) 16/ (15.7) (65) (8) (2) 16/ (15.7) (65)! (7) (2) 16/ (15.7) (65) (725) (2) 16/ , (15.7) (89) (975) (125) 16/ , (15.7) (89) (675) (125) * D md1cates double-pont loadng, S ndcates sngle-pont loadng. 3/8 n. (9.5 mm) strand, stress releved, fpu = 263 ks (1813 MPa). 1/2 n. (12.7 mm) strand, low relaxaton, fpu = 276 ks (193 MPa)..62 n. (15.7 mm) strand, low relaxaton, fpu = 26 ks (1793 MPa). ' h fse n. Age ks l Loadng (mm) days (MPa) type* Falure mode !57 D Flexural crushng (2) (185) !57 D Small slp- flexural crushng (2) (185) 7.9 3!59 D Flexural crushng (2) (195) !59 D Slp- bond/flexure/shear (2) (195) D Flexural crushng (2) (lll7) D Flexural crushng (2) (1117) D Flexural crushng (2) (124) D Slp- flexural crushng (2) (1136) D Flexural crushng (2) (1175)!' D Flexural crushng (2) (1177) D Flexural crushng (225) (1254) s Slp- bond/flexure/shear (225) (1254) D Slp - bond/flexure/shear (225) (1254) !51 D Flexural crushng (2) (144) D Flexural crushng (2) (128) D Flexural crushng (225) (1254) s Flexural crushng (225) ' (1254) !82 s Slp - flexural crushng (225) (1254) ' D Flexural crushng (2) (1153) !69 D Flexural crushng (2) (1167) !85 D Flexural crushng (175) (1278) !84 D Slp - bond/flexure/shear (175) (1272) ~~ s Small slp- flexural crushng (25) (126) !53 D Slp - bond/flexure/shear (25) (156) 9.8 4!53 D Slp - bond/flexure/shear (25) (156) s Slp- bond/shear (25) (186) D Flexural crushng (25) (198) !59 D Flexural crushng (25) (197) !59 s Flexural crushng (25) (197) s Flexural crushng (25) (197) !59 s Slp - flexural crushng (25) (196) !59 s Slp - bond/flexure/shear (25) (196) D Slp -bond/shear (175) (832) D Slp- bond/flexure/shear (175) (838) -

9 Fg. 7. Appearance of specmens wth.62 n. (15.7 mm) dameter strand havng embedment lengths of 59.1 n. (15 mm) (top), 7.9 n. (18 mm) (mddle) and 73.4 n. (1865 mm) (bottom). maxmum stran n the prestressng strand of.22, whch corresponds to a stress of251 ks (1732 MPa). A comparson of the dstrbutons for the two specmens shown n Fg. 8 llustrates the dfferences n behavor due to the nfluence of concrete strength. An ncrease n concrete strength from 45 to 943 ps (31 to 65 MPa) has resulted n a smaller transfer length, larger values of fseo a smaller development length and a hgher flexural capacty. Fgs. 9 and 1 show the appearance of two pars of specmens at falure. n both of these fgures, the top specmen has a concrete compressve strength of 943 ps (65 MPa) and the bottom specmen has a concrete compressve strength of 45 ps (31 MPa). All four of the specmens n these two fgures faled by flexural crushng. The ncreased concrete compressve strength results n much shorter embedment lengths needed to develop the strand and, as can be seen from Fgs. 9 and 1, results n a sgnfcantly smaller concrete compresson zone, as s evdent from the larger depth of flexural cracks. Fg. 11 shows the varaton of prestressng stress at ultmate determned from the stran gauges on the strands of Specmens 16/ and 16/ As can be seen, the ncrease n the concrete strength results n hgher steel stresses, fps beng developed for a gven embedment length. Also shown n ths fgure s the varaton of steel stress predcted by the AC Code.' The AC Code predcts the 6 stress development very well for the specmen havng a concrete compressve strength of 45 ps (31 MPa), but does not account for the benefcal effects of the hgher strength concrete. Table 4 presents a comparson of the expermental falure moments wth predctons usng the AC Code expressons' and usng the computer program, RESPONSE.' 8 Ths program uses a stran compatblty approach together wth complete stress-stran relatonshps for the prestressng strand and the dfferent strength concretes. Also gven n Table 4 are the strand stresses at flexural ultmate predcted by these two methods. As ndcated, those specmens whch faled n flexure attaned capactes exceedng the predcted capactes. The expermentally determned flexural capactes, M, 11 were calculated based on span lengths measured to the quarter ponts of the 4 n. (1 mm) long neoprene bearng pads. Fg. 12 shows the development of strand stress for specmens whch were just able to reach flexural crushng wthout bond falure. The development of stress has been dealzed by a transfer length porton and a flexural bond length porton. n the transfer length, the steel stress vares from zero at the end of the beam to the expermentally determned value of fse at a dstance of l, from the end of the beam. The flexural bond length porton was determned usng the values of fps predcted by the AC Code expresson and the specmen embedment length, le. Also shown are the predcted varatons of strand stress accordng to the followng expresson: Usng ks and n. unts: f"j ld =.33fpdb -, + ~ fc (fps- fse)dbt (Sa) Usng MPa and mm unts: Ths expresson for development length assumes that, for a gven strand dameter, the transfer length component s a functon of fp; and the concrete compressve strength at the tme of transfer, f~; The expresson also assumes that the flexural bond length component, lfb, s a functon of the requred stress ncrease n the strand, fps - fse as well as the concrete compressve strength,.f~. As shown n Fgs. 11 and 12, Eq. (5) provdes a conservatve expresson for determnng the steel stress n the strand for the specmens tested. Also shown n Fg. 12 are the strand stresses predcted by the AC Code expresson. The AC Code equaton s not conservatve n the transfer length component for the lower strength concretes and does not account for the benefcal effects of hgh strength concretes. PC JOURNAL

10 [ [ r r: 1r~ ~ } n. 24 Specmen Mmld, ft-kp 16/ (knm) 2 G-B-El ~ c G---e--- ) !... /!r-& !... (.) ::::E Dstance along beam, mm [ ~ ~,,( ( ( \ {.'"\ J n. 24 Specmen Mmld, 16/ :ft kp (knm) 2 G-B-El: ~: ~: c G---e--- ) : !... /!r-&--6: !... (.) ::::E 8 used, or the followng smpler, more conservatve expresson for the transfer length, can be used: Usng ks and n. unts: :T 1 1 = 5db \: ~:-, (6a) ' let Usng MPa and mm unts: l =SOd t 2 b \: E', let (6b) Snce ths expresson typcally results n shorter transfer lengths than the more complete expresson gven by Eq. (4), t can be conservatvely used for checkng stresses n the concrete at transfer, but should not be used to calculate the transfer length component of the development length. Development Length The followng proposed expresson for the development length of pretensonng strand s a modfcaton of the AC Code development length expresson: Usng ks and n. unts: Usng MPa and mm unts: Dstance along beam, mm Fg. 8. Measured strans n strand for Specmens 16/ and 16/ DESGN RECOMMENDATONS Transfer Length for Servce Stress Checks t must be noted that the transfer length s used n two dstnct stages n the desgn process. The frst stage, nvolvng checkng the stresses near the PC JOURNAL ends of the member, s typcally more crtcal for shorter transfer lengths. The second stage, nvolvng checkng the flexural strength and shear strength, s a functon of the development of stress n the strand, and hence s more crtcal for longer transfer and flexural development lengths. n checkng stresses mmedately after transfer, ether Eq. ( 4) can be The transfer length and flexural bond length components of ths development length expresson nclude factors whch account for the concrete compressve strength, both at transfer and n servce, for the case n whch the strands are released gradually. EXAMPLE CALCULATONS Consder a standard precast sngle tee (ST36) pretensoned wth fourteen Yz n. (12.7 mm) low-relaxaton strands wth an ultmate stress of 27 ks ( 186 MPa). The eccentrcty of the prestressng s 18. n. (457 mm). The 61

11 Fg. 9. Appearance of specmens wth % n. (9.5 mm) dameter strand havng concrete compressve strengths of 943 ps (65 MPa) (top) and 45 ps (31 MPa) (bottom), both falng by flexural crushng. Fg. 1. Appearance of specmens wth.62 n. (16 mm) dameter strand havng concrete compressve strengths of 943 ps (65 MPa) (top) and 45 ps (31 MPa) (bottom), both falng by flexural crushng n :::~-- () :::... ; - -_-::_ -:#... -_ ::::E 12 ~ 16 en Q) BOO 12 Q) L L +- G-e- J 16/ End A +- (11 (11 ~ 16/ End B G--B- 16/ End A 8 4 ~ 16/ End B "'-t:r -t:. AC code 4 <>- -~--~ Equaton Dstance from free end, mm Fg. 11. Varaton of strand stress for Specmens 16/ and 16/ at maxmum load. 62 en strands are tensoned to.75 /pu n the pretensonng bed and are released n a gradual manner. To demonstrate the use of the proposed equatons, the results of the transfer and development lengths wll be determned for three dfferent concretes havng the strengths as ndcated: 1. f ~ ; = 3 ps (2. 7 MPa) and f ~ = 45 ps (31. MPa) 2. f ~ ; = 4 ps (27.6 MPa) and f ~ = 6 ps (41.4 MPa) 3. f ~; = 7 ps (48.3 MPa) and = 1, ps (69. MPa) f ~ The transfer and development lengths obtaned from Eqs. (6) and (7) are compared wth those obtaned usng the AC Code expressons n Table 5. Ths table also gves the estmated values of fp f se and f ps for the three cases nvestgated. The ntal stress n the strand after transfer, f p PC JOURNAL

12 Table 4. Comparson of predcted and measured flexural capactes. Test ACCode Response Specmen Mn ft-kp (kn-m) Mn ft-kp (kn-m) 9.5/31-12, 9.7 : 8.8 (13.1) (11.9) 9.5/ (12.3) (11.9) 9.5/ (14.6) (12.6) 9.5/ (14.2) (12.6) 9.5/ (14.8) (13.2) 9.5/ (15.2) (13.2) 9.5/ (13.9) (13.4) 9.5/ (14.6) (13.4) 9.5/ (14.4) (13.7) 9.5/ (15.8) (13.7) fps ks (MPa) 236 (1628) 236 (1628) 241 (1662) 241 (1662) 246 (1698) 246 (1698) 248 (1713) 248 (1713) 251 (1729) 251 (1729) Mn fps!! ft-kp ks (kn-m) (MPa) Falure mode Flexural crushng (12.5) (1699) Small slp - flexural crushng (12.5) (1699) Flexural crushng (13.) (172) Slp - bond/flexure/shear (13.) (172) Flexural crushng (13.6) (175) Flexural crushng (13.6) (175) Flexural crushng (13.8) (1772) Slp - flexural crushng (13.8) (1772) Flexural crushng (14.1) (1788) Flexural crushng (14.1) (1788) 13/ (27.1) (26.6) 13/ (21.4) (26.6) 13/ (18.1) (26.6) 13/ (22.8) (21.3) 13/ (23.2) (21.3) 13/ (3.8) (29.5) 13/ (32.) (29.5) 13/ (31.) (29.5) 13/ (24.7) (23.9) (24.1) (23.9) 13/ (21.4) (2.5) 13/ (2.7) (2.5) 16/ (46.6) (43.6) 16/ (42.5) (43.6) 16/ (39.) (43.6) 16/ (42.1) (43.6) 16/ (49.2) (47.9) 16/ (5.4) (47.9) 16/ (52.) (47.9) 16/ (54.4) (47.9) 16/ (51.8) (47.9) 16/ (48.1) (47.9) 16/ / (19.3) (27.3) (11.6) (27.3) 3/8 n. (9.5 mm) strand, stress reheved, fpu = 263 ks1 (1813 MPa). 1/2 n. (12.7 mm) strand, low relaxaton, fpu = 276 ks (193 MPa)..62 n. (15.7 mm) strand, low relaxaton, fpu = 26 ks (1793 MPa). 255 (1758) 255 (1758) 255 (1758) 246 (1696) 246 (1696) 263 (1814) 263 (1814) 263 (1814) 256 (1767) 256 (1767) 26 (1794) 26 (1794) 242 (1667) 242 (1667) 242 (1667) 242 (1667) 249 (1716) 249 (1716) 249 (1716) 249 (1716) 249 (1716) 249 (1716) 239 (1647) 239 (1647) Flexural crushng (27.3) (1789) Slp - bond/flexure/shear (27.3) (1789) Slp- bond/flexure/shear (27.3) (1789) Flexural crushng (22.1) (1758) Flexural crushng (22.1) (1758) Flexural crushng (29.8) (1832) Flexural crushng (29.8) (1832) Slp - flexural crushng (29.8) (1832) Flexural crushng (24.3) (181) Flexural crushng (24.3) (181) Flexural crushng (2.8) (1816) Slp - bond/flexure/shear (2.8) (1816) Small slp - flexural crushng (44.5) (1688) Slp- bond/flexure/shear (44.5) (1688) Slp- bond/flexure/shear (44.5) (1688) Slp - bond/shear (44.5) (1688) Flexural crushng (48.4) (1732) Flexural crushng (48.4) (1732) Flexural crushng (48.4) (1732) Flexural crushng (48.4) (1732) Slp - flexural crushng (48.4) (1732) Slp- bond/flexure/shear (48.4) (1732) Slp - bond/shear (27.8) (1677) Slp - bond/flexure/shear (27.8) (1677)

13 16 ~ 12 ~ 8... U'l ~ 12 ~ 8... U'l ~ 12 E soo... U'l G---a ps (31 MPa) G---a ,88 rs (75 MPa A -tr -t~ AC code o--~--$ Equaton (5) n ~ 8 3/8 n. (9.5 mm) strand 4 ~-'---'---'---_j_--'--l-...l. j J_..J,_--J l.l JQ Dstance from free end, mm n. G---a ps (31 MPa) G---a ps (65 MPa) A -tr -t~ AC code o--+-~ Equaton (5) n. (12_7 mm) strand ~-'----'----'----'--L-L-~~~ J J J~~~~--'---'---' Dstance from free end, mm n. G---a ps (31 MPa) G---a ps (65 MPa} A -tr -l AC code o--~-- Equaton (5) n. ( 15.7 mm) strand o~_l_j_~_l_j_~_l_j_~_l_j_~_l_j_~_l_j_~o Dstance from free end, mm 12 Q) U'l ll ll 12 ~ U'l 16 ~ 12 Q) Fg_ 12. nfluence of concrete compressve strength on the development of stress n pretensonng strand accounts for the elastc shortenng loss and s a functon of the modulus of the concrete at the tme of transfer. The stress n the strand after all losses, fseo s a functon of the shrnkage, creep and long-term modulus of the concrete, as well as the relaxaton losses n the strand. The stress n the strand at flexural ultmate, ps s determned from the AC Code expresson. As shown n Table 5, the AC Code expresson gves transfer lengths whch are too large for the hgher strength concretes and therefore "!re unconservatve for checkng stresses at transfer near the ends of the member. The desgn recommendatons gve a 7 percent longer development length than the AC Code expresson for Case 1, an 8 percent shorter development length for Case 2 and a 31 percent shorter development length for the very hgh strength concrete for Case 3. CONCLUSONS The conclusons from ths ex permental program are gven here: 1. An ncrease n the concrete compressve strength at release, f~;. results n a reducton of the transfer length. 2. The proposed expresson for the transfer length, Eq. (4), s based on the current AC Code expresson, modfed by replacng fse wth fp; and by an addtonal factor to account for the concrete compressve strength at the tme of transfer. Ths expresson s applcable mmedately after transfer for the condton of gradual release. 3. n desgn, when checkng the stresses mmedately after transfer at the ends of the members, Eq. (6) provdes a smple conservatve expresson for the transfer length. 4. An ncrease n the concrete compressve strength, f~, results n a reducton of the flexural bond length and hence a reducton of the strand development length, ld. 5. The proposed desgn expresson for the development length of pretensonng strand, Eq. (7), s a modfcaton of the AC Code development length expresson. Ths equaton ncludes factors whch account for the concrete compressve strength, both at transfer and n servce. Ths expres- PC JOURNAL

14 Table 5. Comparson of transfer and development lengths calculated usng the proposed expressons and AC Code expressons. 1 for stress check ld =t+ lj'b. Concrete strengths Strand stresses Eq. (6) AC ' Eq. (7) AC ps (MPa) ks (MPa) n.(mm) ' n. (mm) n. (mm) n.(mm) Case 1 fp = 192 (1324) f~ = 3 (2.7) fse = 159 (196) 25. (635) 25. (635) = 85.2 =79.7 ~~ = 45 (31.) fps = 266 (1834) (2164) (224) Case 2 fp = 193 (1331) f~ = 4 (27.6) fse = 165 (1138) 21.7 (551) 25. (635) = 71.3 ~~ = 6 (41.4) fps = 266 (1834) (1811) =77.7 (1974) Case 3 fp = 194 (1338) f~ = 7 ( 48.3) fse = 173 (1193) 16.4 (417) 25. (635) =52.7 = 76.1 ; ~~ = 1, (69.) fps = 268 (1848) (1339) (1933) son s applcable for the condton of and Mass, Mark A., "nfluence of Strand for Prestressed Concrete," the gradual release of the strand. Concrete Strength on Strand Transfer PC JOURNAL, V. 29, No. 4, July- Length," PC JOURNAL, V. 8, No. 5, August 1984, pp October 1963, pp Za, Paul, and Mostafa, Talat, "De- ACKNOWLEDGMENT 5. Hanson, N. W., and Kaar, P. H., velopment Length of Prestressng "Flexural Bond Tests of Pretensoned Strands," PC JOURNAL, V. 22, The authors gratefully acknowledge Prestressed Beams," AC Journal, No. 5, September-October 1977, the Natural Scences and Engneerng V. 55, No.7, 1959, pp pp Research Councl of Canada for fund- 6. Lane, S. N., "Development Length of 13. Janney, J. R., "Nature of Bond n ng ths research under the Strategc Prestressng Strand," Publc Roads Pretensoned Prestressed Concrete," Grants Program. Ths research was - A Journal of Hghway Research AC Journal, V. 5, No. 9, 1954, completed under the Networks of Cen- and Development, Federal Hghway pp tres of Excellence program funded by Admnstraton, V. 54, No.2, Septem- 14. Janney, J. R., "Report on Stress the Mnster of State, Scence and ber 199, pp Transfer Length Studes on 27K Technology n Canada. The ready-mx 7. Cousns, T. E., Johnston, D. W., and Strand," PC JOURNAL, V. 8, No., concrete was provded by Francon-La- Za, P., "Bond of Epoxy-Coated Pre- January-February 1963, pp Farge and by Demx n Montreal. The stressng Strand," Federal Hghway 15. Hanson, N. W., "nfluence of Surface ~and.62 n. (12.7 and 15.7 mm) d- Admnstraton, Publcaton No. Roughness of Prestressng Strand n FHWA/NC/87-5, Washngton, ameter prestressng strands were do- Bond Performance," PC JOURNAL, D.C., December V. 14, No. 1, January-February 1969, nated by Betcon Graybec nc. 8. Kaar, P. H., and Hanson, N. W., pp "Bond Fatgue Tests of Beams Smu- 16. Cousns, T. E., Johnston, D. W., and 1atng Pretensoned Concrete Za, P., "Development Length of REFERENCES Crosstes," PC JOURNAL, V. 2, Epoxy-Coated Prestressng Strand," l. AC Commttee 318, "Buldng Code No. 5, September-October 1975, AC Materals Journal, V. 87, No.4, Requrements for Renforced Con- pp , pp crete (AC )," Amercan Con- 9. Cousns, T. E., Johnston, D. W., and 17. Deatherage, J. H., and Burdette, E. crete nsttute, Detrot, Ml, Za, P., "Transfer Length of Epoxy- G., "Development Length and Lat- 2. AC Commttee 318, "Buldng Code Coated Prestressng Strand," AC era! Spacng Requrements of Pre- Requrements for Renforced Con- Materals Journal, V. 87, No.3, stressng Strand for Prestressed Concrete (AC )," Amercan Con- 199, pp crete Brdge Products," PC Report, crete nsttute, Detrot, Ml, Cousns, T. E., Johnston, D. W., and Transportaton Center, Unversty of 3. AASHTO, Standard Specfcatons Za, P., "Transfer and Development Tennessee, Knoxvlle, September for Hghway Brdges, Ffteenth Ed- Length of Epoxy-Coated Prestressng 1991, 127 pp. ton, Amercan Assocaton of State Strand," PC JOURNAL, V. 35, 18. Collns, M.P., and Mtchell, D., Pre- Hghway and Transportaton Off- No.4, July-August 199, pp stressed Concrete Structures, Prencals, Washngton, D.C., Dorsten, V., Hunt, F. F., and Preston, tce Hall, Englewood Clffs, NJ, 4. Kaar, Paul H., LaFraugh, Robert W., H. K., "Epoxy Coated Seven-Wre 1991, 766 pp. PC JOURNAL 65

15 APPENDX - NOTATON b = wdth of beam!p = ntal stress n prestressng ld = development length db = nomnal strand dameter strand just after release le = embedment length provded f~ = compressve strength of con- fps = maxmum stress n strand at n test specmen crete at tme of testng nomnal strength crete at tme of release ng strand ljb f~ = compressve strength of con- fpu = ultmate strength of prestresslt = flexural bond length = transfer length fpbed = stress n strand n prestressng fse = stress n strand after losses Mmd = moment at mdspan bed h = overall depth of beam Mn = nomnal flexural strength \. 66 PC JOURNAL