VE VAN OE CHIEU DAI TRUYEN TRONG CAC KET CAU CAU BE TONG Dl/ I J N G Ll/C KEOTRaOC
\y
Ngd Dang Quang
ABSTRACT
Nowadays the transfer length of tendons in pretensioned prestressed concrete structures is predicted based on formulas of ACI Code which developed in the 1960th. These ones may not suitable for the current concrete strengths. Incorrect calculation of transfer length may lead to the inaccurate prediction ofthe behaviour of local areas in the beam ends as well of the whole structure.
This paper summarizes some research results about the influence of concrete strength on transfer length. It also presents the behaviour ofthe so-called
"SuperT"beam ends simulated using the suggested value of transfer length and the ones calculated accordingly to ACI Code.
This simulation shows that the inaccurate transfer length should be one of reasons causing cracks at the beam ends in the construction stage.
TS Ngd Dang Quang Bo mdn Ket cau xay diTng Trirdng Dai hoc Giao thong van tdi
1. Oat van de
Trong cac ket cau be tong d u Ung lUc keo trudc, chieu dai truyen la khoang each tU diem dau cua cot d u Ung lUc den diem ma tai do, Ung s u i t do d u Ung lu/c dat den gia tri Idn nhat. Viec xac dinh chinh xac chieu dai truyen CO y nghTa quan trpng den viec tinh toan Ung xU va thiet ke cac khu vUc neo cot d u Ung lUc cung n h u toan bp ket cau.
Tuong t u nhU chieu dai trien khai, dp I6n ciJa chieu dai truyen phu thupc chu yeu vao luc dinh bam giQa be tong va cot thep hay cot dur Ung lUc. Khi lUc dinh bam Idn, chieu dai truyen nho va ngupc lai. IVIpt trong cac yeu to CO anh hudng Idn nhat den dp Idn cua li;c dinh bam va, qua dd, den chieu dai truyen la cudng dp be tong.
Vdi sU phat trien cua cong nghe vat lieu xay dij'ng thdi gian qua, be tong co cudng dp den SO MPa hoac cao hon dang duoc sU dung rat pho bien d cac cong trinh cau d nudc ta.
IVlac du vay, chieu dai truyen dupc sU dung trong thiet ke ket cau be tdng d u Ung luc cang trudc hien nay van duac xac dinh theo cong thUc cua Tieu chuan ACI, von dUa tren cac nghien cUu thUc nghiem vdi be tong tU nhQng nam 1960. Cong thQc nay chi xet den anh hQdng cua dQdng kinh tao thep va dp Idn cua dQ Qng iQc cd hieu den chieu dai truyen ma khong cho phep xet den anh hQdng cua cac yeu to khac nhQ cQdng dp be tong, phQong phap cat cap,... Vdi cac be tong cd cQdng dp kha cao hien nay, chieu dai truyen dupc xac dinh theo cong thQc cua ACI thQdng Idn hon thij'c te va, do d6, khdng thien ve an toan khi tinh cho khu vQc dau dam. Day cd the la mot trong nhQng nguyen nhan gay ra cac vet nujt dau dam trong mot so ket cau quan sat dQpc trong thdi gian qua.
Bai bao nay gidi thieu mot so ket qua khao sat ve anh hudng cua cQdng dp be tong den chieu dai truyen cung nhQ khuyen nghi mot so gia trj cd the dQpc sQ dung trong thQc te thiet ke.
2. Chieu dai truyen xac dinh theo tieu
chuan ACI va AASHTO
TQ nam 1963 Tieu chuan ACI [2], dUa tren cac nghien cQu cua Hanson va Kaar, khuyen nghi chieu dai truyen cho cac tao thep dQ Qng iQc dang 7 spi de dam bao cho cot dQ Qng li;c cd the dat den Qng suat cd hieu, f ^ la
, ( M P a ) (1)
Qng vdi cQdng dp dinh bam bang 5,21 MPa trong sudt chieu dai truyen va iQc dinh bam dQpc tinh toan dQa tren chu vi danh dinh (tQc la n d j . Cong thQc tren dupc Tieu chuan AASHTO ap dung tQ nam 1983 [4]. Tieu chuan thiet ke cau cua Viet Nam hien nay, Tieu chuan 22 TCN 272-05, cung sQ dung cdng thQc tren.
Vi duj, theo cong thQc tren, chieu dai truyen cho cac tao du Qng iQc cap 270 cd dp chung thap vdi Qng suat cd hieu trong khoang f = 1000 ^ 1200 MPa la r, = SOd^. Trong thUc te thiet ke, gia tri nay dQpc sQdujng trong khoang
\ =(50^55)d[5. ACI cho phep sQ dung cdng thQc dpn gian nay de tinh toan sQ lam viec tong the cua ket cau cung nhQ de tinh toan cac gidi han Qng suat d khu vQc dau dam va tinh toan sQc khang cat danh dinh.
Tuy nhien, cd the thay rang, cdng thQc (1) cuja ACI khdng cho phep xet dupc anh hQdng cua sQ thay doi cQdng dp be tong den chieu dai truyen cua cot d u Qng \uc. Hon nQa, cong thQc nay sQ dijng dQ Qng li;c cd hieu (dQ Qng iQc sau khi da xay ra cac mat mat) khdng thich hop de tinh toan chieu dai truyen cot dQ Qng iQc ngay khi cat cap la dai iQong can thiet de tinh toan sQ lam viec cue bp cho khu vQc neo trong giai doan thi cdng.
3. Quan he lUc dinh bam - trUcrt trong ket cau be tong cot thep
Chieu dai truyen cua cot dQ Qng \uc phu thupc vao lu/c dinh bam giQa chung vdi be tdng xung quanh. TQOng tQ nhQ iQc ma sat, lute dinh bam xuat hien khi cd chuyen vi tuong doi (trupt) giQa be tdng va cot thep. LUc nay phu thupc vao thanh phan va cudng dp cua be tdng, dudng kinh thanh thep, cau tao be
06.2011 BWniI(l9« 5 7
mat cung n h u vi tri cua chung trong qua trinh do be tong.
De m d phdng Qng xU dinh bam - trQpt giQa be tdng va cot thep da cd rat nhieu mo hinh dQdcde xuat nhQ cac m d hinh cua Eligenhausen, Bigaj,... Cdng thQc sau md ta quy luat lUc dinh bam trupt dupc Tieu chuan CEB-FIP Model Code 1990 khuyen nghi va dupc sU dung kha rpng rai trong thuc te (Hinh 1).
( s 0 < s < S i
' ^max v^max ^f)
S, < S < S 9
S, < S < S ,
T = I f S 3 < S Trong dd, a = 0,4, r^^^, T^ la cudng dp dinh
bam, cac t h a m sd S,, S^, S^ phu thupc vao dac diem dinh bam cung n h u dac tinh kiem che (confined) cua be t d n g .
Hinh 1. M6 hinh quan he li/c dinh bam - triTcrt Ndi chung, tat ca cac md hinh dupc de xuat deu phan anh sUphu thupc cua luc dinh bam vao cudng dp chiu nen cua be tdng. Vi du, m d hinh cua Tieu chuan CEB-FIP Model Code 1990 de xuat gia tri cUdng dp dinh bam, i^ax =2,0^f(^
cho cot thep co g d va i^gx = 0 . 1 ^ ' ^ '^^° "^^c spi keo ngudi vdi f'^ la cudng dp chiu nen cua be tdng. Tuong tU, theo md hinh cua Bigaj, tYnax = 2.5^0,88f^y vdi f'^^ la cUdng d d chiu nen cuJa be tdng dupc xac dinh theo mau lap phuang. Cd the thay rang, khi cudng dp be tdng tang tU khoang 28 MPa len khoang 50 MPa, cudng dp dinh bam tang len khoang 33%.
Cac m d hinh dinh bam - trupt la co sd de tinh toan va chieu dai trien khai trong ket cau be tdng cot thep, ndi chung, va chieu dai truyen trong be tdng d u Ung luc.
4. Xac dinh chieu dai truyen tren ctf s6 quan he lUc dinh bam - trUort
4.7. Tinh toan giai tich
Cho den nay, da cd rat nhieu tac gia de xuat cac cdng thQc khac nhau de tinh chieu dai chieu dai truyen d thdi diem cat cap cua cot dQ Ung iQc keo trQdc. Theo Guyon, chieu dai truyen cua cot d u Qng iQc cd the duoc tinh toan theo cong thuc
' t = " S / £ s i (2) Trong dd, a la he so phu thupc vao dang
ham mo ta quan he iQc dinh bam - truat, S la dp tut cua cot d u Ung lUc vao be t d n g sau khi budng dU Qng iQc va e^^ la bien dang ban dau cua cot dQ Qng iQc. He so a cd gia tri nam trong khoang tQ 2 den 3. Cac ket qua t h i nghiem vdi cac be t d n g t h d n g thQdng cho S = 1,4 H- 3,0 [5].
Tren co so bien doi cdng thUc cua Guyon de xet den sU phan bd phi tuyen cua iQc dinh bam theo dp truot cung n h u xet den anh hudng cua cudng dp be tdng, Balazs da de xuat cdng thUc sau de tinh toan chieu dai truyen, ap d u n g cho cac tao cd d u d n g kinh 12,7mm [5]
' , = 3 , 5 f 3 , / ^ f ^ ( M P a , m m ) (3, Vdi f^, f\^ lan lupt la Qng suat trong cot dQ Ung iQc va cQdng dp be t d n g d thdi diem cat cap. Ap dung cdng thQc tren vdi f^^ = 1300MPa, f'_ = 40MPa va S = 2 m m chieu dai truyen cuia cac tao dQ Ung iQc cd dQdng kinh 12,7 m m la ' ( = 6 0 0 m m = 47d[3, kha gan vdi cdng thUc dQpc sQ dung trong Tieu chuan ACI. Tuy nhien, khi thay doi cudng dp be tdng, chieu dai truyen se thay doi dang ke (Bang 1).
DQa tren cac ket qua thi nghiem dQpc thuc hien vdi cac dam be tdng di/Ung luccd cudng dd tQ 30 MPa den 90 MPa, cac tac gia Mitchell, Cook cung cac cdng sQ [4] da de xuat cdng thQc sau de xac dinh chieu dai truyen d thdi diem cat cap
' t = 0 , 0 4 8 f 5 j d b ^ ' 2 0 f^, (4) Vdi f = IBOOMPa va f = 40MPa, chieu
51 CI
dai truyen tinh theo cdng thQc (4) cho ket qua ' , = 44db cho cac tao thep cd dQdng kinh 12,7 mm. Chieu dai tuyen tinh theo cdng thQc (4) theo CQdng do be t d n g cung dupc t h d n g ke trong Bang 1.
4.2. Tinh toan bang phUdng phap phan tit hCtu han
Cd the sQ dung p h u a n g phap phan tU huu han de m d phdng Ung xQ dinh bam - trUpt giQa be tdng va cdt thep va qua do, xac dinh chieu dai truyen, vdi viec sU dung cac cdng cu nhQ phan tU tiep xuc (interface elements). Thdng thQdng, phan tU tiep xuc dQOc m d ta cd chieu day bang khdng hoacrat nhd, cd cac nut trung vdi cac nut cua cac phan tUdQpc lien ket (Hinh 2).
Hinh 2. Phan tuf tiep xuc co 6 nut va 4 nut Quan he giua cac thanh phan Qng suat T, O vdi cac thanh phan bien dang tQong Ung cua phan t U t i e p x u c c d dang y, £
\^a\ L J
|AEJ Vdi la ma tran dp cUng.0 K, D =
Trong do, K^ va K^ la ma tran dp cQng phap tuyen va dp cQng tiep tuyen. Quy luat dinh bam - truat se dupc m d ta trong cac thanh phan cua ma tran dp cUng nay.
Vdi viec sQ diJng phQpng phap phan ti) hQu han, anh hQdng cua cQdng dp be tdng den chieu dai truyen dQpc khao sat tren mdt ket cau dang thanh bang be t d n g dQ Ung lure keo truroc Cdt d u U n g lUc bao g o m 4 tao d u d n g kinh 12,7 m m cd dp chung thap vdi dU Qng iQc ban dau la f^i = 1 BOOMPa. Be t d n g dUclc m d hinh hoa bang cac phan tU khdi va cdt dQ Qng iQc dupe mo hinh hoa bang cac phan tQ thanh khdng tuang thich lam viec chung vdi be t d n g thdng qua cac phan tQ lien ket. M d hinh iQc dinh bam - trUot dQpe sQ d i j n g trong cac phan tQ lien ket la mo hinh cua Tieu chuan CEB-FIP Model Code 1990 da dQpe gidi thieu d tren. Phan mem dQpc sur d u n g de thue hien phan tich nay la phan mem ATENA cua hang Cervenka (CH. See). Phuong phap phan tich dupe sQ d u n g la phQong phap Niuton-Raphson cai tien (Modified Newton- Raphson Method).
DQa tren ket qua ve sQ phan bd Qng suat tren chieu dai cae tao cap, cd the xac dinh dufoc chieu dai truyen la khoang each tU dau thanh d u Qng lue den diem ma Ung suat trong nd dat den 1300 MPa (va dupc g i u la hang sd tren chieu dai eon lai eua eau kien) (Hinh 3). Ket qua tinh toan chieu dai truyen vdi eae eUdng dp be tong khae nhau 28 MPa den 90 MPa theo phUPng phap phan tQ hQu han va eac cdng thQc (3) va (4) dQpc cung cap trong Bang 1
Hinh 3. Bieu do ufng suat trong cot dU ufng li/c
4.3. Nhan xet
Ket qua tinh toan theo eac edng thQc (3), (4) va p h u a n g phap phan tQ hUu han dQpe neu trong Bang 1 kha phu hpp vdi nhau va eung deu khSng dinh rang, khi cudng d p be tdng tang, chieu dai truyen giam. Cac ket qua tinh toan nay eung so sanh dupe vdi cac ket qua thue nghiem do Byung Hwan Oh va cdng sU [7], Mitchell va edng sU [4] eung n h u Ramirez va cdng sQ [6]
thQc hien.
Vdi CQdng dp be t d n g t r o n g khoang 28 MPa
5 8 ^^^niiin^ii 06.2011
Bang 1. Ket qua tinh toan anh hQdng cua cQdng dp be t d n g den chieu dai truyen eua tao dQ Qng iQe 12,7 m m
CQdng dp chiu nen cua be tdng (MPa)
28 35 40 45 50 60 70 80 90
Chieu dai truyen - m m (d^ ) Theo PP PTHH
570 (45) 530(42) 510(40) 465 (37) 450(35) 420(33) 390(31) 373 (29) 367 (29)
Theo edng thQc (3) 723 (57) 647(51) 605 (48) 570(45) 541 (43) 494 (39) 457 (36) 428 (34) 403 (32)
Theo cdng thQc (4) 670 (53) 599 (47) 560 (44) 528 (42) 501 (39) 458 (36) 424 (33) 396(31) 374 (29)
vdi cae be tdng ed cQdng dp khdng cao va do dd, ed the khdng cdn phu hpp vdi thQc te sQ dung be tdng hien nay d nQdc ta. Cac cdng thQc (3) va (4) da dQpe cac nha nghien cQu xay dQng tren ea sd phan tich sd lieu ly thuyet va t h i nghiem cd xet den anh hudng eua eUdng dp be tdng den chieu dai truyen. Phuang phap phan tQ hQu han vdi cac phan tU tiep xuc cd the cho phep md phdng sQ lam viec dinh bam - trQot giQa be tdng va cdt thep eung cho eae ket qua kha phu hpp vdi tinh toan theo cae cdng thQc (3) va (4).
Tuy vay, trong khi chQa ed cae cdng thQc sQa ddi cua Tieu chuan thiet ke cung nhQ chQa cd so iQong du Idn eae sd lieu t h i nghiem kiem chQng, de thien ve an toan, tac gia kien nghi:
• Khi tinh toan si; lam viec va thiet ke cac khu vQc dau dam, mau neo, v.v. trong cac ket cau d u Qng iQc keo trQdc, xem xet sQ dung cac edng thQc (3) va (4) hoac cae sd lieu cua Bang 1 de tinh toan chieu dai truyen va qua dd, xac dinh iQc do dQ Qng lute tac dung nen dau dam,
• Khi tinh toan sQ lam viec tong the eua ket eau trong trang thai gidi han cQdng dp va trang thai gidi han sQ dung, tiep tuc sQ dijng cdng thQc eua Tieu chuan ACI (ASSHTO). •
Hinh 4Cau true vet nuftddaudam"SuperT" khi chieu dai truyen duoc lay bang 635 mm
Hinh 5 Cau true vet nuftddau dam "Super T" khi chieu dai truyen duoc lay bang 460 mm
den 40 MPa ket qua tinh toan ndi tren kha gan vdi ket qua tinh toan theo cdng thUc (1) eua ACI.
Tuy nhien khi cQdng dp be tdng tang len, chieu dai truyen tinh toan dupe lai nhd hpn dang ke.
S. Anh hiTorng cua chieu dai truyen den sU lam viec cua dau dam "Super T"
Dam "Super T" la mdt trong nhQng dang ket cau dam d u Qng iQc dQpc sQ dung rat phd bien trong eac edng trinh cau d nQdc ta hien nay. Tuy nhien, tai mot sd dam, dac biet la dam cd cSt khae, ngQdi ta da quan sat thay mot sd vet nUt xuat hien d dau dam ngay trong qua trinh che tao. Cae tinh toan m d phdng tren cac phan mem bang phQPng phap phan tQ hQu han da eho thay rang, viec Qde tinh khdng chinh xac chieu dai truyen eua cot dQ Qng iQc cd the la mdt trong nhQng nguyen nhan gay ra eae vet nQt nay.
Trong eac thiet ke hien nay, chieu dai truyen cua eac tao dQ Qng iQc van dQpc lay bang ' , = SOdjj = 635mm mac du cQdng dp be tdng d thdi diem eSt cap ed the dat den 45 MPa hoac hon. LQC do dQ Qng \Uc tac dijng len khu vUc dau xac dinh theo chieu dai truyen nay nhd hon dang ke so vdi iQc dQpe xac dinh theo Bang 1 ( ' t = 460mm). Viec m d phdng bSng phQPng phap phan tQ hQu han cho thay r i n g , khi lay chieu dai truyen ' , = 635mm, dp m d rpng vet nQt d dau
dam ed the d mQc khoang 0,1 mm - 0,2 mm tQc la d dQdi mQc nhin thay dQpe bang mat thQdng.
NgQpc lai khi lay chieu dai truyen ' ; = 460mm, dp m d rpng vet nQt d dau dam cd the dat den khoang 0,2 mm - 0,3 mm va kha gan vdi gia tr|
quan sat dupc d eac cdng trinh thUc te.
6. Ket luan, kien nghi
Cac phan tich va tinh toan cd tinh vi du ke tren eho thay rang, viec xac dinh chinh xac chieu dai truyen trong cac ket eau be tdng d i ; Qng iQc keo trUdc cd y nghTa quan trpng den viec tinh toan sU lam viee cua ket cau cung nhQ thiet ke ehuJng. Trong eae ket cau dam gian don nhu dam
" I " hay "Super T", neu chieu dai truyen dQpc xac dinh qua nhd, khu vQe dau dam cd the dupe thiet ke thien ve an toan nhQng kha nang chiu cat, dp cUng cung nhQ kha nang chdng nut d khu vUc giQa nhip cd the dupc xac dinh Idn han thue te. NgQpc lai, neu chieu dai truyen dupc xac dinh qua Idn, viee thiet ke cho khu vuc giQa dam ed the la thien ve an toan nhQng iQc do du Qng luc tac dijng len khu vUe dau dam cd the Idn hon d u kien va gay nut Idn hoac hu hdng cho khu vUc nay.
Cdng thUe xac dinh chieu dai truyen eua Tieu chuan ACI hien nay van dupc dUa tren cac thi nghiem dUpc thue hien tQ nhQng nam 1960
TAI LIEU THAM KHAO
1. Bo Giao thong van tai, Tieu chuan thiet ke cau 22 TCN 272- 05,2005
2. ACI Committee 318, ACI 318 Building Code, ACI 318-05, 3. Collins va Mitchell, Prestressed Concrete Structures, Response Publications, 1997.
4. Denis Mitchell, William Cook, et al. Influence of High Strength Concrete on transfer and development length of pretensioning strand, PCI Journal, so 38,1993.
5. Gyorgy Balazs, Transfer Length of Prestressing Strand as a Function of Draw-In and Initial Prestress, PCI Journal, 1992.
6. Julio A. Ramirez, Bruce W. Russell, Transfer, Development, and Splice Length for Strand/Reinforcement in High-Strength Concrete, NCHRP REPORT 603,2008.
7. Byung Hwan Oh, Eui Sung Kim, and Kwang Soo Kim, Correct Prediction of Transfer Lengths in Pretensioned Prestressed Concrete Structures, SmiRT 16,2001.
