# # # # # KHOA HOC - CONG NGHE
DANH GIA MOT SO CONG THUTC TINH TOAN LOG CAT COA 0AM BTCT OUL NGOAI PHAN DOAN
NGUYEN DiNH HUNG, CHU QUOC THANG Truing Bai hoc Qudc ti, DHQG - HCM
BUI KHAC DIEP
Vy Kit ciu ha ting giao thdng, Bo GTVT
Tom tat: Ket cau BTCT DUL ngoai phan doan dang dwoc sd dung rong rai tren the gidi va da bat diu difQc dp dijng a Viet Nam. Bai bao nay neu len kit qua so sanh cac cong thuc tinh toan ILK cat cua dim BTCT DWL ngodi phan do^n di/a tren pha huy tai sudn dim va moi noi. Cac cong thuc duuc dung di so scinh la ciic cdng thuc du'oc sddung trong cac tiiu chuan hay duxyc ap dung tren the gidi, Viet Nam va cdc cdng thuc de xuat bdi cac tac gia khac. Ket qua chi ra ring cac cong thdc tinh toan trong cac tieu chuin thien ve an toan va do chinh xac cOa cac cong thCec cung co si/khac nhau.
Td khda: Sdc khdng cat, moi noi khd, m6i n6l epoxy, khda chong cat, BTCT DWL ngoai phan doan.
Abstract: Segmentally prestressed concrete structure with external tendons has been applied widely in the world and recently in Vietnam. This paper presents camparison of predicting shear carrying capacity of segmentally prestressed concrete beams with external tendons from some equations based on the failure at web and segmental joint. The compared equations are applying in standards, specifications and codes In the world, Vietnam and proposed by some researchers. The result shows that the equations are conservative and the accuracy of predicted shear canrying capacity from these equations are much different.
I.Gldl THIEU CHUNG
Kit d u be tdng cot thep dy ung lye (BTCT DU'L) ngodi dang dugc su dgng rdng rai trong cae kit d u d u , bdi vi nd ed nhilu uu dilm nhu giam gia thanh xdy dyng, tilt kidm thdi gian thi cdng vd giam un tie trong qud thi cdng do tilt kidm mat bdng thi cdng.
Do dd dac bigt cd y nghia dii vdi kit d u ha ting trong cdc thanh phi ddng ddn. Thdng thudng vide thilt ke mdt dam chlng lai ngoai lye thdng qua viee kilm todn mdmen vd lye clt, Khi pha huy uln xay ra trong kit d u be tdng thudng ed du thdi gian canh bdo con ngudi trudc khi phd huy hodn todn. Tuy nhien, phd huy d t , ddt bi^t Id kit d u BTCT DU'L ngodi.
thudng xay ra dot nggt. Vi ly do dd, thilt k l theo SLPC khang clt eua kit d u thudng dugc dae biet ehu y d l dam bao kit d u dugc an todn.
Co chi pha huy theo clt trong kit d u BTCT ndi chung Id rat khd xac djnh chinh xdc, bdi vi dd Id mdt CO chi rat phuc tap, dae biet dii vdi kit d u BTCT DU'L nggdi phan doan. Trong kit d u BTCT phdn doan, toi uu nhlt Id bo tri mil nil vudng gde vdi vlt nut nghidng do clt. Thuc t l thi vigc xdc djnh do nghieng cua vlt nut clt Id rat phuc tap, khd chinh xdc va phg thggc vdo cac co che pha huy d t khde nhau. Hon nua, b l tri mli noi nghieng se rlt khd khan cho viec thi cdng vd bat Igi
khi ehju cac lye khac. Nen trong thyc t l d l thuan tien cho thi cdng, cdc mli nli thudng dat vudng gdc vdi true dim.
Do cung vd cudng dd sue ehdng clt tai mli ndi thudng nho hon so vdi cdc mat d t ben trong cua doan dim do clt thep thudng trong be tdng khdng lien tgc tai vj tri moi nli vd eg chi do md rdng cua mli ndi dudi tac dgng cCia ngoai luc d giai doan tdi han Id rdt phuc tap. Do dd, viec xac djnh sue khdng d t cua dim BTCT DU'L phan dogn ndi chung vd dim BTCT DU'L ngodi phdn doan ndi rieng cdng phuc tap va kho dat dugc dd chinh xdc.
Vi kit d u ed t h i do sy phd
So 9 nam 2012
KHOA HOC - C O N G NGHE d£.
hijy tai sudn d i m hoac cung cd t h i do su phd huy eua m l i n l i giCfa cac doan d i m . Rdt nhilu nghien cuu da dugc thyc hien d l tim h i l u CO c h i pha huy c l t cua d i m vd moi n l i trong d i m BTCT DU'L phan doan nhu xem xet d i n anh hudng cua luc dy ung luc trong hay ngodi [1], hinh dang eua khda chlng d t vdi ed hay khdng su dung keo epoxy [2], mdt khda chlng d t hay nhilu khda ehdng c l t [3], cdc md hinh phan tich bdng phuong phap p h l n t u hOu han [4], vi tri cua m l i n l i vd mCrc dd eua lye DU'L [5], cap nghieng vd vj tri cua vdch chuyin hudng trgng nhjp ehju c l t [6] v.v.. Dya tren k i t qua phan tich co e h i truyin luc qua moi n i l vd co c h i pha huy trong cac md hinh thi nghiem, mdt s i cdng thijc dugc d l xuat d l dy doan sue chlng c l t cua dam BTCT DU'L ngoai phan doan, Mdt trong so eae cdng thuc dd da dugc ap dgng trong cdc tieu chuan thilt k l dang dugc su dgng tren t h i gidi vd Viet Nam
2. CAC CONG THUTC
2.1 Cong thufc cua tieu chuan
AASHTOTrong mgc tinh todn SLPC khdng d t trong tieu c h u l n cua AASHTO [7], xuat ban nam 2007, SLPC khdng danh djnh eua d u kien dugc lay gia trj nho hon, xac djnh trong cdng thuc (1) va (2):
K-- l + ^ < 2
K„ =v^ + v^ + v^
y„=4f'cbJ
Trong dd, V^ vd V^nhu sau:
V,=Kf,bJ
S
So 9 nam 2012
(1) (2) dugc tinh
(3) (4)
(5)
/ = 0 , 1 6 6 ^ (6) Lugng c l t dai t i i thilu trong
su'O'n. A„,,i„ Id:
Jy (7)
Trong dd, V^ Id SLPC khang do be tdng, V^ la sue khang do c l t dai, Vp Id sue khang do lye DU'L nghieng, b^ b l rdng ban sudn, d Id chieu cao d i m ed hieu, K he sd thay ddi ipng suit, s Id khoang each eua c l t dai, f^^ Crng s u i t trong be tdng tai trgng tdm eua mat c l t do lye DU'L sau m l t mat, f'^ la cudng do chiu nen eua be tdng, f, Id ung s u i t keo chinh va f la cudng do chiu keo cua c l t dai.
Trong tieu chuin AASHTO [7], mdi n i l khd da bj loai bd. Vi hien tugng dn mdn c l t thep DU'L keo sau da dugc phat hien trong mdt sd c l u [8], Tuy nhien, khi su dung edp DU'L ngodi, mdi n i l khd v i n dugc dp dung trong mdt sd sy an cua d u BTCT DU'L ngodi phan doan. Trong trudng hgp dd, SLPC khdng c l t eua d u BTCT DU'L su dgng moi n l i khd hay m l i ndi dung epoxy dugc xac djnh bdi cung mdt cdng thue (1) vd (2), He so sue khdng eua k i t d u su dgng m l i n l i epoxy va mdi n l i khd l l n lugt Id 0.85 va 0,65, Hon nua, v i n cdn thilu cac phdn tich d l giai thich mdt each hgp ly cho CO c h i phd huy c l t cho trudng hgp k i t d u DU'L ngodi. G i n day, Avendano [9], d l x u l t khdng gidi han gia tri eua K do eudng do ehju nen cua be tdng ngay cdng cao hon so vdi luc cdng thue dugc d l xuat, Tuy nhien, do phan tan eua k i t qua thi nghiem so vdi gid tri d u dodn v i n cdn rat Idn d i i vdi ea trudng hgp gidi han hay
khdng gidi han gid tri eua K, Do vide xac djnh gid tri ft trong cdng thLPC (6) dua tren pha huy do nen tren sudn d i m Id dua vdo hien tugng phd huy do nen d t ed t h i x u l t hien trong cdc d i m be tdng cd chilu ddy sudn d i m mong vd thudng tao ra sue khang c l t Idn nhlt trong d i m ,
Nhu giai thich d tren, moi n l i khd cd t h i dp dgng trong k i t d u BTCT DU'L ngodi, Khi mdi ndi khd dugc su dung, sue khang c l t cua m i l ndi d n thilt dugc danh gid, Dac biet cae mdi ndi trong thdi gian thi cdng hoac cdc m l i ndi g i n trg c l u , noi phai ehju luc c l t Idn nhlt, Trong tieu chuln cua AASHTO [10] cho k i t d u phan doan, x u l t ban l l n 2 nam 2003 phien ban thu nghiem, sue khang c l t danh djnh eua mdi ndi khd, V, dugc tinh todn bang cdng thue (8):
F^ =^,(l2+2,466/J>,792xl0'X +0,6^4, (8)
Trong dd Ai^ Id dien tich cua chan cac khda chdng c l t trong mat phing bj phd huy, A^^ Id dien tich t i l p xuc giua edn lai tren mat phdng bj phd huy. Tuy nhien, SLPC khang cua m l i noi cua epoxy khdng duoc xem xet trong tieu chuln nay,
Cdng thue (8) dugc x u l t phat t u k i t qua cua cdc thi nghiem cat tryc t i l p vdi mdt khda chlng cat. Sue khang c l t dugc bao gdm sue khang c l t truyin qua bdi khda chdng d t vd luc ma sdt cua p h l n cdn lai cua b l mat t i l p xuc tai mat phang pha hoai, Cac hang sd trong cdng thuc (8) dugc xac djnh dua tren nhilu gia thilt ma chi xay ra trong cae d i l u kien dac biet, nhu co c h i truyin lye theo phuong 45° vd ung s u i t keo
CSillaES
# # # # KHOA HOC - C O N G NGHE
chinh dugc tinh nhu cdng thuc (9):
/, =0.62237Z
(9)Dya tren cung mdt trilt ly tinh todn nhung gid tri tinh toan Crng s u i t keo chinh trong cdng thuc (6) de tinh cho cdng thuc (1) vd cdng thuc (9) d l tinh cho cdng thuc (8) lai cd gid tri hodn todn khac nhau.
Hon n(ra, cac thi nghiem dugc thuc hien d l xac dinh cae h i n g sd cua cdng thuc (8) dugc thyc hien vdi be tdng thudng (f^ <55 MPa), Do dd doi vdi k i t d u su dgng be tdng eudng do cao, dd chinh xdc cua cdng thLfc tren giam di dang k l . K i t qua thi nghiem bdi Buyukozturk [2] dd chi ra r i n g sue khdng d t cua m i l ndi cd nhilu khda chong d t id idn hon so vdi m l i n l i sijf dung mdt khda chong c l t . Hon nua, viee b i t ngudn tCp thi nghiem d t tryc t i l p nen cdng thuc (8) chi phij hgp vdi m l i ndi ehju mdmen tuong ddi nhd va kha nang ehju lye c l t chilm uu t h i , Viec anh hudng eua dd md rdng m l i noi khi ehju tac ddng eua mdmen thi do chinh xdc eua cdng thuc giam di dang k l .
2.2 Cong thuic cua tieu chuan Eurocode 2
ok xac djnh sue khdng d t cua k i t d u BTCT DU'L ngodi phan doan, Eurocode 2 [11] chi xem xet tac ddng khdng thuan Igi vd cdn thilu cdc minh chung cho viec xac djnh gid tri ndy. Doi vdi mat d t khdng cd cot thep thudng trong k i t d u be tdng di qua,
Eurocode 2 quy djnh chilu cao ehju nen eua mat c l t it n h l t phai bang 2/3 ehilg cao cua mat d t khi d giai doan tdi han. Eurocode 2 cung chua phdn biet moi ndi ed sQ' dgng epoxy hay m l i ndi khd cho k i t d g d i m phan doan.
Hinh1:
Huang truyen luc CO kha nang truyin qua moi noi cua dim phan doan
O l i vdi thilt k l k i t d g phan doan khdng cd c l t thep thudng c l t qua mdi ndi, trong Eurocode 2 mdi [12], sue khdng d t danh djnh eua d i m BTCT DU'L phan doan, VRd,max se dugc xac djnh nhu sau:
cot0 + tani9 dinh id:
= 0,6 1 Jck 250 l<cot6i<2,5
(10)
(11) (12) He so phu thudc vao luc DU'L a . , duoc xac dinh nhu sau:
«™=(i+'^.,/^) khi 0<<T,„<0.25/^
a„=1.25 khi
(13)
0.25/,, <o-,,< 0,5/^ (14)
« „ = 2.5(l-<7,,/^) khi 0 , 5 / ^ < < 7 , , < l , 0 / ^ (15) Trong dd, b^ la chilu rdng sudn; z la canh tay ddn cua ndi luc dugc xdc djnh it n h l t la 2/3 chieu cao mat c l t ; f^ Id cudng do thilt k l cua be tdng; v, Id he s i ; f^
Id eudng do cua be tdng; 6 Id gdc nghieng eua dudng truyin lye di qua m l i n i l so vdi trgc d i m ; va CT^p la ung s u i t nen trung binh trong be tdng do luc DLfL gdy ra,
TCf cdng thuc (12), dd nghieng cua dudng truyen luc la tCp 21.8°
(0^,„) d i n 45° (G^J (gia trj ndy trong AASHTO gia djnh Id 45°).
Cac kha nang cua dudng truyin lye qua mdi noi cd t h i xac dinh nhu trong Hinh 1. Do dd, viec xdc djnh gdc cua dudng truyen lye chua dugc giai thich cu thi trong tieu chuan. Hon nua viec d i l u khiln luc DLfL sao cho tai thdi d i l m tdi han, chilu cao ehju nen cua mat cat tai m l i n l i bang it n h l t 2/3 chilu cao eua mat cat la r l t phuc tap vd khd xac djnh chinh xac trong giai doan thiet ke.
Viec xac dinh nay phg thudc rat nhilu vao kinh nghiem cua ngudi thilt k l . Suy cho cung thi v i n la v l n d l xdc djnh hudng truyin luc qua mat c l t hay vi tri cua v l t nut do c l t , Dd cung la bdi toan su phuc tap trong v l n d l nghien cuu v l CO e h i pha huy c l t .
2.3 Cong Ihuic cua tieu chuan cda Nhat Ban
Theo tieu chuln thilt k l cau kien be tdng c l t thep cua hdi ky su Nhat Ban nam 2007 [13], sue khdng c l t eua d u kien BTCT DU'L, V^^ dugc xdc djnh bdi cdng thuc (16):
' w; ~ '^cJ ^ ''^sd "*" ' W (16) Trong dd:
y^=PdP,P„LAd (17)
y^^ /i,,/,^, (sin a, + cos a,) / s, +'ip.fp. (sin a , + cos a , ) / i .
.(18)
y^=p^^^'^ccp (19)
Jval = 0 . 2 3 ^
vol f,^ <0,72 N/mm2 (20)
So 9 nam 2012
KHOA HOC - C O N G NGHE MJA
A=Viooo77 khip^>1,5
t h i p , = 1.5 (21) Pp='^l^^. khiPp>1,5
thipp = 1.5 (22)
;5„ = 1 + 2M„/M,„ (A^;,>O) hoac =l + 4M„/A/„, (A'i/<o)
khi p„ >2,0 thi p^ = 2,0 (23) Trong dd,V^, Id sue khang cua be tdng; V^, Id SLPC khang cua c l t dai; V^^, Id sue khang cua d u lye DU'L nghieng; N', Id lye dgc trgc; Mud Id sue khang mdmen khdng k l d i n lye dgc trgc; M;, Id mdmen d n thilt d l triet tieu Crng suit do lye dgc trgc gay ra tai thd ngodi eCing; b^ Id b l rdng sudn;
d la chieu cao d i m cd hieu cua mat cat; p^ la he so cot dai; f ^ Id cudng dg ehju nen cua be tdng;
f\^ Id dien tich cua cdt dai; A^^ id dign tich cua cap DU'L nghieng;
CTp^ Id ung s u i t trong edp DU'L nghieng; f ^ , ung s u i t cua cdt dai; ttj la gdc nghieng cua cdt dai;
a^ Id gdc nghieng eua cap DU'L nghieng; a^ Id khoang each eua cot dai; a la khoang cdeh cua edp DU'L nghieng; z dugc xdc djnh bang d/1,15; P^, Id lye DLTL.
Sue khang d t theo cdng thuc (16) cung dugc dp dgng cho k i t d g BTCT DU'L ngodi phdn doan.
Do cd quan nidm cho rang khi moi n l i cd kha nang ehju nen du Idn thi k i t d u dd cd t h i coi nhu k i t d u liln khoi.
Tieu c h u l n t h i l t k l d u kien BTCT cua Hdi ky s u Nhat Ban nam 2007 [13] cung xdc djnh sue khang cat cua m l i n l i cho k i t d u BTCT DU'L phan doan, V ^ theo cdng thuc sau (24):
Trong dd:
T,=O.OSf^/a
a = 0,75a-10
J yd
(25) (26)
(27)
, = {(r,+pr,sin'fl-ap/,,jSin9cose)/f, + r,}
(24)
Trong dd, p Id ty Id cdt thep qua mat d t dang xet, doi vdi mdi n l i phan doan, l l y p = 0; 9 Id gde gi&a mat d t pha huy vd cot dai trgng mat c l t phd huy, doi vdi m i l n l i phdn doan l l y 9 = 0; f . Id cudng do ehju keo eua c l t dai;
A^ la dien tich eua mat c l t bi pha huy; M^ id sue khang c l t cua khda chong d t , V^ = O.IA/^,, A,, la dien tich tai chan eac khda chong cat tai mat c l t bj phd huy, f'^ Id cudng do cua be tdng; <3^ la ung s u i t phap trung binh tren mat d t bj pha huy, vdi k i t d u chiu nen snd ed t h i xac dinh la -CT' 72, a ' ^
nd ' nd
Id ung s u i t chiu nen trung binh tdc ddng len mat c l t bi pha huy, trong mgi trudng hgp (apf^, -a J phai ed gid tri duong; b la hg sd hinh dang cQa mat d t , d i i vdi mdi noi phdn doan l l y b = 0,5; vd
|i. Id he sd ma sat ed gid tri Id 0,45.
Cdng thuc (24) gia djnh ring ung s u i t c l t rai d l u tren mat phdng bj pha huy. Hon niJa, giong nhu hai cdng thuc tren, anh hudng eua do md rdng m l i n i l dudi tac dgng eua mdmen Id chua dugc k l d i n .
2.4 Cong thufc cua tieu chuan Dure
Theo de x u l t eua Que [14] cho viec thilt k l d u BTCT DU'L phan doan, s y truyin lye qua m l i ndi la lye ma sdt tren b l mat moi n l i . Sue khdng cua khda chdng d t dugc bd qua d l tang dd an toan cho k i t c l u . Khac vdi cdng thuc (8), dien tich de truyen lye ma sdt duoc tinh Id todn bd dien tich
cua mat c l t ehju nen, bao gdm ca dien tich tai chan eac khda chlng c l t vd dien tich t i l p xuc trong mat phang bi phd hoai, dudi tac dgng cua lye DU'L sau m l t mat. Sue khang d t cua m l i ndi dugc tinh theo cdng thue (28):
^r^^'A
(28)Trong dd, V id sue khang d t eua mdi ndi; \i Id he sd ma sat, H = 0,7; a^ Id ung s u i t nen trung binh trong p h l n chiu n I n cua mat c l t mdi n i l ; A^ la dien tich vung ehju nen cua be tdng tai mat d t m i l ndi,
Cdc thi nghiem cua Buyukozturk [2] da chi ra rang sue khang c l t cua m l i ndi su dung khda chong d t Id ldn hon moi n i l phlng. Hon n&a. Tumor [15] cung chi ra rang, he s i ma sdt cua 2 mat phlng be tdng thdng thudng, H chi khoang tCf 0,491 d i n 0,577.
Nhu vay, viec l l y gia tri (i = 0,7 cd t h i coi nhu k l d i n mdt p h l n anh hudng cua khda chlng c l t . Tuy nhien, viec xem xet ndy la chua hgp ly d i n cdng thue ndy qud an todn cho m i l ndi, Cdng thCpc trong tieu chuan cua Bdc cung chua xem xet m i l n l i khd vd m l i ndi epoxy.
2.5 Cong thiic cua Rombacit
Sau khi t i i n cac phan tich md hinh p h l n t u huu han vdi cac thdng sd khac nhau, Romback [16] da phat triln cdng thCpc trong tieu chuin eua Due vd d l x u l t hai cdng thue tinh toan sue khang c l t eua m l i n l i khd va mdi n l i epoxy.
Cdng thuc cua m l i n i l khd Id nhu sau (21):
V^^ = H a A V / A (29)
C d n g t h u c c u a m l i ndi e p o x y Id n h u s a u (22):
So 9 nam 2012
• !CTB1
WMtM KHOA HOC - C C N G NGHE
K,=/io-„^, (30) Trong dd, n Id he so ma sat, n
= 0,65; <s^ la ung s u i t nen trung binh trong p h l n ehju nen cua mat c l t m i l n l i ; A^ Id didn tich vCing ehju nen cua be tdng tai mat c l t m i l noi; A^ la dien tich nhd hon tai chan cae khda chlng d t tai hai mat phlng cd kha nang phd huy tai moi ndi; f Id he s i k l d i n sy khdng khit cua m l i noi khd, f = 0,14; f^ Id cudng dd chiu nen cua be tdng.
Cdng thue eua Romback da xem xet d i n loai mdi noi Id m l i n i l khd hay m l i n l i epoxy. He sd ma sdt cung da giam so vdi cdng thuc de x u l t trong tieu chuln ciJa DLPC. Nhung gid tri ndy v i n edn Idn hon gid tri thyc t l trong thi nghiem eua Tumor [15]. Trong m i l n l i khd, Romback da k l d i n anh hudng cua khda chlng d t vd ke d i n sy khdng khit eua m l i noi trong qua trinh thi cdng. D i i vdi cdng thCpc (22), v l n giu' nguyen nhu d l x u l t trong tieu chuln cua OLPC va he s i ma sdt lai giam di do k l d i n c h i t lugng cua thi cdng epoxy vd tuoi thg eua cua epoxy.
Do dd gid tri dy doan bdng cdng thue (22) nhd hon gid tri cua cdng thue (20) vd cung nhd hon gid tri eua cdng thuc (22),
2.6 Cong thiiic cua Wai<asa
Wakasa [1] cung d l x u l t mdt cdng thLPC d l dy dodn sue khang c l t cua d i m BTCT DU'L ngodi phdn doan, Khac vdi cae cdng thuc neu tren, mat phang pha huy Id mat phlng tai cdc chan khda chlng d t , cdng thue cua Wakasa dya tren co e h i pha huy ed kha nang xay ra tai m l i n l i nhu tren Hinh 2, Trong trudng hgp phd huy xay ra tai vung A, SLPC khdng d t cua d i m la do ma sdt vd duoc
viing B Cot dai
Hinh 2:
Kha nang cua vet nut va cc che pha huy
tinh bdng cdng thue (23). Trong trudng hgp phd huy xay ra d VLing B, anh hudng cua c l t dai dugc k l d i n , do dd sue khdng c l t cd t h i dugc tinh theo cdng thLPC (24). Gid tri nhd hon trong hai cdng thue (23) vd (24) se Id gid tri sue khdng d t cua d i m .
S = i^aA^
s = s , + S3 so = xhB
r = ^jaf-a,cr„
(31) (32) (33) (34) Trong dd, |x la he sd ma sat,
|i = 0,45; a Id ung suit ehju nen trung binh tai moi ndi trong vijng ehju nen; A^ Id dien tich viJng ehju nen; Sj, la sue khang c l t cua be tdng dugc djnh nghTa theo cdng thue (33); Sg Id sue khang d t cua c l t dai trong khoang 0,9d/2;
d la chilu cao d i m ed hieu; B Id chilu rdng trung binh; h la chilu cao tCp thd dudi eiJng d i n viJng khda chlng d t phia dudi (chilu cao vung ehju nen ed k l d i n sy md rdng cua mdi ndi); vd x Id LPng s u i t c l t tinh theo cdng thuc (34), trong dd a. Id ung s u i t keo cua be tdng tai mat v l t nijt, CT^ Id ung s u i t nen trung binh cua be tdng vljng ehju nen,
D i l m ndi bat eua cdng thCpc nay la da k l d i n su md rdng eua m l i n l i . Trong cdng thue (32), do ehinh xac cua viec xac djnh dien tich vung ehju nen vd ung s u i t cua be tdng vung ehju nen tai giai doan gidi han Id khdng cao va
dugc xdc djnh dua tren nguyen t i e can b l n g luc tai mdi noi. Mac khac, vide xdc djnh chieu cao vung ehju nen cua vCing B trong cdng thuc (33) khi d i m phd hoai cd k l d i n anh hudng eua do ma rdng m l i ndi lai khdng dugc de cap d i n , Trong thyc t l chilu cao vung chiu nen cua viJng B phu thudc vdo r l t nhilu y l u to nhu luc dy ung luc va vj tri eua m i l nli [5, 6] nen r l t khd xdc djnh dugc chilu cao cua viJng B. Them vao dd, gia tri ung s u i t keo tren be mat v l t nut eijng r l t khd xac djnh dugc ehinh xdc vd cung r l t phuc tap, vi do md rdng v l t nut do cat thudng khdng Id gilng nhau tren todn bd chilu ddi v l t nut. Do do, ung s u i t tren b l mat v l t n&t cung khdng b l n g nhau tren chilu dai v l t nut, Ndi each khde, phuong phdp ndy Id r l t phuc tap vd khdng d l dy dodn chinh xdc sue khang d t eua d i m BTCT DU'L ngodi,
3. DANH GIA CAC CONG THUfC Vdi KET QUA THUC NGHIEM
Bang 1 Net ke 39 d i m BTCT DU'L phan doan va mdt sd thdng s i quan trgng trong viee danh gia sue khang c l t eua d i m BTCT DU'L phan doan, dat biet id cho k i t d u DU'L ngoai, Ty so giu'a chilu ddi nhjp chlng c l t (a) vdi chilu cao ed hieu eua mat cat (d), a/d la tCp 1,5 d i n 4,4. Dilu dd nghTa Id eae d i m ndy id cac d i m manh (a/d tO 1,5 d i n 6,0) do dd eo c h i phd huy cua cac d i m
So 9 nam 2012 I
KHOA HOC - C O N G NGHE # # # #
B A N G 1 : 00" lieu thyc nghiem dung de danh gia cac cong thu'c cho k i t c l u BTCT DU'L ngoai phan doan
Ten tac gia
Nguyen et al.
(2010) [5]
Nguyen et al, (2011) [6]
Sivaleepunth et al, (2008) [18]
Tumor et al, (2006) [19]
Hosoda et al, (2002) [20]
Ito et al, (1995) [21]
Ramirez (1989) [22]
T§n dam SJ25 SJ15 SJ-05 SJ10-19 SJ10-10 SJ10-03 SJ10-06 DSJ10-06 DSJ10-10 D09-200 D09-600 D14-600 S40 S80 H40 H80 V1-PC-35 V1-PC-70 V1-SFRC-35 V1-SFRC-35 V3-PC V3-SFRC Seg-1 Seg-2 Seg-3 Seg-4 NS HS lll-B lll-UB 1E-1,5 1E-2,5 1E-3,5 2E-1,5 2E-2,5 2E-3,5 D-1,5 D-2,5 D-3,5
a/d
3,5
6,38
3,6
4,44
1,5 2,5 3,5 1,5 2.5 3,5 1,5 2,5
a/d 2,5 1,5 0,5
1.0
0,5
1,28
0,4
0,74
0,8 1,3 1,8 0,8 1,3 1,8 0,8 1,3 3,5 1,8
d (mm)
400
470
500
320
508
f'ANI mm^) 65,7 65,4 64,6 65,7 65,7 65,7 67,1 67,1 67,1 65,1 35,6 32.1 67,6 65,8
33,9
33,0 38,0 52,9 54,0 58,8 44,5 55,0 72,8 42,3 44,8 51,7 51,0 47,6 53,8 56,5 49,6 47,6 45,5
r(%)
0,16
0,16 0,16 0,16 0,16
0,47
2,00 0 0,25 0 0 0,53 0 0,65 0.68 0,65 0,68 0,71 0,71 0.65 0,65 0,65
o, (N/mm^;
19,5 19,2 19,9 20,0 10,7 3,0 6,8 7,0 11,5 19,6 19,6 19,2 11,3 11.0 18,5 19.6 4,1 8,2 4,1 8,2 2,9 2,9 10,8 10,8 10,8 10,8 9,8 14,7 10,0 5,7 5,7 4,6 4,3 5,1 5,4 5,0 5,9 4,6
Loai mdi nSi
Epoxy
Kho
Epoxy
Kho
Epoxy
Kho
Vj tri cap DLPL
Ngoai
Trong dinh bam
Trong khong dinh bam
V ^ ( k N ) 240,15 203,40 211,50 226,95 197.30 166,70 183,05 175,05 195,10 244,60 215,80 261,70 125,70 115.45 219,70 219,85 40,50 68,00 • 37,00 63,00 67,00 66,00 162,00 224,00 177,50 42,00 91,20 104,00 86,00 92,00 164,60 237,10 200,60 160,15 214.15 198,50 166,80 214,15 198,50
nay la dang pha huy cat, Nghien cuu g i n day [5,6] chi ra rang vj tri moi cung anh hudng tryc t i l p d i n sue khang c l t cua d i m , Trong p h l n c h i l u ddi nhjp chong d t cd n h i l u moi noi, m l i n l i g i n d i l m dat luc n h l t se quyet djnh eo c h i pha huy vd sue khdng d t cua
d i m . Vi tri mdi noi dugc t h i hien bdi ty sd giOa khoang each mdi ndi d i n vj tri dat lye (ap vdi c h i l u cao d i m ed hieu cua mat d t , a^d Id tLP 0 d i n 2,5. C h i l u cao d i m cd hieu cua mat d t , d la tCr 320 d i n 508 mm. Cudng do cua be tdng, f , trong cdc d i m dugc thu
thap la t u 32,1 N/mm^ d i n 72,8 N/
mm^. Da p h l n trong s i eac d i m thu thap d u g c id s u dgng be tdng cudng do cao (f^ 55 N/mm^
d i n 80 N/mm^). Be tdng cudng do cao cung Id loai be tdng dang dugc su dgng rdng rai so vdi be tdng thudng trong k i t c l g BTCT
S6 9 n§m 2012
#### KHOA HOC -
C O N GNGHE
DU'L. 5 trong so 39 d i m dugc thg thap khdng s u dgng cdt dai. Cac d i m edn lai s u dgng cot dai, he so cdt dai t h l p n h l t Id 0,16% va Idn n h l t Id 0,71%. He so c l t dai nhd n h l t cOng idn hon he s i nhd
nhat theo yeu cau cua tieu chuan cua JSCE [13] (0,15%). Luc DU'L cung Id mdt y l u t l quan trong anh hudng d i n sue khang c l t cua d i m . Muc dd lye DU'L dugc t h i hien qua tri sd eua ung s u i t
nen tai thd ngcdi cung cua mgt d t d i m . Gid tri ung s u i t nen cua be tdng t u 3,0 N/mm2 d i n 20,0 N/mm2. Trong sd 39 d i m , chi cd 5 d i m su dgng moi n i l khd, cdn lai 34 d i m sij' dgng moi n l i
B A N G 2: So sanh gia trj thirc nghiem va gia trj tinh toan
Beams SJ25 SJ15 SJ-05 SJ10-19 SJ10-10 SJ 10-03 SJ 10-06 DSJ10-06 DSJ10-10 D09-200 D09-600 D14-600 S40 S80 H40 H80 V1-PC-35 V1-PC-70 V1-SFRC-35 V1-SFRC-35 V3-PC V3-SFRC Seg-1 Seg-2 Seq-3 Seg-4 EX-NS EX-HS lll-B lll-UB 1E-1.5 1E-2,5 1E-3,5 2E-1,5 2E-2,5 2E-3,5 D-1,5 D-2,5 D-3.5
V
EXP
(kN) 240,2 203,4 211.5 227,0 197,3 166,7 183,1 175,1 195,1 244,6 215,8 261,7 125,7 115,5 219,7 219,9 40,5 68,0 37,0 63,0 67,0 66,0 162,0 224,0 177,5 42.0 91,2 104,0
86,0 92,0 164.6 237,1 200.6 160,2 214,2 198.5 166,8 214,2 198,5
Tieu chuan AASHTO co qiai han K V^JkN)
127,2 126,2 124.0 125,2 125,2 95,4 101,4 101,4 101,4 168,0 167,7 200,9 98,8 94,8 127,7 126,2 160.8 171,7 160,8 171,7 482,9 486,5 96,2 132,1
99,5 88,6 130,0 148,6 69.1 69,1 154.3 161,4 159.2 149,6 156,5 159,3 159,7 162.2 156.6 Trunq binh
Phipang sai He s6 phan tan (%)
y^^jy^, 1,89 1,61 1,71 1,81 1,58 1,75 1,81 1,73 1,92 1.46 1.29 1.30 1.27 1.22 1.72 1,74 0,25 0,40 0,23 0,37 0,14 0,14 1,68 1,70 1,78 0,47 0,70 0,70 1,24 1,33 1,07 1,47 1,26 1,07 1,37 1,25 1,04 1,32 1,27 1,23 0,54 43,65
Tieu chuan AASHTO khonq qlai han K
\/,„(kN) 174,3 173,0 172,2 175.6 136,2 95,4 120,4 121,6 127,3 211,4 211,9 239,7 113,9 110,0 172,1 174,2 160,8 184,5 160,8 184,5 482,9 486,5 96,2 132,1
99,5 91,2 134,3 164,3 82,7 82,7 154,3 161,4 159,2 149,6 156,5 159,3 159,7 162,2 156,6
V N 1,38 1,18 1,23 1,29 1,45 1,75 1,52 1,44 1,53 1,16 1,02 1,09 1,10 1,05 1,28 1,26 0,25 0,37 0,23 0,34 0,14 0,14 1,68 1,70 1,78 0,46 0,68 0,63 1,04 1,11 1,07 1,47 1,26 1,07 1,37 1,25 1,04 1,32 1,27 1,09 0,46 42,13
Tieu chuan AASHTO cho m6i n6i kho V/„(kN)
942,4 931,1 930,1 975,7 586,9 302,1 457,5 466,0 627,3 892,9 901,8 845,3 448,3 425,6 924.5 952.7 376.6 615.0 376.6 615,0 306,1 319.0 447,2 450,3 463,4 422,3 426,8 613,4 432,4 432,4 383,6 432,0 369,4 346,3 399,6 422,8 409,4 456,5 369,3
V N 0,25 0,22 0,23 0,23 0,34 0,55 0,40 0,38 0,31 0,27 0,24 0,31 0,28 0,27 0,24 0,23 0,11 0,11 0,10 0,10 0,22 0,21 0,36 0,50 0,38 0,10 0,21 0,17 0,20 0,21 0,43 0,55 0,54 0,46 0,54 0,47 0,41 0,47 0,54 0,31 0,14 45,26
Tieu chuan cua JSCE - Nhat Ban V,„(kN)
101.9 101,4 100,3 100.2 100.2 100,2 101.4 101,4 101,4 162,5 162,2 207,3 86,7 84,4 101,6 100,9 179,0 204,5 179,0 204,5 473,0 476,0 120,1 156,2 124,4 113,4 296,6 341,3 65,5 65,5 136,1 138,9 140,4 135,6 137,9 138,9 139,8 139,0 138,1
V^^N^.
2,36 2,01 2,11 2,27 1,97 1,66 1,81 1,73 1,92 1,51 1,33 1,26 1,45 1,37 2.16 2,18 0,23 0,33 0,21 0,31 0,14 0,14 1,35 1,43 1,43 0,37 0,31 0,30 1,31 1,41 1.21 1,71 1,43 1,18 1,55 1.43 1,19 1,54 1,44 1,31 0,66 50,24
So 9 nam 2012 I
epoxy, 27 d i m Id k i t d u BTCT DU'L ngodi phan doan vd 11 d i m Id d i m BTCT phdn doan s u dgng cap DLfL trong nhung khdng dinh bdm va 1 d i m s u dung cap DLCL trong dinh bam.
Bang 2 liet ke gid tri sue khdng d t eua cdc d i m thu thap dugc t u cdc thi nghiem eua cdc nghien CLPU trudc nhu dugc liet ke trong Bang 1 vd sue khdng c l t tinh toan dua tren cac cdng thue da
KHOA HOC - C O N G NGHE # # # #
liet ke d tren, trij* cdng thuc cua Eurocode 2. SLPC khang d t tinh toan se dya tren s y pha huy tren sudn d i m hoac tren m i l ndi, hay cd s y phdn biet giua m l i n i l khd vd m l i n l i epoxy cung dugc tinh B A N G 2: E
Beams
SJ25 SJ15 SJ-05 SJ10-19 SJ10-10 SJ10-03 SJ 10-06 DSJ 10-06 DSJ10-10 D09-200 D09-600 D14-600 S40 S80 H40 H80 V1-PC-35 V1-PC-70 V1-SFRC-35 VI-SFRC-35 V3-PC V3-SFRC Seg-1 Seg-2 Seg-3 Seg-4 EX-NS EX-HS lll-B lll-UB 1E-1,5 1E-2,5 1E-3,5 2E-1.5 2E-2,5 2E-3.5 D-1,5 D-2,5
io sanh
^ EXP
(kN) 240,2 203,4 211,5 227,0 197,3 166,7 183,1 175,1 195,1 244,6 215,8 261.7 125,7 115,5 219,7 219,9 40,5 68,0 37,0 63,0 67.0 66.0 162.0 224,0 177,5 42,0 91,2 104,0
86,0 92.0 164,6 237,1 200,6 160,2 214,2 198.5 166,8 214.2
D-3,5 198,5
gia trj thirc nghiem va gia trj tinh toan (tilp)
Cong thuc cua Wakasa V..,(kN)
546.4 542.0 550.2 572.9 289.0 80,9 190.6 • 196,7 313,7 354,3 516,7 475,7 258,5 251,0 527,4 553,6 227.5 455.0
• 227.5 455,0 162,5 162,5 215,6 215,6 215,6 215,6 171,4 257,1 205,5 205,5 354,3 399,2 335,1 313,3 364,0 386,2 378.8 429,4 339,0 Trunq binh
Phuo'nq sai He so phan tan (%)
y A/
0,44 0,38 0,38 0,40 0,68 2,06 0,96 0,89 0,62 0,69 0,42 • 0,55 0,49 0,46 0,42 0,40 0.18 0.15 0.16 0.14 0.41 0,41 0,75 1,04 0,82 0,19 0,53 0,40 0,42 0,45 0.46 0.59 0.60 0.51 0,59 0,51 0,44 0,50 0.59 0,54 0,32 59,94
Tieu chuan cua Due
Vr.,m)
588,4 583,7 592,5 617,0 311,2 87,1 205,3 211,9 337,8 549,5 556,5 512,3 278,4 270,3 568,0 596,1 245,0 490,0 245,0 490,0 175,0 175,0 232,1 232,1 232,1 232,1 184,6 276,9 221.3 221.3 381.6 430,0 360,9 337,4 392,0 415,9 407,9 462,4 365,0
V N 0,41 0,35 0,36 0,37 0,63 1,91 0.89 0.83 0,58 0,45 0,39 0,51 0,45 0.43 0,39 0,37 0,17 0,14 0,15 0,13 0,38 0,38 0,70 0,96 0,76 0,18 0,49 0.38 0,39 0,42 0,43 0,55 0,56 0,47 0,55 0,48 0.41 0.46 0.54 0.50 0.30 60.40
Cong thuc cua Romback - m6i ndi
epoxv
VrAm
546.4 542.0 550.2 572.9 289.0 80.9 190.6 196,7 313,7 510,3 516,7 475,7 258,5 251,0 527,4 553,6 227,5 455,0 227,5 455.0 162.5 162.5 215.6 215,6 215,6 215,6 171,4 257,1 205,5 205,5 354,3 399,2 335,1 313,3 364,0 386,2 378,8 429,4 339,0
V N 0,44 0,38 0,38 0,40 0,68 2,06 0,96 0,89 0,62 0,48 0,42 0,55 0,49 0,46 0,42 0,40 0.18 0,15 0,16
• 0.14 0.41 0.41 0.75 1,04 0,82 0,19 0,53 0,40 0,42 0,45 0,46 0,59 0,60 0,51 0,59 0,51 0.44 0,50 0.59 0,54 0,32 60,40
Cong thuc cua Romback - m6i ndi kho
VrAm
767,1 758,7 757,8 791,3 507,4 299,3 416,0 422,2 539,1 729,0 735,5 694,4 378,2 358,9 754,6 774.6 341,4 568,9 341,4 568,9 273,4 290,2 393,3 397,0 413,1 365,1 356,2 501,7 347,7 347,7 395,3 446,5 381,8 356,8 413,2 437,9 424.2 472,9 380.6
V N 0,31 0.27 0,28 0.29 0,39 0,56 0.44 0,41 0,36 0.34 0,29 0,38 0,33 0,32 0,29 0,28 0.12 0.12 0.11 0.11 0,25 0,23 0.41 0,56 0.43 0.12 0.26 0.21 0.25 0.26 0.42 0.53 0,53 0.45 0,52 0,45 0,39 0,45 0.52 0.34 0,13 38,48
S6 9 nam 2012
# # # # KHOA HOC - C O N G NGHE
toan cho t i t ca cdc d i m , Theo AASHTO, k i t qua dya tren sudn d i m , theo cdng thue (1) vd (2), viee gidi han gia trj K theo cdng thLPC (5) hoac khdng gidi han gia tri cua K nhu ggi y eua Avendano [9] dugc tinh toan d l so sanh, Vigc so sanh k i t qua tinh todn vd gid trj thue nghiem dugc danh gia tren ly thuylt phan tich thdng ke.
K i t qua ehi ra rang, doi vdi tieu chuan cua AASHTO, khi khdng gidi han gia tri cua K, do chinh xdc eua cdng thuc dua tren pha
huy tren sudn d i m t i t hon so vdi khi gidi han gia tri eua K, Cu t h i id gid tri trung binh eua ty sd gi&a gid tri thyc nghiem vd gid tri tinh todn giam t u 1,23 xuIng cdn 1,09, Gia tri phuong sai vd gid tri cua he s i phdn tdn cung giam, Tuy nhien, gid tri tuyet d i i cua phuong sai va he s i phan tdn v i n edn ldn, N l u su dgng cdng thue tinh toan SLPC khdng cat cua m l i n l i d l quylt djnh sue khdng d t cua d i m , do ehinh xac la khdng cao, Cg t h i gid tri trung binh giua
gid tri thyc nghiem vd tinh toan la 0,31, Gid tri phuong sai tuy kha nhd nhung gid tri eua he sd phdn tdn cung kha Idn, 45,26%, Noi cdeh khde, n l u dung cdng thuc tinh todn sue khang d t eua moi ndi d l quylt djnh sue khang cat cua d i m se Idm cho d i m khong an todn, Dd Id do mdt s i nhugc d i l m nhu da phan tich trong muc 2.1. Gid tri trung binh cua giua gia tri thue nghiem vd gid tri tinh toan bdi cdng thue (16) eua tieu chuln JSCE Id 1,31. D l ddng nhan thay ring gia tri trung binh, phuong sal va he s i phan tan theo tieu chuln cua JSCE la cao hon so vdi gia tri trung binh trong cdng thuc cua AASHTO. D i l u dd nghTa Id cong thue cua JSCE Id an todn hon so vdi cdng thuc cua AASHTO.
Gid tri trung binh cua ty so giua gid tri thyc nghiem vd gia tri tinh todn theo cdng thuc eua Wakasa, theo tieu chuln cua OCrc, theo Romback cho m l i n l i khd hay m l i n i l epoxy d l u khd nhd. He so phdn tan d l u khd Idn. Gid trj trung binh cua Wakasa, theo tieu chuin eua Oifc, theo Romback cho moi n i l epoxy x i p xi blng nhau. Dieu dd chung td ring n l u su dung cae cdng thue nay d l xac djnh sue ehju tai cua d i m se Idm cho d i m khdng an todn.
4. NHAN XET
Mdi cdng thuc d l u dugc de x u l t dua tren cae k i t qua nghien CLPU bdng thyc nghiem va ly thuylt. Moi cdng thCpc ed mdt trilt ly tinh toan khac nhau,
Cdng thuc cua AASHTO va cua Eurocode 2 dya tren co che truyin luc giCra hai doan d i m qua mdi n i l , Co che truyin lye giOa hai doan d i m phu thudc vdo tung vj tri cua m l i ndi bdi nd bj chi phoi
So 9 nam 2012
KHOA HOC - C O N G NGHE MMk
bdi anh hudng cCia mdmen cd t h i d i n d i n dd m d rgng ciJa m i l n l i lam giam dign tich truyen lye vd Idm cho co c h i truyin luc cdng trd len phuc tap iio'n d giai doan tdi han, Cdng thuc de x u l t trong tieu chuan AASHTO Id dya tren nghien cuu ciJa Ramirez and Breen [17], Trong khi dd cdng thuc tinh toan cua tieu c h u l n 22 TON 272-05 lai dya tren tidu c h u l n eija AASHTO, trong dd cdc hang so v l c o ban Id tuong duong vdi cdc h I n g so trong cdng thuc cua Ramirez and Breen, Do dd, d n cd cae nghien CLPU sau hon d l Idm rd CO c h i t r u y i n lye vd de nghj nghien cuu sua ddi, dieu ehinh cdng thue ndy trong tieu c h u l n 22 TON 272-05,
D i i vdi cdng thuc eua Romback vd cua JSCE, mac dD khac nhau v l nguyen ly tinh todn nhung cdng thdc lai g i n g i l n g nhau khi k l d i n anh hudng cua khoa chong d t . Cdng thuc (24) Id d y a tren i>ng s u i t t i l p tren mgt phang phd huy, nhung ung s u i t t i l p tai mat phang phd huy cua m i l n l i lai d u g c xdc djnh thdng qua ung s u i t nen trung binh taJ moi n l i . Trong khi dd cdng thuc (29) lai tryc t i l p dya tren ung s u i t ehju nen tai mat p h l n g bj pha huy. Cac he so ma sat, anh hudng cua do khit cua cua moi noi cung phat hien cd s y sai lech.
Ngoai trO cdng thuc cua Wakasa Id cd k l d i n s y anh hudng cua do m d rdng v l t nut. Tuy nhien, each xdc djnh cdeh thdng so trong cdng thCpc Id rat khd vd khd phuc tap va dan d i n do chinh xdc cdn chua cao.
[2]
[3]
[4]
[5]
[6]
[9]
TAI LIEU THAM KHAO
[I] Wakasa T, Otsuka H, Yabuki W, Experimental Study of the Shear Strength of Precast Segmental Beams with External Prestressing, Structural Concrete, 6(2), pp.63-80, June (2005).
O. Buyukozturk, M. M. Bakhoum, S. M. Beattie, Shear Behavior of Joint in Precast Concrete Segmental Bridge, Journal of Bridge Engineering, ASCE, Vol. 116 (12), pp.3380-3340, Dec. (1990).
M. A. Issa and H. A. Abdalla, Structural Behavior of Single Key Joint in Precast Concrete Segmental Bridge, Journal of Bridge Engineering, ASCE, 12(3), pp.315-324, May (2007).
J. Turmo, G. Ramos and A. C. Aparlcio, FEM Modelling of Unbonded Posttensioned Segmental Beams with Dry Joint, Engineering Stnjctures, 28, pp.1852-1863, 2006
Nguyen, D. H., Watanabe, K, Niwa, J. and Hasegawa, T., Modified Model for Shear Carrying Capacity of Segmental Concrete Beams with External Tendons, Journal of Materials, Concrete Structures and Pavements, JSCE, 66(1), pp.53-67, 2010
Nguyen, D. H., Matsumoto, K., Niwa, J. and Hasegawa, T , Shear Carrying Capacity of Segmental Concrete Beams with Draped External Tendons, Journal of Materials, Concrete Structures and Pavements, JSCE, 67(4), pp.564-577, 2011.
/\ASHTO, LRFD Bridge Design Specifications, 4th Edition, American Association of State Highways and Transportation Officials, 2007.
Z. Kamaitis, Field Investigation of Joints in Precast Post-Tensioned Segmental Concrete Bridges, Baltic Journal of Road and Bridge Engineering, 3(4), pp.
198-205,2008.
Avendano, A. R. and Bayrak, O., Recommendation for the Shear Design Provisions for Segmental Box Girder Bridges of /\ASHTO-LRFD Bridge Design Specifications, 4th Edition, 2008 Interim (2008), 2008,
[10] AASHTO: Guide Specifications for the Design and Construction of Segmental Concrete Bridges, 2nd Edition 1999, 2003 interim,
[ I I ] DD ENV 1992-1-5:1996 Eurocode 2: Design of Concrete Structures, Part 1-5, General Rules, Structures with Unbonded and External Tendons, 1996, [12] BS EN 1992-1-1:2004 Eurocode 2: Design of Concrete Structures, Part 1-1,
General Rules and Rules for Building, 2004,
[13] Japan Society of Civil Engineers (JSCE): Standard Specifications for Concrete Structures, Structure Performance Verification, 2002,
[14] Deutscher Beton-Verein: Empfehlungen fur Segment fertigteilbriicken mit externen Spanngliedern, April 1998,
[15] J, Turmo, G, Ramos and A, C, Aparicio, Shear strength of dry joints of concrete panels with and without steel fibres Application to precast segmental bridges, Engineering Structures, 28, pp,23-33, 2006,
Romback, G,: Precast Segmental Box Girder Bridges with External Prestressing - Design and Construction, INSA Rennes, Feb, 2002,
Ramirez, A. G., and Breen, J. E., Experimental Verification of Design Procedures for Shear and Torsion in Reinforced and Prestressed Concrete,"
Research Report 248-3, Center of Transportation Research, University of Texas at Austin, Austin, Texas, November 1983.
Sivaleepunth, C , Niwa, J., Nguyen, D. H., Hasegawa, T and Hamada, Y., Shear Carrying Capacity of Segmental Prestressed Concrete Beams, Journal of Materials, Concrete Structures and Pavements, JSCE, 65(1), pp,63-75,2009, [19] Turmo, J,, Ramos, G,, and Aparicio, A, C , Shear Behavior of Unbonded
Post-Tensioned Segmental Beams with Dry Joints, Engineering Structures, 103(3), pp,409-417, 2006,
[20] Hosoda, A „ Kobayashi, K„ and Kino, J „ Shear Properties of PC Segmental Beams Using External Tendons Cable Method, Proceeding of JCI, 24(2), pp,409-417, 2002 (in Japanese),
[21 ] Ito, T , Yamaguchi, T, and Ikeda, S„ Flexural Shear Behavior of Precast Segmental PC Beams, Proceeding of JCI, 17(2), pp,773-778,1995 (in Japanese), [22] Ramirez, A, G „ Behavior of Unbonded Post-Tensioning Segmental Beams with
Multiple Shear Keys, PhD Thesis, University of Texas at Austin, Texas, 1989, [16]
[17]
[18]
So 9 nam 2012