l6t phiFcng phap xac dinh kha nang khang cat cua dam

\/l6t phiFcng phap xac dinh kha nang khang cat cua dam :ao SLP dung sm thep

\r\ simple approach for estimation of shear resistance of steel fiber reinforced concrete leep beams

Igay nhan bai: 15/10/2014 Igaysira bai: 22/12/2014 Jgay chap nhan dang: 5/01/2015

rOMTAT:

3an day, phfldng phap dflng sOi thep cho thay dfldc tinh kha thi va hieu qua trong viec im tang khi nang khang cat, sfl liun viec deo dai va kha nang hap thu nang Ifldng cua iam cao. So vdi cot dai truyen thong, phflong phap dung sai thep c6 nhflng flu diem ihfl: (i) kich thflflc spi nho nen de dang sfl dung cho cau kien dam cao von co be rong iet dien be; (2i) sell phan tan d^u trong be tong lam gia tang cfldng do chiu keo cfla be ong va vi vay gop phan han che sfl xuat hien cfla vet nflt li ti trong ket c3u va tang tinh oan khoi cua ket cau. Bai bao nay gifli thieu mot cong thdc mcfi d^ dfl doan kha nang diang cat cua dam cao sfl dung soi thep. Tinh chinh xac cua cong thflc de xuat dflOc (tern chflng tren dfl li^u 77 mau dam cua cac tac gia khac va 12 dam cfla chinh tac gii.

26ng thflc cung dflpe so sanh vdi 4 cong thflc da co. Ket qua cho thay cong thflc de xuat ifl doin chinh xac k h i nang Iching cit cua dam va co mfle do sai lech nho nhat trong :ac cong thdc da c6.

rfl khoa: dam cao; sdi thep; kha nang khang cit; cong thflc; kiem chflng.

ABSTRACT

Recently, the usage of steel fibres in the concrete matrix is well-known to mcrease effectively ts shear strength, ductile behaviour and capacity of the energy absorption. Steel fibres iniforraly dispersed in the concrete have some important advantages over traditional itirrups. Firstly, fibre spacing is incomparably smaller than spacing practically achievable )y using stirrups. It is very beneficial because, due to small spacii^, fibres can bndge cracks hroughout the entire concrete matrix. Secondly, an adequate amount of fibres increases he tensile strength of the concrete matrix, which increases the cracking shear force. The )aper presents a new formula for estunation ofthe ultimate shear resistance of steel fibre einforced concrete deep beams. The proposed formula was evaluated using 77 published ind 12 new test results and its accuracy was compared with four already known formulas.

rhe obtained results indicate the validity of the new formula for a wide range of beam and naterial parameters and prove its appUcability for a reasonably precise estimation of the iltiraate shear resistance of steel fibre reinforced concrete deep beams.

Ceywords: deep beam; steel fibers; shear resistance; formula; evaluation.

rs. Nguyin Minh Long

Jfl mSn Cong trinh, Khoa Ky diuat Xay dimg, Truong Dai hpc Bach Khoa Tp. Ho Chi 'linh, E-mail: nguyenminhlongi@hcmut.edu.vn

rhS. Trinh LSm Minh Ti^n

'h6ng phat m a n du an, Cong ty Dia 6c Novaland, E-mail: minhtien2785@gmail.com 'hS. Tran Quoc Toan

Ihoa Ky thuat Cong trinh, Trucmg Dgii hpc Ton Due Th5ng, E-mail: toantran2003@

mail.com, Dien thoai: 093 528 5391

Nguyen Minh Long, Trjnh Lam Minh T i e n ,

Tran Quoc Toan

l.GlOlTHlEU

Hien nay, cac cong tiiflc d u doan khS nang khang cat trong dam SFRC deu la cong tiiflc thUc nghiem [16], [4] hoSc b^n thuc nghiem [14], [91. Cic cong thflc nay duoc xay dUng theo gia thiet dam Bernoulli Tuy nhi^n, flng x f l cua dam Bemouili vi dam cao c6 nhieu fliem khac biet, vl vay d f l chinh xac cua cac cong thflc nay khi ap dung cho dam cao SFRC van chua dUoc

\im ro. NgoSI ra, tat c i cac cong thflc (ngoai t r f l cfla Nguyen Minh va Rovnak [9]) deu khong xet d^n hi^u flng chot chan va m o t vai cong thflc khong ke den 5nh hu'dng cfla kfch thi/flc d^n kha nang chiu lu'c cfla dam, trong khi cacy^u t o nSy cfl i n h hu'dng dang k^ den k h i nang chiu luc cfla dam cao. Tfl thUc ti nay doi hdi p h i i cfl mot cong thflc xem x^t d^n dSy d f l hon cSc cO che khang cat trong dam cao Bai b i o n^y de xuat cdng thflc m d i dU d o i n Ichi nang k h i n g c i t cila dam cao SFRC. Tinh chinh xac cfla cong thflc de x u i t duoc k i l m chflng vci so s i n h vfli 4 cdng thflc gan 6iy dua tren sd lieu s i n cd cila cac tac g i i khac va sd lieu cua chinh t i c g i i .

Z O e x u A T C O N G T H t f C

Cong thflc xac dinh k h i nang k h i n g c^t cfla dam dUOc x i y dflng dUa tren m o hinh pha hoal theo tiet dien nghieng (Hinh 1]; dieu kien c i n b i n g flng suat v i sfl tUOng thich ve bien d^ng trong tiet dien. Theo d o c i c co che chfl dao tham gia vdo vigc k h i n g c i t n h u sau 1) k h i nang k h i n g c i t cfla vflng chiu n^n b l tdng V^ 2} k h i nang khang cat cfla cdt dai V^ 3) k h i n i n g k h i n g cat do hieu flng cai mdc cfla cdt lieu V^; 4) k h i nang khang cat cua cdt doc V^

do hieu flng chdt c h i n (dowel action] va 5) k h i nang k h i n g cat ciia soi thep p h i n b d dpc theo bS mat v i t nflt xignFp

Ddi vdi dam cao, do h i m lu'ong cdt t h i p doc trong dam Idn, nen khi dam bj pha hoal, bien dang cCia t h i p doc tai vi t r i mat p h i hoai xien chUa dat tdi bien dang c h i y d i o [7]. Khi dd hieu flng chdt chan tham gia dang ke vao k h i nang khang c i t cua dam. d t h d i diem phd hoai.

be rdng vet nflt xien trong dam xap xi 4 m m v i vdl be rdng nay l i m cho hieu flng cai mdc V bj g i i m di dang ke, cho n i n cd the dUpc bo qua.

4.20i5k!«iiii:wa.'i 8 !

Hinh 1- Mo hinh phan t'di khi lung khang cat dia dam T h e F ^ F , v i F ^ v i o ( 1 ) :

H1nh2 Quanh§ilngiultbifndang n^nciiabStfing

D i l u k i f n c i n b i n g Iflc theo phUcmg ngang duoc t h i hi^n nhu sau (Hinh 1 )•

F, + F,smcx = F, (1) F, la thdnh p h i n ngang cfla luc keo trong

thep d o c Luc k l o nciy duoc xac dinh t f l mdi quan he gifla flng s u i t va bien dang. Trong truflng h p p dam cao, bien dang cua cdt doc tai V! t r i mat p h i hoal xien co the lay b i n g 0 . 8 E ^ [7], trong d d E,^ l i b i l n dang c h i y cfla cdt doc.

Tfl dd, Iflc keo trong cdt dpc F^ cd the dUpc x i c dinh n h f l sau:

F^=pbd0.8f,, (2) Vfli p l i h i m lu'png t h i p dpc, b va d l i be

rdng vd c h i l u cao Idm vide cfla dam, f^ la flng suat c h i y cua t h i p dpc. Luc keo cua spi thep F, trong cdng thflc (1) dUoc x i c dinh:

F, = A.T (3) Trong do, T la flng suat bam dinh trung binh

cua be tong va spi t h i p , T = 4.15 MPa [15], \ la t d n g dien tich t i l p xflc cua scA t h e p vdi be t o n g tren m i t vet nflt x i i n :

. ' n,nD.L,

2 ^ (4) Vcfi n, l i h i sd ke den i n h hudng cfla hinh

dang sol thep v i loai be tdng lay theo [8] (spi mdc 2 d i u , n, = 1; spi x o i n n, = 0.75, spi t h i n g , n, - 0.5), D, v i L, la dUdng kinh va chieu dai soi, L, /2 la chieu dai chiu keo trung binh cua spi thep, n la sd luong spi t h i p p h i n b d tren d i l n tich mat c i t nghieng.

Theo [12), sd lUOng s d tren mdt d o n v i dien tich mat c i t :

ecA=0002

V...

1.64V,

(5) Trong d d V , la ham lUOng spi t h i p tinh theo t h i tich (%). V i y tdng sd sOi t h i p doc theo be mat vet nflt xien Id:

^ a, 1.64V, ba, n = n j ) - — J — = 7 ^ — —

cosa nD, cosa (6) Tfl dd, t d n g dien tich t i l p xflc cfla scfi t h e p vfli be t d n g dUoc x i c dinh nhU sau:

^ 1.64V, ba; n,jiD,L, p g , V , L . b a ,

^ jtDj cosa 2 ' D, cosa (7) Thay cdng thflc (7) vao (3), lUc k h i n g c i t cfla SOl thep F ;

D, cosa (8) Luc nen be tdng F^ trong cdng thflc (1) dUcfc

x i c d i n h nhusau (Hinh 1):

F.-b£-M» _ ,5, Mdi quan he gifla flng s u i t nen va bien dang cfla b l tdng dUpc x i c djnh theo de xuat cOaMander[10](Hinh2):

Trong dd, c^ la bien dang vflng chiu n i n cfla be tdng; E^ la bien dang nen tuong flng vdi cuflng do chiu nen f ' cCia b l t o n g , e^ = 2f^7E^' E^

la md-dun d i n hdi cua be t d n g , E = 4700(f 'f^

° 2350

= 0 . 8 p b d f +0.82 ' ' ^ TSina ' D, cosa Thien ve an t o i n v i t nflt c i t thudng dupe gia thiet nghieng gdc 45° so vdi truc dim.Thay the c i c g i i trj E^ =2V/E^ E ^ =0.002 a =45°, a,

= d - x , F = V ^ / D , v i o c t . ( 1 S ) : x ^ ( 4 . 7 ^ - 7 . 3 8 )

= 0-8pdf^ -(-0.82Ft(d-X5„) Tfl dd, chieu cao v u n g be t d n g chju nen x^:

0.8pdf,+0.82FTd

* ^ ( 4 . 7 7 V - 7 - 3 8 + 0.82FT) ^^^

Nhfl vay, chieu d i l hinh c h i l u cfla m|it phi hoal xien len true d i m la.

(16}

0 1 )

0 . 8 p d f + 0 . 8 2 F T d a , = d \—r ^ T =kd(l81

' (4.77f; - 7 . 3 8 + 0 . 8 2 F x j Trong do, k Id h& sd,

0.8pdf. +0.82Fxd ( 4 . 7 ^ - 7 3 8 + 0.82Fi) G i i thiet su phdn b d flng suat nen cd dang gan dflng nhU Hinh 1, k h o i n g c i c h t f l trong t i m tiet dien vflng be tdng chju n i n d i n mep chju nen cfla t i l t dien b i n g 0.43x^. Tfl dfl, dilu kien c i n b i n g m d men tai trpng t i m tiet di^n vung b i t d n g chiu n i n dUOc t h i h i l n nhusau:

V^a = Vja,+F,(d-0.43x^)-i-V„^

a. (191 -i-F,( ' +Q.57x^sina) ' '

2 c o s a

Trong dd, V^ la kha nang khang c i t oia oft d p c

Lfle khang c i t ndy t i I I nghjch v& btin dang k l o trong cdt dpc.Theo [3], V^ dupc xac ^nh nhusau: ^

(20) (21)

= 0 . 7 8 i ) ) ' . ^ ^

e, = ^ 5 * ^ (12) Vdi e.^^^ la bien dang cilia b l tong khi d i m bi

p h i hoal do cat, e^^^ = 0.002 [1], x,,^ l i chieu cao vflng be t d n g bj nen cfla dam tinh t f l mep chju n i n den true trung hoa,

T h i (11) vd (12) vao (9), lUc nen cfla b l tflng Fj dupc tinh n h u sau

Trong do, <t> la dudng kinh cdt d p c Luc khdng c i t trong cot dai dupc x i c S\n\(i- v. = A „ i f „ = p M f . 1^, T h e ( 2 1 ) v i { 2 2 ) v a o ( 1 9 ) :

V ^ a = 0.78iti',J^aT. + 0.8bdf^p(d-0.43x,) + P . f , v b — + 0-82bFT:aT.(aT-i-0.57x,) ' Ce d o n g i i n trong v i f c t i n h t o i n , dai liipng luc keo F^ cfla cdt doc trong cdng thflc (23), dupc thay t h i b i n g luc nen cfla be tdng F, theo nguyen ly can b i n g luc {thien ve an t o i n vd rf d o n g i i n hda cdng thflc tinh, bfl qua i n h hfldng cfla s d theo phuong doc true). T i l n h i n h nit gpn, k h i nang k h i n g c i t cfla dam cao c6 t&|S

86EVV1Vii9V 4.2015

xac djnh t h e o cdng thflc sau (vdi sai sd < ±5%):

^ d o . 8 5 ( i - k ' ) f ; ' ' ' + o j k V , v

" a|+o.2k{1-(-k»=T (24)

+ 0 . 7 8 k - « ' ^ 3.DANH GlA C O N G T H Q C D ^ X U A T Cdng thflc de xuat (24) v i 4 cdng thflc cua cac t i c g i i k h i c (Bang 1) duoc kiem chflng dfla tren d f l lieu thuc n g h i i m 89 mau dam dupc lay tfl thf n g h i i m cfla [11], [13], [2], [5], [14], [4] va CLia chinh t i c g i i .

3.1.K.1.ovdRovnak(2011}hdn.

K i t q u i kiem chflng theo Hinh 3 cho t h i y , cong thflc d l x u i t cd d d chinh xac cao cho c i dam cao v i d i m n g i n . G i i trj d f l d o i n sat vfli g i i tri thuc nghiem v i dn d i n h . D i l u ndy t h i h i l n rd qua g i i tri trung binh cua t i sd V^ A/^^^p bang 0.96 va he sd b i l n thien COV bang 0.13.

3.2. So sdnh cdng tit&c dixuSt vdi cdc cdng thOc dded

Theo Hinh 4, k i t q u i tinh t f l cac cdng thflc da cd chua chinh x i c v6i g i i tri t r u n g binh t i n h todn chenh lech so vdi gid t n thuc n g h i i m t f l 15% d i n 45%. D p phan tdn theo cdng thflc cfla Imam; Kwak va c6ng sfl; Cho v i Kim; Nguyen vd Rovnak cdn tUOng ddi Ipn vdi g i i tri COV tUOng flng l i n lUpt la 0.28,0.25,0.24 va 0 30

Hinh 5(a) t h i hien mdi quan h i gifla tl sd

400

§ 300 .3 200 100

BDam ngitn

J"

^

^

Mcnn: 0 Wi

<.(>\ (113

500

% 400

200 100

x ^

"

^>«

' h j T

%^' .

^

V ^^yv vfli cuflng d p chju n i n cua be t d n g f/. Ttnh toan t f l c i c cdng ttiflc cfla Imam va Kwak cho k i t q u i khong an todn va cd d d p h i n t i n Ifln tren tc}in mien k h i o s i t Khi g i i tri f'^ tang, dp phan t i n cua hai cdng thflc nay cung gia t i n g . Cdng thflc cfla Cho va Kim, Nguyen vd Rovnak cho k i t q u i t u o n g ddi dn dinh. Trong dd, cdng thflc ciJa Nguyen va Rovnak cho k i t qua thien v l an t o i n nhat.

Hinh 5(b) the hien mdi q u a n h l g i f l a t l s d V ^ J^^^d\

hdm lupng cdt d o c Cdng thflc cfla Imam cd xu hudng cho k i t q u i Idn hon thUc nghiem, d o phan t i n Idn va gia t i n g khi hdm lupng cdt dpc tang.Trong khi dd, cdng thflc cua Kwak cho ket q u i vfli d d phan tan g i i m khi ham luong cdt doc tang. Cdng thflc cfla Cho va Kim cho k i t q u i n i m trong mien an todn va tUong ddl on (Sjnh vfli ham lu'png cdt doc nho hon 3%. Khi

B i n g 1: C i c cdng thflc d f l d o i n k h i n i n g k h i n g c i t da c6

Hinh 3: So sinh khi nang khang cJt tinh theo cong thdc de xuat va khi ning khing cSt thifc nghif m

200 300 400 500

(yhi chti XC6nglhvc Nguyen el al D cang Ihiic Cho vd Kim A Cdng Ihuc Kwak el al

Tac g i i

Imam (1994)

Kwak va cdng sU (2002) Chova Kim (2003) Nguyen

va Rovnak (2011)

Cong thflc

V , -

• f . " " ( l + F " ' )

4 5 7 0 . / ^ . V(a/d)' 2 . 1 e f , ; ; , f p ^ l + 0 . 8 ( 0 . 4 1 t F ) " "

bd

bd

V..105J^1-0.355Jf„bd+112.52A,(^^j

C « b d + 0 - 7 0 7 ^ F i f l n - + l j p " ' b d + ^ 0 , 9 f „ b d

« Cdng thuc de xudl Hinh 4. Bern chlhig tinh chinh xit ciia cic cong thiJc

H'inh S. fiinh gii c^g thiic theo (a) cuong do chju nen be f'; (b) ham lurnig th^p doc p; (c) ham lUOng soi thep V^

h i m Iflpng cdt doc Idn hon 3%, k i t qua tinh t f l cdng thflc cfla Cho va Kim bat dau cd sU phan t i n . Cdng thflc cCia Nguyen vd Rovnak cho ket q u i t h i l n ve an t o i n trong toan mien k h i o s i t . Viec dd phan t i n cfla cac cdng thflc thay ddi khi h i m IflOng cot dpc gia tang Idn h o n 2 cd t h e la do, trong m d hinh tinh cua Imam va Cho Kim da bd qua i n h huflng cCia h i l u flng chdt chan. Khi h i m lUOng cdt dpc trong dam cdng ldn se lam g i i m d i n g k l b i l n dang cua cdt dpc t f l d o lam gia tang lUc chdt chan trong cdt doc.

Hinh 5(c) the hien mdi quan he gifla tl sd V ^fV ^ vdi ham lUpng spi thep. Cdng thflc ciia Imam va Kwak cho thay sU chenh lech ldn r i t Ifln vdi ket q u i thuc nghiem, dac biet tai gia t n V,= 0.5 den 0.8%. Cdng thflc cua Cho va Kim, Nguyen v i Rovnak cho k i t q u i an toan vol d d phdn t i n k h i deu tren todn m i l n k h i o sat.

4 . K ^ T L U A N

Tfl k i t q u i nghien cflu da dUpc trinh bay 6 tren, m d t s6 k i t l u i n cd t h i dUOC rflt ra nhUsau:

1) Cdng thflc ciia Imam, Kwak, Cho vd Kim, Nguyen vd Rovnak dU doan k h i nang k h i n g dam cao spi t h ^ p chua chinh x i c . Ket q u i tinh theo cac cdng thflc tren c6 sfl p h i n t i n Ifln.Tinh khdng dn dinh cua cac cdng thflc dUpc the hien qua hai gia tt\ la d o lech c h u i n trung binh b i n g va he sd bien thien trung binh l i n lupt la: 0 41 % vd 0 28% ; 0.29% va 0.25% ; 0.2% vd 0.24% : 0.21 % v a 0.3%.

2) Cdng thflc de x u i t cho k i t q u i sat vdl k i t q u i thuc nghidm vdi tinh d n dinh cao vd dp phdn t i n thap. Dieu nay duoc t h i hien qua gid tri trung binh cfla t l sd gifla k i t q u i d f l d o i n k h i ndng k h i n g c i t theo cdng thflc de x u i t vfli k i t q u i thflc nghiem Id 0.96 va he sd bien thien l i 0.13(13%).

3) Cdng thflc d l x u i t xet duoc i n h hudng cOa c i c y l u t d nhU: chieu cao vflng chju n i n be t d n g ; t i sd nhip chiu c i t v i c h i l u cao t i n h t o i n , i n h hudng cCia hieu flng chot chSn cfla cot doc

So vdi c i c cdng thflc thuc n g h i i m , cdng thflc g i i i tich g i i i thich duoc m d t c i c h dinh lUcmg i n h hudng cfla c i c cO c h i truyen flng s u i t c i t trong dam, t h i hien dUOc ban c h i t vat ly mdt each rd rdng hon.

5. L O I C A M O N

Nghien cflu nay dUpc tdi t r p bdi TrUdng DH Bich Khoa TP. Hd Chi Minh trong d l tdi ma sd T-KTXD-2015-48.

TAIUEU THAM KHAO

[11 ACI 445-R99,1999 Recent Approach to shear Design of Slmdural Concrete

[2] Aihour, A F. 2000. Shear Capaoty of Reinforced Concrete Deep Beams. Ioumal of Sbiictural Engineering, 126|9), pp 104S- 1052

[3] CE^FIP Model (ode 2010 First complete draft - Volume 2. Lausanne. Switzeil and, 2010,311p

(4] D, Oupont. and L., Vandewalle, Shear capaaty of concrete beams containing longitudinal leinforcement and steel fibres, in Innovations in Hbre-Reinforced-ConcTele for Value. N..

Bsnthia, M, Cnswell, P.Tatnall, and K., Folliard., e d s , ACI-SR 216, 2003, pp,78-94

[5] Dawood Abdulhai Pandor, Behavior of High Strength Rber Reinforced Concrete Beams in Shear. Submitted to the Department of Ciuil and Environmental Engmeering in partial fulfillmem ofthe lequirements forthedegree of Master of Saence in Civil and Environmental Engineering at the HASSflCHUSEnS INSTITUTE OFTECHNOLOGY, February 1994

[6] Imam, M., Vandewalle, L „ and Mortelmans, F Shear- Moment Analysis of Reinforced High Strength Conoele Beams Containing Steel Fiber. Canadian Joumal of Gvil Engineenng, 22, 199S, pp. 462-470

[7] Gaiay-Moian, J. D., and Lubell, A. S Behaviour of Concrete Deep Beams w i t h High-Sttength Reinforcement Structural Engineering Report No 277, 2008, Department of Civil and Environmental Engineenng. University of Alberta, Edmonton, AB, Canada, 283 pp

[8] Khuntia M, Stojadinovic B, God SC. Shear strength of normal and high-strength fiber reinforced concrete beams without stinups ACI Struct f o u r n a l . 96(2), pp.282

[9] L , Nguyen-Minh, and M., Rovnak. New fdnnula for the estimation of shear resistance of fibre-reinforced beams.

CanadianJoumalofCivil Engineering, 3S(1).2011. pp. 23-35 110] Mander, ] . B., Pnestley, M. J. U., and Park, R (1988).

"Theoretical stressstrain model (or confined concrete.'!, of Struct Eng,, 114(8), 1804-1826

[11] Narayanan, R.. and Darwish, L Y. S. 1987. Use of Steel Fiben as Shear RemftircemenL ACI Structural Joumal, 84 (3), pp.

216-227

[12]Romualdi.J.P.&Mandel,JJ* 1964.'Ten5ile Strength of Concrete Affected by Unifiirmly Distnbuted Closely Spaced Short Lengths of Wire fieinfi)rcement'. ACI J. Pmc 61 (6)

[13] Sachan, A. K. and Kameswara Rao, C. V. S. Behaviour ofFlbfe-Reinfbiced-ConcreteDeepBeams Cements and Concrete Composites. 12,1990, pp.211-218

[14]S H , Cho andY I , Kim, Effects of steel fibres on short beams loaded in shear, ACI Structural Ioumal, 100[ 61,21X13, pp 7 6 5 - 7 7 4

[15] Swamy, R, N „ and Ali, S, A. R. (1982).'Punching shear behavior of reinforced slab-column connections made w i t h steel fiber concrete 'ACI Struct J , 79(5), 3 9 2 - 4 0 6

[16] Y. K,. Kwak, M 0., Ebeihard, W. S., Kim, and J., Kim, Shearstrength of steel fibre-reinforced-concrete beams without stimips ACIStrudural Journal, 9 9 ( 4 ) . 2 0 0 2 , p p . 5 3 0 - 5 3 8 .

8 8 f^*SIE[IBIl 4.2015