Tuy nhien, vdi su hd trg ciia may tinh dien tir v i cac phan mem phin tieh ket ca'u dua tren co sd ciia phuong phip phan tir hUu han, ngay nay chung ta co the xac djnh dugc irng sua'[r]
Trang 1r^n/\Kj OMI - m i E l KE X A Y D U N G
ANH HUdNG CUA COT DAI DEN KHA NANG CHfU LLTC CUA COT BE TONG COT THEP CHIU NEN DUNG TAM
ThS THAI DCrc KIEN
Trudng Oai hgc Vinh
Tom tat: Dua tren ly thuyet ve be tong bi han che
na hdng, trong bai bao nay tac gia tnnh bay ket qua
khao sat anh huang ciia cot dai den kha nang chiu
nen eita cot be tdng cot thep tiet dien chOr nhat Su
anh huang cua cot dai ddgc xac dmh dua tren ket qua
nghien ciru ly thuyet,'dong thdi dugc khao sat bang so
tren phan mem ANSYS Ket qua da dugc so sanh,
danh gia
1 Dat van de
Cot l i mgt trong nhOng bg phan quan trgng nha't
ciia cOng trinh Su phi hoai cDa cot c6 the anh hudng
ddn su phi hoai eiia cac kdt ca'u khae hoac l i nguyen
nhin chinh din den su phi hoai toan bg ket ca'u cdng
trinh Nhieu nghien ciru trugc diy deu cho rang, kha
nang chju nen ciia be tong (chii yeu la trong cot) co
tang len khi be tong bj han che nd hong giy ra bdi cdt
dai [5] Viec nghien cUu su anh hudng nay la rat can
thiet, gdp phan bd sung cho ly thuyet tinh toin ci'u
kien chju nen bang be tong cdt thep
De xac djnh cudng do chju nen dgc true (f^^) ciia
be tong khi co ap lifchan che nd hong thi can phai xac
djnh duge irng suit han che nd hong ( y [4] Trong cot
be tong cdt thep, ap luc ngang (han che nd hong Q lai
dugc xac djnh dua vio urng sua't trong cdt dai Trong cac nghien ciru truoc day, irng sua't trong cdt dai thudng dugc xac djnh bang cac bieu thurc thuc nghiem
d i dugc kidm chirng vdi khoang 80 miu thir khae nhau [4]
Tuy nhien, vdi su hd trg ciia may tinh dien tir v i cac phan mem phin tieh ket ca'u dua tren co sd ciia phuong phip phan tir hUu han, ngay nay chung ta co the xac djnh dugc irng sua't trong cae vat lieu bang viec mO hinh hoa ca'u kien be tong cdt thep chju nen vdi ket qua dang tin eay ma khOng qua tdn kem Trong bai niy, gidi thiiu ket qua khao sit su anh hudng ciia edt dai den su thay ddi Ung sua't va bien dang ciia be tong chju nen bang ca bieu thUe ly thuyet v i sir dung phan mem ANSYS
2 Cd sd ly thuyet ve be tong han che nd hong
2.1 Quan he dthg suat - bien dang trong be tong han che nd hong
Mdi quan he Ung sua't - bien dang eOa be tdng chju nen trudng hgp han che nd hong da dugc cac tac gia nhu Popovics (1973) [6] va Mander (1988) [7] de xua't nhu hinh 1
Be tong 'hzm che no hong
0 r,\ if.^^ e.'j ecjSQ
Bien dang dpc true «£
H i n h l Quan he Ung suat - bien dang ciia be tdng han che na hong
Dudng cong quan he trong hinh 1 xua't phat tU Trong dd: f, - cuong dO chju nen ciia b i tOng nhirng bieu thUe sau: khong.han che nd hong; f',, - cudng dO chju nen cda
/ ; = f'rrXk J CC
k-\ + x' (1)
be tong trudng hgp bj han che nd hOng
(2)
Tap clii KHCN Xdy dmg - sd 212011 15
Trang 2KHAO SAT - THIET KE X A Y D U N G
k = ^^^— (3)
d day: s, - bien dang tuong ddi cue han cua be
tong khong han che nd hong; f „ - bien dang tuong ddi
cue han ciia be tong han che nd hong
£c=5000Vy; (MPa) (4)
L
s
E, =:^-^ "" Sec (5)
Trong do: £< module bien dang tiep tuyen; Eseo
-Module bien dang phap tuyen; /^^ - cudng do chju nen
eiia mau thif hinh tru (15x30cm) d ngay thU 28
Bieu thirc (1) chi dung vdi trudng hgp khi s^ < s^^
Trong trugng hgp e^ < £•„ thi Fafitis va Shah (1985) [4]
d i de xua't mdi quan he do theo bieu thurc sau:
/, -/„,exp[^,(^,-^,J*^J (6)
Trong dd; /(, va ki la hai hang sd dieu chinh do ddc
v i do eong eua bieu dd quan he Ung sua't - bien dang
Dua vao tii lieu eua Cusson va Paultre (1994), cac he
sd do duge xic djnh nhu bieu thO'c sau:
k,=\ + 25{I^,,y- (8)
Trong dd: l^so - chi sd anh hudng ap luc han che
nd hong tai vj tri bien dang E^^^O (hinh 1)
2.2 Mo hinh cpt tiet dien tron boc tam dai Hen tuc
Xet trudng hgp mgt cot tiet dien tron vdi duOng
kinh la c, dugc bao bgc bdi mgt tam dai lien tuc vdi
chieu day la e (e ri't be so vdi c) Ap luc chdng nd
hong f, dugc xac djnh qua viec xet trang thai can bang
luc va bien dang tudng thieh Trang thai can bang giUa
i p luc trong tam lien tuc va ap lue chdng nd hong tic
dung len phan loi be tong cho tha'y nhu hinh 2
^K
r n / t 1111" t f t f
t^A
fi =
Hinh 2 Sucan bang Ung suat
Trong do: /^ - urng sua't eang trong cdt thep va cGng la ap luc chdng nd hong
TU dieu kien bien dang tuong thich va gia thiet rang bien dang cua phan be tong phia ngoii bang bidn dang cDa tam dai lien tuc (£>, co gia trj duong) dugc xie djnh bang bieu thO'c:
s-ye - ( i z O A (10)
fl cc cc
J Ecc
Trong dd:
v^-c - he sd Poisson phap tuydn va E^^ - md dun
bien dang phap tuyen ciia be tong han che nd hong theo phuang ngang, ca hai bien sd trong ham cua bidn
dang dgc true e^^
2.3 Cfng dung vao cpt tiet dien chff nhat dat cot dai
Dd ddn gian, chiing ta co the thay the tuong duong cot be tong cdt thep tiet dien chu nhat, dat cd!
dai vdi khoang each dai la s, bang mgt cot co tiet dien trdn dugc bao bgc bdi mgt tarn thep lien tuc cd chieu diy khong ddi e (hinh 3) Cot tuong duong cd dudng kinh bang kich thudc phan loi b i tong cda cSt chQ' nhat, do tU tim den tim cua cdt dai ngoai ciing Tam thep dai bgc loi be tong thay thd su lam viec ciia cdt dai, dugc tinh toan sao cho tuong duong vdi sir lim viec cua cdt dai trong tidt diin cot chif nhat
L ^ - 4 ^ = 3.41.4,
Q Hinh 3 Khai niem cot tuang duang
16 Tqp cfli KHCN Xdy dung - so 2/2011
Trang 3K
Chieu diy ciia tam vd bgc quanh cot trdn tuong
duang dugc xae djnh bang bieu thUe:
e = K ^
"• 2s
(11)
Trong do: A,^,y - tdng dien tich mat cat ngang eiia
tam vd bgc theo phuang true y trong khoang each giUa
cic dai s Ap luc ngang tic dgng len loi be tong theo
phuang y se la:
Ke - he sd ke den hinh dang dai Vdi edt dai ngang,
Ke xic djnh theo bieu thire sau [6]
K, (\-s/Acf
Trong do: p^^ - [^ le dien tieh cdt thep dgc tren dien
tieh be tong han che nd hong; s - khoang each giUa
cic Idp dai theo chieu cao cot; c - dudng kinh loi be
tong
Phai nhi'n manh rang f^, la mgt him sd cQa bien
dang dgc true trong cot e^c- Biy giO chiing ta djnh
nghia t^ sd tiet dien hOu dung ciia ap luc chdng nd
hong theo phuang y, ky hieu la p^^y
SC
TU do, bidu thUe (13) co the viet thinh
flay=PsJ, (15)
Cfng sui't han che nd hong hieu qua /jey bie'n ddi tU
khOng, khi ma urng sua't trong thep dai bang khong ddn
gia trj ldn nha't la gidi han chay cua thep dai, tire la: f;, =
i^y Nam 1995, Cusson va Paultre [4] da do dugc mirc
do ciia ap luc ngang bang chi sd ap luc ngang hieu
qua khong thU nguyen: /^ = ffe/fV
Phuang trinh tuong thieh bien dang la:
Ddi vdi dai xan, cac bieu thurc tren vin phu hgp khi
coi rang s l i budc cua dai xoan Ddi vdi cot chU nhat
va cot trOn vdi ap luc ngang ddi xirng, trong tinh toan
thuc hanh lay chi sd the tich cua cdt thep ngang la:
sc
(17)
Trong do, A^^, - l i tdng dien tich dai ngang theo
phuong true x va true y TU dd, chi sd the tich hieu qua
ciia cdt ngang se la:
A e = ^ A = ^ ^
Va ap luc chdng nd hong hieu dung se la:
f - 1 f
he ~ r PseJh
(18)
(19)
2.4 Cu&ng dp cffc dai trong be tong han che' nS hong • bieu thffc cua Legeron va Pauitre (2003)
Biy gid chiing ta se di xac dinh gia trj cudng do ldn nha't trong be tong han che nd hong v i quan he Ung sua't - bien dang (£•'<,„ f J LTng suit trong cdt dai
tai diem do l i i\, tuong urng vdi bien dang la s\ Ap luc
han ehe nd hong hieu dung dugc xac djnh theo bieu (13) thUc(13)trdthinh: y = j ^ : V y
-Bien dang tuong ddi trong cdt dai l i :
E\
(20)
(21)
Trong do: E'„ va V^^ tuong urng la mo dun bien
dang phap tuyen va he sd Poisson phap tuyen ciia
be tong xac djnh tai didm cue dai cua bidu dd quan
he Q'ng sua't - bien dang ciia be tong han che nd hong
Cudng do va bien dang cua be tong phu thuge vao him lugng v i irng sui't cda edt dai (Sheikh v i Uzumeri (1982)) Mgt sd tic gia da thUa nhan rang irng suit trong dai dat de'n cudng dd chay deo khi irng sui't trong be tong dat cue dai Tuy nhien, Cusson v i Paultre (1994) cQng nhu Li (1994) deu cho rang urng sua't trong cdt dai cd the khong dat den cudng do chay deo khi Q'ng suit be tong dat cue dai, die biet la vdi edt dai cudng dO cao sir dung vdi b i tong cudng do thudng Ket qua thi nghiem da duge thuc hiin bdi Sheikh va Uzumeri nam 1980 eho thay su chay ddo khong thudng xuyen dat dugc vdi be tong thong thuang (ed cudng do trung binh) Cusson va Paultre (1995) ed gidi thieu mgt quy trinh tuong hd dd xac djnh mo'c do irng sua't trong cdt dai tai diem cue dai cua be tdng han ehe nd hong Tuy nhien, trong bai niy khong
de cap den each do
Ggi /'e la chi sd ap luc chdng nd hong hieu dung tai diem cue dai, duoc xac djnh theo bidu thirc:
(22)
Trang 4KHAO SAT - THIET KE X A Y D U N G j r
4.0
3 0
2 0
10
-— 0.25.10/;>a43
f, i i i f / i i ' l L- ' " " « , '» "
|^U0.(/,) ^^>„ ^ -^1+2.4 (f;F^
0 Thuc nghiem
" O ^ ^ 0 C '^
0.20 0.25
Hinh 4 Quan he giii'a e'l/e'c va I',
Tren hinh 4 the hien mdi quan he giOa s't/s'^ v i /'e,
dugc xac djnh qua e i c ket qua nghien cUu thuc
nghiim TU ket qua nghien ciru ciia Cusson va Paultre
(1995), cac mdi quan he mdi duge dd xua't cho phep
ap dung vdi nhieu loai be tong k h i c nhau nhu sau:
hfc(MPa)
fcni=28
0,4fcm=11.2
£i = 30x10-'MPa
0 0,373 2,0 3,5 tU%,)
Hinh 5 Bieu do quan he irng suat - bien dang ciia be tong
J c
^ - l + 35(/J'
(23)
(24)
3 Khao sat sir anh hirdng cua cot dai bang ANSYS
3.1 Thie't ice'ca'u Aien 3.1.1 Vatlieu •
a Be tdng
Be tong cot dung loai C20/25 theo tieu chuan
Eurocode 2 cd f^k = 20 MPa, f,„ = 28 MPa; module dan
hdi: £b = 30x10^ MPa, he sd Possion: v = 0,2 Bieu dd quan he urng sua't - bidn dang cCia b i tong nhu hinh 5
b Cot thep
Cdt thep dgc va cdt dai deu dung mOt loai thep co
cudng do ehay deo fy = 295 MPa, cudng do ben f,„ =
483 MPa Bieu dd quan he Ung sua't - bien dang khi keo thep nhu hinh 6
Module dan hdi cua thep: £ , = 21x10' MPa, h i sd Possion: v = 0,3
—il
Hinh 6 Bieu do quan he irng suat - bien dang khi keo thep
3.1.2 Md hmh cdt
De khao sat su lam viec eua ca'u kien chju nen dung t i m , c i e mau cot ngan sau d i y dugc lua chon
Bang 1 Cac thong so ca ban cua cac mau cot ngan
STT
1
2
3
4
Mau c6t/ma hieu
A
B
C
D
NCC CRCC_D8S100 CRCC_D8S50 CRCC_D10S50
Kich thudc 320x320x1200 320x320x1200 320x320x1200 320x320x1200
Cdt dpc 8(j)20 8(t>20 8(t)20 8(1)20
Cdt dai khdng
<t)8a100 (l)8a50 (t)10a50
Chi tiet cac m i u cot ngan dugc thiet ke cu the nhu hinh 7
Trang 5KHAO SAT - THIET KE XAY DUNG
8»20
8«20 ,
320
X
1
'^ 320 ""
MAU B: CRCC_D8S100
«8al00
8020
320
o
08a100
8(920
' / /
^
\ ''
\ /
II
• ^ 320 ' '
o csl
M A U C: C R C C _ D 8 S 5 0
08o5O
8920
320
o
ID
o
m
o
i n
o
o
i n
o
i n
o
i n
c
o
i n
o
i n
o
i n
o
i n
o
i n
o
i n
o
m
c
iT
i n
o
i n
o
i n
o
o
m
o
i n
o
i n
o
i n
o
a
»8o50
8«20
' / /
^
\ ^
\ /
(1
•^ 320 "^
"\
M A U D: C R C C _ D 1 0 S 5 0
alOaSO
8020
»10a50
8920
320
i n
o
i n
o
i n
o
i n
o
i n
o
i n
o
i n
o
i n
o
o
tn
c
o
i n
o
m
o
i n
o
i n
c
tn
o
in
o
m
o
m
o
m
o
in
o
i n
o
i n
O
i n
c
r
(
, / ^ '
\y o CM
1
•*" 320 "*•"
H\nh7 Chi tiet 3.1.3 Md hinh hda bang ANSYS
MO hinh hinh hgc ciia cot dugc mo hinh hoa trong
ANSYS bang cie phan tir miu co san Be tong dugc
mO hinh bang phan tir khdi "SOLID65", ehia luOi phan
tir hinh khdi 6 mat (Hexahedral-shaped elements) vdi
kich thudc 20x20x50mm Cdt thep dgc v i cdt dai dugc
md hinh bang phan tir thanh "LINK8", dung phan tir
dang LINK8 - 3D Spar, chia ludi kich thudc 50mm
Liin ke't ciia cot dugc mo hinh hda mgt dau ngam, mgt
cac miu cot ngan
dau tu do, chju tai trgng nen dgc true dang phin bd deu dat trin dau cOt
Trong bii niy, lue dinh khong dugc ke den trong
mo hinh hoa vi trin thuc te chua co sd lieu thuc nghiem ve van de luc dinh giOa b i tSng v i cdt thep
De khae phuc dieu do, viic ehia ludi phan tir dugc thuc hien d dang ludi nhd, do do lien ket giUa cic nut eua phan tir ra't gan nhau lam cho edt thdp v i b i tong ddng thdi lim viec dugc tdt hon
Table :•*- M£LA
3 i ,
S.:G - ,
a
C c n f i o o t a c HC Col-oiai
/
/
/
3
l i n e a r kna l y a i
T a b i c PTftwie«
1
: i A 3 - S d 2 0 ; f i b e r :
ANSYS
-IS;S':; JS
Ish-.ft 2«r i liEXft 7ohlit P i e
J'f'!.';0
3iG
300
SIC- - j g
-,n
100
—
1
/
i 1.3 I
EPS
C a r f t r e s e : ^ t RC C o l i ^ n H o r - l i n c a r A r i a l y o i s : iXs=QdZ
i : * 3 :
2.e 3 6
:•; ? ^ b e r : d i v o S C )
ANSYS
JTO li
2G1C-I i ; S T : ; i
: T a P ' — ; >
Hinh 8 Khai bcio quan he Ung suat - bien dang be tong
Tqp cfli KHCN Xdy dmg - so 2/2011
Hinh 9 Khai bao quan he Ung suat - bien dang cot thep
19
Trang 6KHAO SAT - THIET KE XAY DUNG
ANSYS
ContiriKiaeat RC C c l u a u i N o c l i n e a c & i i « l y 3 I S j s = £ d 2 0 ; F i b e r ; cl8 sliC \
HAT VOK
ANSYS
, ScT-J.inaar a n a l y s i s : (a3=0d20; F ^ i e i : : dlOsSOj
Hinh 10 Khai bao phan tir cot thep Hinii 11 Khai bao va chia ludi phan tir be tong
3.2 Anh hffdng cua cot dai cdt dgcy^ (MPa); irng sua't trong cdt d a i / , (MPa);
^r,, „ v , , , ^ , ,,^^ ;,.,ov/o Lfng sua't trong be t o n g / ' , (MPa) va bien dang
3.2.1 Ketqua khao sat bang ANSYS , ^ , , , , „ , r,-^^ \ A ,vr,^ o,,;^*
^ ^ tuong doi ^, (MPa) Bieu do quan he ung suat
-Cac miu cot dugc khao sat tren nhieu cap tai bidn dang cua be tong han chd nd hOng do cac
khae nhau Tuong Ung vdi mdi cap tai, co the x i c truong hgp bd tri cdt dai khae nhau g i y ra, dugc
djnh duge cac dai lugng sau diy: Qng sui't trong the hien tren hinh 12
: 6
:o •
10
-a
0
/
-»r ^v ^v (T -v^
^w-StJin
B CRCC _OES100
: c •
25 • ,' 20
t
« ! £ 1C
-c
«^
I 1 I
""ill'f'
; ; I I I 1 !
i4|4|4|
-# 'T P&-#34; -# -# *^
\ - V N- V V ^•
strain
c
30 •
2 : • o2C •
1
3 15
10
-c
CRCC.DES 5C
• ^ T '
•fi-H-s?>" >^ f ^-p- •:>
Strain
D
35 •
30 •
2 6
-£ 2 0 •
15
10 •
i: ,
0
/
CRCC_B1CS50
itl'M""
J
• f i l "
•-.^ c' S if ^* %*
Stt-ah
Hinh 12 Biiu do quan he Ung suat - bien dang ciia be tong han che na hong do cac trudng hgp cdt dai gay ra
3.2.2 Ket qua tinh toan theo mo hinh ciia Legeron va Paultre
Bang 2 Ket qua tinh toan theo Legeron va Paultre
STT
1
2
3
4
Mau cot
A
B
C
D
Cot dai Ktiong (|)8a100 (t)8a50 (t)10a50
Ke
-0,8799 0,9676 0,9712
Aey -0,00269 0,00592 0,00928
f,(MPa)
-110
117
109
r,e
(MPa) -0,296 0,693 1,012
(MPa)
- • 0,011 0,025 0,036
fee (MPa)
28 30,7821 33,0434 34,5764
£\o
0,002 0,0023 0,0028 0,0033
3.2.3 So sanh ket qua
So sinh Qng sua't cue han va bien dang tuong ddi tU ket qua khao sat bang ANSYS v i ket qua tinh toan
theo mo hinh ciia Legeron dugc the hien nhu bang 3
Trang 7K H A U SAr - THiET Kc XA? DUNG
Bang 3 So sanh ket qua khao sat va tinh to^n
STT
1
2
3
Miu cot
B
C
D
Theo ANSYS fee (MPa) 30.021 33.002 34.391
^ CC
0.0025 0.0031 0.0039
Theo Legeron fee (MPa)
30.78 33.04 34.58
^CC
0.0023 0.0028 0.0033
4 Nhan xet va ket luan
4.1 Nhan xet
- Ap luc ngang do cdt d a i g i y ra co anh hudng de'n
su phin bd urng suat - bien dang trong be tdng v i cdt
thep, ddng thdi co anh hudng dang ke ddn kha nang
ehju nen eua cot be tong cdt thep v i do deo cua vat
liiu Cdt dai bd tri cang day va dudng kinh cang ldn thi
bidn dang dgc true eiia cot b i tong c i n g giam, va kha
nang chju nen ciia cot tang l i n ;
- Ket qua khao sat bang ANSYS la k h i phu hgp
vdi cae mO hinh ly thuye't, thuc nghiem Nhu vay, co
t h i sir dung phan mem ANSYS de giai quye't cae bai
toin tuong tu nham giam bdt khdi lugng nghien cQ'u
thuc nghiim
4.2 KS'tiuan
Cie ke't qua nghien cQu n i y cho tha'y, kha nang
chiu nen cua be tOng han che nd hong bdi cdt dai tang
l i n khoang 7% - 23%, tuy thuge v i o c i c h bd tri edt
dai Viec nghien cQ'u mgt each cu the, co he thdng su
anh hudng ciia c i c h bd tri cdt dai den cudng do be
tOng han che nd hong la ra't can thie't, l i m can cir de
thidt ke cac ca'u kien chiu nen trong ke't ca'u cdng trinh
TAI LIEU THAM KHAO
1 vo QU6c ANH, Tinh ket ca'u bang phan mem ANSYS,
Nha xuat ban Xay dung Ha Ngi, 2006
2 L£ NGOC HONG, Co sd ca hpc mdi trudng Hen tuc va
ly thuye't dan hdi, NXB Khoa hoc va Ky thuat Ha Noi,
2002
5
6
THAI D Q C KIEN, Luan van thac sy ky thuat, Dai hoc
Xay dung Ha Noi, 2010
NGUYiN TRUNG HOA, Tieu chuan chiu Au Eurocode
EN 1992 -1 - 1 , thiet ke ket ci'u be tdng va b i tdng cdt
thep, NXB Xay dung, Ha Ngi, 2006
F LE'GERON and P PAULTRE, Uniaxial Confinement Model for Normal- and High-Strength Concrete
Columns, Journal of Structural Engineering, Vol 129,
(2), 241-252, 2003
K.SHARMA, P BHARGAVA, P SHINGH and K KAUSHIK, Confinement Reinforcement Design for Plain and Fibre Reinforced High Strength Concrete Culumns,
Journal of Advanced Concrete Technology, Vol 5, (1), 113-127,2007
7 R EID, A.N DANCYGIER, Confinement effectiveness
in circular concrete columns Journal of ScienceDirect,
Engineering Structures 28, 1885-1896, 2006
8 J MOKARI and A.S.MOGHADAM, Experimental and Theoretical Study of Reinforced Concrete Columns with Poor Confinement Retroffited by Thermal Post Tension
Steel Jacketing, Journal of Applied Sciences 8 (24),
4579 - 4586, 2008
9 GUPTA A.K and AKBAR H., A Finite Element for the Analysis of Reinforced Concrete Structures,
International Journal for Numerical Methods in Engineering (19), 1705- 1712, 1983
10 TCXDVN 356 : 2005, Tieu chuan thiet kg ket ca'u be tong cot thep
Ngay nhan bai: 5/5/2011
Tqp cfli KHCN Xdy dmg - so 2/2011 21