tinh Phan tich phi tuyen dam lien hap thep - be tong chju tai trong

Phan tich phi tuyen dam lien hap thep - be tong chju tai trong tinh

Nonlinear analysis of steel-concrete composite beam under static load

Ngay nhan bai: 24/01/2015 Ngay siTa bai: 15/3/2015 Ngay chap nhan dang: 25/04/2015

Hoang Hieu NghTar Nghiem Manli Hien,

Vu Quoc Anh

T6M TAT

Bii bio trinh bay anh hUdng phi tuyen vJit U$u cua dSm lidn hdp thep-be tong (dim lifin hi?p) thong qua ly thuyet giai tich, phildng phap khdp deo va d^o lan truyen.

D|c trung vat li^u cua dSm lign hgp cd bien ddi dang ke qua m | t cat cua no tii thep chay deo tdi be tong bi dp vd, dieu do duoc t h i hien rd qua dUdng quan he mo men - dg cong ddn vi (M-i|;). Phin rii thanh dam dd xuat dugc chia thanh n phan tii con va c6 bien dang deo xuat hien tai hai dau phan tit con, ma tran dec dddc thiet lap trong su6t qua trinh phan tich di thi hifin sit lan truyen bien dang deo doc theo ehieu dai phan ta. Xic dinh hi s6 tli trong gi6i han ciia kit cau, xdc dtnh noi liic, chuyin vi ciia dam lien hop dOn gidn ting v6i tiing cap tai trgng tac dyng, ket qua nghien ciiu 11 ding tin cay vi da diidc so sanh vdi kit q u i phan tich tii phin mem ABAQUS va cac ket qua nghien ciiu da dd^c cong bo [ 11 ].

Tii khda: Chay deo, dam hen hq(p, ly thuyet giai tich, phtidng phap khdp d^o.

Abstract: The paper presents nonlinear material effects on composite beams with recourse to the analytical theory, the plastic hinge method and the spread of plasticity appproach. The material properties of composite beams vary remarkably across its section from ductile steel to brittle concrete, that clearly showned by moment - curvature curve (M-y). The proposed element is divided in to n elements and plastic deformation only has at the end element, plastic matrix is established while analysis structure to shown the spread of plasticity deformation along the member length. Determine the ultimate load factor of structure, determine internal force, displacement of simply supported composite beam by each load steps, the numerical results obtained by the analysis are reliable, compared well with ABAQUS results and other researching [11].

Keywords: Yeild, Composite beam, analytical theory, the plastic hinge method.

NCS.Ths Hoang Hi^u Nghia

Khoa Xay ddng Tri(6ng DH H i i Phong, hoanghieunghia@gmail.com TS, N g h i i m Manh Hien

Khoa Xay ddng TrU6ng £>H Kiln triic Ha N6i, hiennghiem@ssisoft.com PGS.TS, Vu Quoc Anh

Khoa Xiy ddng Trddng DH Kiln tnic Ha Ngi, anhquocvu@gmaiI.com

1.GlOlTHl£u

Tai Viet Nam viee nghi&n edu iJng dung va phat tnen kit eau lien hop th6p - bi long trong linh VLfc ket eau eong trinh nhei eao tang da va dang duac quan tam. Ket eau dam lien hop 1^

ioai ket cau sil dung thep ket cau ket hop vdi be long edt thep de ehung ciing tham gia chju luc.

Trong cac tieu ehuan Viet Nam ve tfnh loan ket du cong trinh, chung ta mdi chl dCfng iai 6 viee linh toan ket cau trong glai doan dan hoi.

V61 ket eau lien hop dUOC linh toan Iheo EUROCODE 4 dda tren siJc b^n d^o eua mat eat tilt dien [1].

Viee tinh loan ket cau trong giai doan dan hoi se gay den lang phi v l m|t vat lieu eiia kit

du. Do do c^n ph^l c6 nghign eOu cu the kit cau

iien hop lam viee ngoai gidl han ddn h6i. Cae nghien cuU ve phi tuyen vat lieu (phan tieh ngoai gidi han dan hoi) mdi ch! tap trung dung mo htnh dddng cong M-iy \j tddng 2 doan thang hoac 3 doan thang [1] vh chda ke d i n sd chuyin tilp td dan hoi sang dio bSng t dddng cong tron nhd eac dng xdthdc t l [5], [6]. Do vSy b&i v l l l ndy gidi thieu phdOng ph^p phan Id hdu han vdi phin td thanh dam lien hop d l xuat, xay ddng ma trdn d^o thay doi trong su6t qua trinh phan tieh d l the hien sd lan truyin bien dang d^o doc theo chilu dai phan tCf. Xac dinh he so tdi trpng gidl han ^ciia kit cau dam Uin hap, xae dinh ngi idc, chuyen vi cua dam lien hgp ddn giSn dng vdi tdng cap tai trong tae dung

2. DAT SAI T O A N V A GlA THI^T BAI T O A N

2.1. Dat bai loan

Bai bao tap Irung ehii ylu nghiln cdu 2 loai

bh\ loan eo ban lien quan d i n do ben d^o ciia

kit du dam lien hop:

- Bai loan phan tich kit du dan - deo (tinh toan trddc khi pha hoai d^o). Nhi&m vu cila bai toSn nay la xac dinh trang thii ngi Ide va chuyin vj thdc cua he IUdng dng v « bit k^" cap t i i trong lac dung.

- Bai loan xac dinh t i i trong gidi han (tdong dng vdi trang thai pha hoai dio). Lien quan din do ben dio eiia ket eau. Nhiem vu cila bai loan nay la tinh loan tdi trgng gidi han khi cho trddc hlnh hgc va dae trdng dio eila kit cau, tde la true

11.2015 Etoniiisi 1 0 5

liep xac d m h he s l l a i trgng X trong vee t o tai trgng { F } dong thdi xac dinh ndi Ide va chuyen vi cila he trong trang thai Iren.

Vec t o tai trgng tae d u n g len he la vec t o tdi trong t m h { F } tuan theo quy luat ehat tdi dOn gidn. Ve mat loan hoe vec l o tai trgng c6 t h i bieu d i l n dddi dang: {F} = X{P},

fPl = f P,. P;... Pn. P,,p2.,Pnl^ V6i

- vec I d Idc eo gia tri da b i e t , / I - h e s l tdi trgng c6 gia tn chda b i l t (hi so tai trong gidi han X^).

2 2. Gid thiet bai loan

- Tat e i eae phdn t d thanh cua he khi chda ehiu lai d i u t h i n g va co dien tich t i l t dign ngang khong doi (d6l vdi tdng phan Id). Khi p h i n t d thanh b i l n dang, t i l t dien ngang van phang vd Irde giao vdi true x (he toa d o cue bg eCia p h i n td),

- B i l n dang d^o xual hien va phat t r i l n trong cac p h i n I d eCia k i t eau id cdc bien dang deo phan bo, do d o b i l n dang deo se t6n tai 6 t i t c d c a c t i e t d l e n trong suot qua trinh chju tdi.

- C a e t h a m s o h l n h h o e e C i a k l t c i u l d c d c d a l l d g n g e h o t r U d e . - Bien dang va c h u y i n vj cCia he k i t cau Id nh6 nen bo qua phi tuyen hlnh hgc.

- Li&n k i t gida sdn b^ I6ng va dam Ihep id Men k i t hoan toan (Hinh 1).

- 66 qua chuyen vi d o b i l n dang cat.

- Mo hinh vat lieu la dan deo phi tuyen.

- Khdp d i o chl xoay d i o ma t h o i , bo qua ciing eo b i e r dang TTUC liinh hpc cua ban be long

Tnjc TH deo moi (PNA)

,€E=21

Tr^c h M h9C ciJa iam thip

zzs:

"7"

I

Ifinh 1. Mat ctit tiet dien dam lien hop vS bi^u do bien dang

3.PHaClNC P H A P P H A N TH HCTU HAN P H A N TfCH P i o K^T c A u D A M LI£N HOP

3.1. Mo hlnh phi t u y i n eila vat lieu be l o n g , thep hinh vd the thanh.

3.1.1. Mo hinh phi tuyen cda vdt lieu be tong

Tae gid sd d y n g phdOng trinh dddng cong quan he dng suat - b i l n dang phi t u y i n ddOc de xuat bdi Kent and Park (1973) [9] vd Vebo va Ghali (1977) cho mo hinh vat lieu be l o n g . Mo hlnh tren dddc n h l l u tae gia s d d u n g d l nghien edu nhd: Kent and Park, 1973; Park and Paulay, 1975, Wang and Duan, 1981; Mander et al.1988a; Hoshikuma et al., 1997 [8];Seung-EoekKIM2012[7].

3.1.1.1 B e t o n g e h j u nen.

PhUdng trinh dddng quan he dng suat - b i l n dang [ C T ^ - S J khi hi l o n g ehiu nen ddde the hi^n dddi day.

cr - K . f . 2

'm

^{Khi 1 (2)}

O c - K . f c . [ l - Z . ( e - e ( , ) ] > 0 , 2 K . f < - Khi a^=0,2.K.f, Khi e > e „ Trong do:

- e : B i l n dang eua t h d be l o n g chju nen tdong dng - a^ 'Cfng s u i t cCia t h d bi l o n g (MPa) - Ej,; B i l n dang t d o n g dng vdi dng suat Idn nhat

- S^: B i l n dang cue han cua be tong

- K: He so x^t d i n su lang cddng d 6 b^ tong d o hieu d n g kiem e h l nd hong

- Z: B o d i e eila dddng b i l n dang

- f^ Cddng d o ehiu nen cua b^ tfing mau tru [MPa)(l) Oc Cnesualnen

Hlnh 2.Sil(ing quan he Qng suat- Bi^n dang phi tuyen cja be long chiu nen Khi t h d be tong vdot qua bien dang Idn nhat, no ddOe gia thiet la den trang thai v d nho, va no ddoe xem xet la khong con kha nang chiu Idc nda. Kent va Park de nghi theo phdong trinh sau de t'nh todn cdc thong so tren dddng bao (Hinh 2):

ej,=0,02K (5)

K = l , Pjy.

3+0,29.f,

-0,75.p,. — - 0 , 0 0 2 K

(6)

e„ =0,004 + 0,9/7,.(f^/300)

(8)

Trong d6:

- fj,^: Gidl han chdy cila e l l t h i p dai

- p^ : n i e d i ^ n t i c h c 6 l l h e p d a i vdi dien tfch 161 b e t o n g - h : C h l l u day be l o n g bdo ve tfnh t d m^p ngodi c o l dai - S|,:Bd6e cot t h i p dai

- Sj,: Bien dang cdc han cua be t o n g 3,1.1.2. Be l o n g chiu keo.

Phdong trinh dddng quan he dng s u a t - b i l n dang ( O c t - E c t ) l^hi be tdng ehm keo dddc t h i hien dddi day.

- E „ . £ - 0 , 5 E , E Khi e < e c i = - ^ = - ^ ^

2.U

Ect ^c

= f c t - 0 , 8 E ^ - . [ E - e „ } = f „ - 0 , 8 E c , ( e - . ^ )

2,625fct

6,1 < e < € , , - —

(9)

0,5,fCT-0,075Ec.(e-

9,292f, 2 , 6 2 5 ^

Khi e^j £ E < £,

(T„-0 Khi e>E(-3 = Trong do:

9,292frt

106>^<l^^'"°'' ''

e : B i l n dang ciia t h d bi tdng chju k^o tdong dng (7„ :lJng suat eua t h d be l d n g chiu keo (MPa) E , : B i l n dang Idong dng vdi dng su3t keo Idn nhat e^^: Biln dang tddng dng vdi 0,5f(^

E^3: Biln dang tddng dng vdi f „ = 0

f^: Cddng d6 ehiu keo doc true cila be tong mau tru (MPa) E(.: Modun dan hoi ehiu n l n cCia b l tong

E „ : Modun dan hoi ehiu k l o cCia b l tdng (E^t = 0, SE^)

Hlnh 3. dilimq quan he iTng suk - Bien dang Tn linear cua Be tong chiu keo 3.1.2. M6 hinh cila vat lieu thep hinh vd t h ^ p thanh

Phdong trinh dddng quan h i Ctng s u i t - b i l n dang ( a ^ j -^a^ '^'^^

IhSp ddoc m6 hinh bdng 4 doan' dan hoi, chdy dio, sau chdy d i o (cilng efi-tdi b i n ) , k^o ddt (Hinh 4a).

o,=E,.E, K h l O S G s ^ E y (13) O j - f y Khi E ^ S E , ^e,^ (14)

= fv- -hh I Khi e,u £ e , < E , „ (15)

o , = f u . 1 - " ' "'" {Uu-fsb)\ Khi E,,SE5<Esb (16) Trong dd:

Os, e,; Cfng suat vd b i l n dang cila t h ^ p fy.s : Cfng s u i t vd b i l n dang chdy eua th^p e ^ : B i l n dang cung cd cOa thep

£,: Modun dan hoi cila thep

fjy, e^: Ong suit Idn nhat va b i l n dang tddng dng

" Ub • £sb '• ^ " 9 5ual vd b i l n dang phd hoai

Ta chl khdo sdt quan he dng suat - b i l n dang d i n chdy d^o

(a) (b) Hlnh 4. a)Du^g quan he Jng sual - Bien dang oia th^p; b) quan h^ liS-BD ly tuAng Quan h i dng suat b i l n dang cila vat li^u t h ^ p :

| e < e w - » o . =E,.Ej

Bang 1. Cac loai thep va gidi han chdy f, theo tiSu chuan Eurocode 1 Maclfiep

ENtoms S235 5275 5355 S275tl/NL S355N/NL S420N/NL 54(0 N/NL S235W 535SW

Bfdaytliiiml t s 4 l

fylNAnitv^

235 275 355 275 355 420 460 235 355

mrn fa{N/mrn>)

360 430 50 390 490 540 570 360 510

4an)in<ts8Qiiifn l,mmif\

215 255 335 255 335 390 430 215 335

F.IN/hiirfl 340 410 490 370 470 520 550 340 490

3.2. Ham momen - do cong ddn vi (M-tp) cila l i l t dien dam lien hop chiu udn thuan tuy M b i n g phdong phap gidi Ifch.

Xet vdi t i l t dien ehiu momen ddong. (bdn sdn BTCT ehiu n l n ) . live hinh hgc cua ban be long

TracTHdeomo](PM)

Tryc hlnh hgc

Hlnh 5 Mat cat tiet dien tong quat va sddd bien dang cOa dam lien hffp T d ( H l n h 5 ) c 6 :

M^ - l^damthep + Mjanbetong = M j + M^ > 0 (18) Ham M la ham phu thuoe vdo do cong don vl y ed dang nhu sau:

= fl(M')+f2f^j = a,n.^

M s - f l ( v ) + f 2 • = a2.<f -b,.v+Ci +

02 + '>2.¥ + C 2 + ^

(19)

(20) Cae he so ai;b,;c,;d,:a3;b2;c2;d2 ddge tinh t d c d c t r d d n g hop chdy deo eua t i l l dien dam lien hop vd ddoc to hop iCf cdc trddng hdp chdy deo cila bdn sdn be tong chm nen vd cila t h ^ p hinh (Hinh 6,7,8,9).

Vl trf True trung hoa d i o mdi (PNA) yoi ddde xae dfnh t d phddng trinh cdn bSng

F , + F „ + F „ = 0 (21) Trong do' Fsa - la hop Idc eCia ph^n d i m t h ^ p ehiu kio

Fji - la hop Ide eiia phan ddm t h ^ p ehiu n l n Ft - la hgp Ide eCia phan b i n sdn b^ tong edl t h ^ p + Xdc dinh b i l n dang t h d dddi eung cCia bdn bi tdng sdn:

E c b = ¥ [ Y - y o ' 2 ^ ' + Xae dinh bien dang t h d Ir^n cung cila bdn b§ tflng sdn:

E r t - M ' - f ' ^ + h . - y o l (23)

11107

t

LL

b- ' 7 ^

\ i V

u y

____v.

_ 1 _ _ _ _ \ ^

ih 8 CacTnfcmg hop S0S6 ITS khi TTH di qua canh dam thep

0 ^

d3

i C ^13

Mai cit na dien HS-jau Hlnh 9. Cac Tmimg hop so do l/S lihl TTH di qua bin san be tfing

Sd dung cong thdc (19) tdi (23) ldp phan m l m SPH VI .0 b5ng ngon n g d Delphi V7.0 the hien d d d n g quan he m o men - d d cong don vj (M-

\]/) ciia mat cat dam ll^n hop chiu udn bSng phddng phdp gidi tich {Hinh 10).

ta^ In

"—•'*"'"

" • • * • "

- ,-,..

tam 1 nwm

lii-

_iraa

•gnu imn

Z

Eri E » mm ata

1:1 1

mm mm mm

z

1 . - , « .

•>»

ma

ZZ

mm

•BCT a i » mm

>*

mja o n ^

°zz

iK'ta 1 S 11.011 gn«c BiajBi

:::

MomenMtolatMn Cunre

«s

" " •

.»

n ojni oiDS aoQ 01

/ ^

[

"

""

^.

Kinh 10 Bifcmg quan he mo men - do cong don vi (M-ip) cQa mat c3t dam lien hop chiu uc bJng phi/ong phap giai tfch

3.3 Phan t d thanh dam lien h g p t h e p - bi t o n g

J

1 n phan tii (4 phan tir) Hlnh 11 Phan tQ thanh dam hen hop thep - be long

Phan t d thanh dam lign hdp 1-2 (Hinh 11) ddge ehia thanh r t d con i-j. B i l n dang tai dau p h i n t d c o n i(j):

phan

Ooi vdi phan t d thanh dSm he true dugc quy dmh n h d sau: True x Id true dl qua trong tam eau k i f n . t r u e y Id true khflecila t i l t d i e n va t r u c z la true yeu eua t i l t dien e^u ki^n. C h i l u duong ddge quy udc n h d trong (Hlnh 11). He true ndy e6n ddpe gpi Id he true dia phddng, Tai mdi niit se c6 thanh phan Idc va thanh phSn chuyen vi.

[ F ] = [Fy, Myi Fyi ' ^ y 2 ] •

[U] = [v, 0 „ V2 Oyj] (24)

3 J . 1 . Ma Iran d 6 cdng cila phan t i l dam vdi nut cdng d hai dau 112K13]

6 3L -e> 3L

W=

3L 2L^ -IL L' ⁽²⁵¹

- 6 -3L 6 -3L 3L L^ -3L 2L^

3.3.2. (Wa tran d#0 ciia phan t i i dam khi ke den sii chdy deo tai dau phjntCTiJ

[kp]-W[T] »«

Trong dd' [ k g ] : Ma Iran do cdng cOa phan t d vdi nut cdng T : Ma Iran c h u y i n phu thuge vao d o cdng t i l p t u y i n ki tai vj tri co biln dang deo

k , = ^ : (27) d\y

06 cdng t i l p t u y i n tai vj trf ed bien dang d i o (Hinh 12)

l^inh 12 Go cUrtg tiep tuyen tai vi tn co bien dang deo 3 32 1 Chdy dead dau I

" 1 0 0 0 "

^ n ""12 °13 °14

0 0 1 0

0 0 0 1

4EIL + k,L^' 4El+k,L

AElL + kiL^ ' ^ 4EI + k,L 3.3a:2.Chdydkodd6u!

1 0 0 0

0 1 0 0

0 0 1 0

B21 622 ^2i 1^24 6EI

4EIL + k2L^ 4EI+k2L

6EI kjL

' ' " ~ 4 E i L + k 2 L ^ ' ' ' ^ ^ ~ 4 E I + k2L 3.3 2 3. Chdy dio tgi cd 2 ddu I vdj

" 1 0 0 0 "

^ 1 9l2 613 '^14

0 0 1 0

021 ^22 023 '^24.

6El(2EI + k2L) L ( I 2 E ^ + 4 E l ( k , + k 2

6El(2EI + ki L [ l 2 E p + 4 E l ( k , + k 2 kiL(4EI + k2L) 12EI^+4El(k, + k2)L4

1 2 E P

L ( I 2 E I ^

L[I2EI

12EI^

2Elk,L + 4 E l ( k i + k 2 ) L

6El(2EI + k2L + 4 E l ( k , + k 2 ) L 6El(2EI + k,L + 4El(k,+k2)L

2Elk2L +4El(ki + k2)L

k2L(4El + kiL) L + k i k j L ^ j

)

L + k,k2L^J

kikjL^

+ kik2L^

+ k,k2L^)

+ k,k2L^)

t k i k j L ^

1 2 E i ' + 4 E i ( k , + k 2 ) L + k,k2L'

Ma tran d&o ciia phan t i f khi k l dgn su chay d^o tai hai dau phSn

12Ei(Lk,k2+Ei(ki + k2) 6Eik,(Lk2 + 2EI) L^(l2EI^+4Ei(k,+k2)L + k,k2L') L ( l 2 E l ^ + 4 E i ( k , + k j ) L + k,k2L^]

6Eik|(Lk; + 2Ei) 4Eik,(Lk; t 3 E i )

12Ei(Lkik2 + EI(k, + k2 i ^ / n p i ^

6Eik2(kiL + 2Ei)

l ( l 2 E p + 4 E l ( k , + k 2 ) L + k , k 2 L ^ ) 12EI^+4Ei(k, + k2)L + k,k2L=

12El(Lkik2-i-Ei(k|+k2)) 6Elki(Lk2 4-2El)

( l 2 E i 2 + 4 E i ( k , + k 2 ) L + k , k 2 L 2 ) L ( l 2 E i 2 + 4 B ( k , + k 2 ) L + k,k2L^) 6Eiki{Lk2+2Ei) 2Eik2kiL L(l2Ei2 + 4Ei(k, + k2)L+k,k2L2) 12Ei'+4Ei(k, + k ; ) L + k,k2L2

12Ei{Lk,k2+El(ki + k2)) 6Eik2(kiL+2El) L ' ( l 2 E i ' + 4 E i ( k , + k 2 ) L + k,k2L2) L ( l 2 E i ^ + 4 E i ( k , + k2)L + k,k2L^)

6Eik;(kiL + 2EI) 2Eik,k2L

L = ( l 2 E | 2 + 4 E i ( k , + k 2 ) L + k,k2L') L(l2Ei2+4Ei(k, + k2)L + k,k2L2) _ 6 a k 2 ( k i L + 2 E i ) 4Eik2(kiH-3El) l ( l 2 E l ' + 4 E i ( k , + k2)L + k,k2L^) 1 2 E l ^ + 4 E I ( k , t k 2 ) l + k,k2L2 " L ( l 2 E I = + 4 E l ( k , + k 2 ) L + k , k 2 L ' ) 12E|2+4El(k,+k2)L + k,k2L2

3.3.3. Vec ta tdi trong nut quy doi cOa phan tCrdSm k/jf ke den st/ chiy dSo tai daoph&n tCl.

Xit tdi trong tdp trung Py trin ph&ntit

101

a) Khi chdy dio d dau trdi i

.P,

Hinh 13, Luc tap trung P, tren phan tilcodiu trai i chay deo + Xdc dinh gdc xoay 0 tai m i l :

K'],{")={/}«['f"'],{0 9, 0 0)'.{/) i'(3a + i)

6 3Z,

3 i 2L'+k,

3L'

e

- 3 i

Tl'

0

S,

0 0

e

L' '

^|36 + » ) ,

Khd d i l u ki^n bien e6n phddng trinh si

HiEI*k,L)

+ V6c t o t^i trong nijt khi cd ke den su chSy d^o tai dau i

i ' • ( 4 £ / + i , I . ) 4 £ / a i ' P

^4P.- ,.

i i- (4£/ + *,t) aU^b + a) 6EI ab'P,

fl-

L' ' L' • ( 4 £ / + *,/.)

2EI ab'P,

L' (4EI + k,L) + Xet trudng h o p dac bidt dau trai i ( k h d p ) ( a . b . L / 2 ) : i | = 0

I - ' * " ' l l 6 ' 16 ' 16 '

b) Khi chdy dio ddSu phdi]

.P,

chdy d i o hodn todn

Hinh 14. Luc tap trung P,tren phan tiled dau phii] chSyd^i Xac dinh tdong I d n h d t r e n :

te)=(f)-[k.].(o 0 (

Bing 3. Gia tri n6i idc vd c h u y i n vi cua dam lien hop dOn qian dng vdi moi bUdc tdi tronci Bdn sdn c6 cdt t h ^ p 2 Idp

Load Case Step

1 5 10 15 20 25 30 35 45 50 60 70 75 80 81 82

Xu 0 0 05 0.1 0.15 0.2 0.25 0.3 0.35 0.45 0.5 0 6 0 7 0.75 0.8 0.81 0 82

Joint 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

MX 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

MY 0 0 0 0 0 0 0 0 0 0 0 0

u

0

u

0 0

u

MZ (kN.m}

0.00 16.85 34.30 50.84 68.31 85.80 101.31 118.04 134.96 152.27 169.74 187.22 204.69 225.77 242.32 259.67 277.23 280.75 284.35

UY (cm) 0.00 0.58 1.17 1.75 2.34 2.94 3.49 4.08 4.67 5.27 5.88 6.48 7.09 8.07 9.40 11.69 16.05 17.31 18 97

Ban san khonc Step 1 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 77 79

Xu 0.01 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.77 0.79

eo cdt thep MZ (kN.m) 0.00 17.13 34.21 50 67 68.15 85.64 101.09 117.80 134 64 151.90 169 35 186.80 203 93 225,74 242.58 260 00 266 98 272 22

UY (em) 0.00 0.61 1.22 1.82 2.44 3.07 3 6 4 4,25 4 8 7 5,50 6 1 4 6 78 7 42 8 57 10 33 13-66 15 84 19.13

=K i

b^(3a + b

a^(3b + a

J

— ^ P . +

i

p „ . 'ip

6EI

B^bP, 4EI + k2L

->'y- 4Ei

ISFI L = ' a^

) (42) a^bP, (4EI + k2L)

a^bP, (4EI + k2L) bP, L^ "{4EI+k2L) (43) c) Khi chdy dio dcd 2 ddu i vdj

Hli* 15 He tip trang P, trin phin i« „ bai Jin iJ d i l ,

110

pj2Ela^b+Lab^k2 + 4Elab^) L/L-^kik2 +4EiLki + 4EILk2 +12EI^ j

pj2Eiab^+La^bk,+4Eia^b) L(L'k,k2 + 4 E i U , +4EiLk2 +12EI^)

j f j ) = ( f ) - [ k . ] . ( 0 e, 0 e 2 f = { l i l IJp f»p l « p ) ( 4 5 )

' ^ ' ^ P , - f ( e - ^ e 2 ) ; , J , = f p , - i ^ ( e , . 9 2 / 2 )

a = ^ V ^ ( e . - e . ) . - f j p = - f P y . > / 2 . 9 2 ) (46, 4.ViDUPHANTfCH

PhUdng phdp Newrton-Raphson eai t i l n [10] ddge dp dung d l gidi bdi todn phi tuyen vat lieu (dan hoi d i o ) cua k i t cau dam lien hop.

Khdo sat dam lien hop don gian co mat cdt l i l t dien dam g o m t h i p W12x27, bdn be tong 102x1219mm (Hinh i 6).

LUc tdp trung tae dung P =100kN tai vi tri gida dam (Hinh 16).

Cddng do ehiu nen eCia b l l o n g ft = 16Mpa, fo =1,2Mpa, m d dun ddn hdi eiia be l o n g Eh = 32,5.10^ Mpa, EQ =0,002, E^ =0,004. tfng suat chdy cCia thep dam f, =252,4Mpa, eddng dd chiu k4o cila thep san f,

=210IVlpa, mo dun ddn hoi cila thep Ej = 2.10^ Mpa, 2 ldp edt th^p san itilOalOO

Bdng 2. Kfch Ihdde mat cdt ngang t h ^ p hlnh trong d i m lien hgp dgn gidn

Clu ki^n W12x27

b((mm) 165

t,(mm) 10,16

d ( m m ) 304

t „ (mm) 6,02 ElSmn

Hlnh 16. Dam lien hop don gian chiu tai lap tmng P=10a!iN tai giDa nhip Xdy ddng phan mem SPH V I .0 bSng ngon n g d Delphi V7.0. Sddung phuong phdp phan t d hdu han vdi phan t d thanh ddm l i l n hgp, ma Iran d i o de xuat vd thudt gidi phi tuyen Newton-Raphson cdi t i l n [10] de thdc hi&n phan tfeh phi t u y i n k i t cau dam lien hop d v i du tren. K i t qud thu duoe n h d sau:

! „

- .^„.,„.. - - -•' Hinh1B.BieudfiquanhehesfitiUronggidi Wnh 17. Bifu do q ^ I h e noi lilc va M J^vJ thuyen vi giiia dSm lien hop chuyin vi cua dam lien hop lilig vdi moi

buAc til trang

• • Nhdn xel:

+ Td Bdng 3 va d o t h j (Hinh 17) cd t h i nhdn thdy rdt ro quan he noi li/c • c h u y i n vi la phi t u y i n , t d dan hoi, dan d i o vd chdy d t o hodn toaii

cd the xde dinh ddde ngi Idc eCia d i m lien hop tai bat ky bdde tdi nao eho tdi khi dam bi phd hoai.

+ T d d o t h i (Hinh 18): h f so tai trong gidi han Ju. cila phddng phdp nghien edu va h i so ^u khi phdn tfch bdng phdn m l m ABAQUS [11]-

^ ? - U - ° ' ^ Q " ° ' ^ ^ X 1 0 0 % = 1,25% ta xap xl bdng nhau -> eho t h i y do tin eay cua phdong phdp n g h i l n cdu.

^ + J d Bdng 3 va d o t h i (Hlnh 18): h i so tdi trong gidi han X. khi eo k l d i n cdt thep sdn la Idn hon khi khdng k l d i n cdt th^p sdn

5.NHAN X E T V A K £ T L U A N

Bdi bao trinh bdy anh hddng phi t u y i n vat lieu cua dam lien hop t h o n g qua ly thuyet gidi tich, phdOng phdp khdp d^o va d^o lan truyen.

Dac trdng vat lieu eila dam l i l n hgp c6 b i l n doi ddng k l qua mdt cat eila nd t d t h e p chdy d i o l d i be l o n g bj ep vd, d i l u dd ddde t h i hien ro qua dddng quan he m o men - dd eong d o n vi (M-y).

Xdy ddng ddge ma Irdn deo cOa phan t d thanh dam lien hgp bdng phddng phap gidi lich.

0 1 xual phan t d thanh dam lien hop eo bien dang d i o trong phddng phap phdn t d hdu han. Phan t d d l xuat dudc chia thanh n phan I d con vd cd bien dang deo x u l t hien tai hai dau phan t d con, ma tran d ^ o ddde t h i l t lap trong suot qua Irinh phdn tieh d l the hien sd lan truyen b i l n dang deo dgc theo chieu dai phdn td.

Xdy d u n g ddge vec t o tdi trong niit quy ddi eila phan t d thanh dam lien hdp khi ke d i n su chdy deo cOa p h i n td.

Quan h^ noi Ide - ehuyen vi Id phi t u y i n , c6 the xae dmh ddde noi Idc eua dam tai bat ky bddc tdi nao eho tdi khi d i m bi phd hoai

Xac dinh ddoc he sd tai trgng gidi han Xu eila k i t c l u ddm lien hop, k i t qud cua nghien cdu ddge so sdnh vdi k i t qud phdn mem ABAQUS [11 ] va eho thay dg tin cdy eila phddng phap nghidn cilu. TU he sd Xu ta CO the ddnh gia ddOe mdc do an todn cila k i t eau khi ehju tdi trong.

TAIUEUTHAMKHAO

f 11CEH. Eurocode 4 (2003), Design of steel and concrete structures Paitl.l.Generaiiuiesand rules for buildings (prEN 1994-1 -1), stage 49 drafledition,

12] ASCE Manual Ho. 4 1 . ASCE. NewYork (1971). Plastic Daiga in Steel, A Guide and Commentaiy.

[31 Michel Bruneau. Chia-Ming Uang and S.E, flafael Sabelli (20111, Ductile Design of Steel Structures.

[4] W M. Viouwenvelder t20031. The plastic behaviour and the calculation of beams and frames subjected to bending, Faculty of Civil Engineering and Geosaences, Technical Unlvenity Delft.

[5] S L. Chan and P.P.T. Chiu (20001. Non-linear Static and Cydic Analysis of Steel Frames with Semi-Rigid Connections, Elsevier

[6] William M, C Guide and Ronald D Ziemian [19981, Matrix Structural Analysis, 2nd Bd.

John Wiley and Sons, Inc

[7] Cuong Ngo Huu, Seunq-Eock Kim (20121, Piadical nonlinear analysis of steel-concrete composite frames using fiber-hinge method, Journal of Constnictional Steel Research,

[8] HoshikLima. J., Kawashima, K,. Naqava, K, and Tavlor, A, W. (19971. Stress-Strain Model for ConMdPeinforced Concrete in Bridge Piers.}. Struct. lt\q ASCE, 123(5), 624-633.

[9] Kent, DC and Park, R, 11971). Flexural Members w i t h Confined Concrete, J. S t n i d . Div.

ASCE,971ST7),1969-1990.

[10] Robert D Cook, David S. Malkus and Michael E Pi esha [19891. Concepts and applications ofUniteelement analysis, 3rd Ed,lohnWe^3ndSons,\nc

f i l l Cuong NOP HUU. Seunq-Eock Kim (20061, Practical advanced analysis of steel-concrete composite struaures using Hber-hinge method, Ph.£) dissertation, Oepartment of Civil and Environmental Engineenng, the Graduate school ofSejong University

[121 Chu Quoc Thang ll997).J'/mimi;pAdppftoJifti'ftiin/ion, Nxb khoa hoc fcy thuat, H a M [13J Vo Nhu Cau (20051, Tmh ket cau theo phuong phdp phdn tihSu han, Nxb xay dtfng, Ha

11.2015siDiiiinoa 1 1 1