Anh hiFO'ng cua lire doc den pha hoai luy tien cua ket cau khung dan - deo
The effect ofthe Axial Forces on Progressive Failure ofthe elasto - plastic frame structures
Ngay nhan bai: 9/10/2014 Ngay su^ bai: 23/11/2014 Ngay chap nhan dang: 27/12/2014
Vu Van Hoang, Nguyen Van Tu
TOM
TAT:
Bai bao trinh bay phiiPng phap tinh toan va ket qua danh gia anh hudng cda liic doc d^n pha hoai luy ti^n cCia k^t c^u khung phing dan - deo. Cac thu^t todn diipc xiy di^ng tren cd sd mo hinh thanh dan d ^ ly tiidng vdi bien dang deo tap trung, tieu chuan pha hoEii d^o theo chuyen vi xoay cua tiet di^n, phiiOng phap phSn tut hflu han, phUdng phap Newmark ket h<^ vdi phiicJng phap lap Newton - Raphson hiin diiu. Kit qua tinh toan b ^ g sd cho thay khi ke den anh hiidng cua li^c dpc dffi vdi mdmen deo cua tiet dien thi qua trinh pha hoai liiy tien ciia ket cau khung din - dec xay i^
nhanh hdn so vdi khi khdng kl din hieu ting tren.
Khda tU: Ket cau khung dan - deo ABSTRACT
The paper presents an analysis technique and evaluation of the effect of the axial forces on progressive failure of the elasto - plastic frame structures. The analysis algorism was formulated by using the elastic - perfectly plastic beam model with concentrated plastic deformation, accepting the plastic - damage criteria according to rotate displacement ofthe section, applying the finite element method and the Newmark approach combined with the modified Newton - Raphson approach. The results show that if the effects ofthe axial forces on ultimate plastic moment of section are considered, the progressive - failure of frame develops faster than without these effects.
Keywords: Elasto - plastic frame structures IhS. Vu Van Hoang
TS. Nguy£n ^ ^ Tii HQC vien Ky thuSt Quan sii, Di d^ng: 0983052725 Email: [email protected]
Trong eong trinh [1] ngtiien ciiu phuong phap tfnh toan dong life hoe sU pha hoai luy tien (PHLT) cilia khung phSng dan d^o ly tUdng (DDLT) vdi g i i thiet khong ke ^nh hiidng cCia liic doc d^n mdmen uon d^o cua tiet dien thanh. Trong thu'c te thudng gap nhi^u dang ket eau khung vci tai trong md vdi chOng Snh hUdng ttin 3in mdmen udn d4o va, d o do, den trang thdi chiu luc ciia ket du \i ldn; inh hudng nay c l n dUoe xem xet trong tinh loan. Phat trien dc ket qud nghign cdu trong eae cdng trinh tren, trong bai bdo nay trinh bdy cdc l h u | t todn 34 phan tich ddng lUe hoe Sli pha hoai luy tien cua khung p h i n g ddn d^o 1>? tUdng cd ke den dnh hudng ci!ia lUc doc ddi vdi momen deo vd ddnh gid bSng sd ve dnh hUdng trin den PHLT cCia ket cau.
1 . M d menudn dio cOa tiet dien thanh khi Ic^ den i n h hUdng cua lUc doc
Khao sat phan t d thanh thude ket du khung chju udn phiic tap,theo do tai trgng tam t i ^ t dien ciia PT chiu tdc dung ddng thdi cda momen udn M va liie doe N (hinh 1) vdi vat lieu bien dang theo mo hlnh BDLT.d trang thdi chdy d^o gidi han (ti^t dien bi chdy d^o hodn toan) bleu dfi iing suat phdp tren tiet dien thanh cd dang nhU tren hinh (a) khi tiet dien chl chju uon thudn tiiy (ehi chju tdc dung cOa rieng M) va cd dang n h i i tren hinh (b) khi t i ^ t dien ehiu uon phdc tap, trong d d : o^ - dng sudt phap trong tiet dien khi dat d^n trang thai chdy d^o.
Hinh 1. Bieu do ikg suit ph^p tren tiet dien thanii do ticdung dong thdi da momen uon va luc doc khi ch^y d^o da phat triln ho^n loan
Ky hieu M ^ - mo men udn d tr^ng thai chdy dio gidi han (gol tdt la md men udn dio gidi han) khi k^ den dnh hUdng cila luc doe, quan he gida momen ufin (M) vdi goc xoay (9) eCia tiet d i f n thanh co dang nhU tren hinh 2, trong do: k- da cdng chdng uon dan hfii ciia tiet dien thanh.
1 M
ifinh 2. Quan he momen uon - g6c xoay cua tie't dien thanhvS vat lieu BLHT TCf dieu k i f n can bdng noi lUC N vd M tr^n tiet dien tUong iing vdi trang thdi chdy d t o gidi han (hinh l b ) cd the xdc dinh dupc gid t n IT
03.2015BSI1limBl|79
udn d ^ gidi ban cua t i ^ dien khi ke den anh hudng eua life d o c Dudi ddy la cac cdng thdc t i n h toan M ddi vdi m d t sd tiet dien thanh thdng dung [2].
•Tiet d i ^ ehdnhdt (hinh 3a)
- H
(1)trong do: M - momen udn d ^ gidi iian cua tietdienchjuiJonthuantuy,Mp = a | , b r f / 4 , N - lUe doe gidi han dia tiet dien chju keo nen d i i n g tam, N, = Opbd; cdc ky hi&u cdn lai dUoc the hien t r ^ cac hinh ve.
•Tiet d i ^ hinh vanh khan (hinh 3b)
— = -|^Sin(p--sin3<pJ, (2) trong dd (p duoc xac djnh ti( phKong ti%4i sau
, - i ^ ^ _ l s i n 2 9 ] = ^ , (3) ttongdd:Mp = c r p t ( d - t ) ' , N p = O p j r t ( d - t ) .
• Tiet di$n c h d I (d x b x t_ x t,) chju udn quanh true chinh (hinh 3e}
- K h i b < N / N „ < 1 / ( l + 2 b t , / t X ) , t a c d : N
u ^ i
Mp - K h M / ( l +
M ^
*^
trong l = d -
<a
1 + 2bt,
-.1
dd:
4-
'[ 2bt Mp-o„[bt N , = c
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p(2t,b + t . t . < ' . ) S N / H , S
-:.h^]
^dl2bt,
t , ) + ( d / 2 - t , ) '
M
< ) . ) •
I t a c o :
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Hnli 3.(ic dang bS di«n thanh thdng dung D d thi bi^u dien quan he M - N eua tiet dien trong trang thdi giiM han deo dUoc goi la mdt dio vi dUde the hien tren hinh 4 doi vdi mdt sd t i l t di&n thanh thdng dung tren hinh 3 vdi ede kieh thude eu t h ^ sau day: tiet dien ehd nhat bxd = 200x400mm (a); Wet dien hinh vanh khdn dxt=200xlOmm (b); tiet di#n chCf I;
Hkih 4. Itit deo dot vA mot sd tiet (Sen thanh thong dung dxbxt_xt^200xl 00x5,5x8mm (c).
2 . PhUtfng p h a p p h a n tich p h i hoai l u y t i e n cua k h u n g DDLT k h i ki Oin i n h h u d n g cua iUc doc d d i v d i m d m e n d e o
2.1. £>dt bdi todn vd cdc gid thiet tinh todn Khao sdt khung phdng dan - d^o chju tac durrg cda tdi trong ddng. Can xay difng dc thuat toan d ^ phan tieh d d n g luc hpc su phd imai luy tien cua khung p h i n g DDLT cd ke den dnh hudng cua lUe doc ddi vdi mdmen deo va ddnh gid b&ng sd ve anh hudng tr^n den PHLT ciia ket c^u. Oe giai bai todn dat ra thda nhan cdc gid t h i ^ sau:
- Cde phSn t i l thanh cua ket eau khung Idm v i f c theo md hinh Euler - Bemoulli.
- Uen ket tai cdc n i h khung la eac l i ^ ket cdng,
- Vdt lieu k ^ cau bien dang theo md hinh ddn deo ly tUdng.
- Bien dang deo trong cac tiet dien thanh cua ket cau la cae bien dang deo tap trung xuat hien tai eac Mit dien ed mdmen udn Idn n h a t
-Tinh den dnh hudng eua life doc N den gia tri md men udn deo trong tiet dien thanh.
- Hieu dng P-Delta trong cac PT thanh vd chuyen vj thdng ciJa ede nut khung duqc coi la l>e CO the bd qua trong tfnh todn.
2.2. Cdc ma t r a n cda p h a n t ^ t h a n h ODLT B e giai bdi toan dat ra se sd dung phuong phdp phan t d huU han (PTHH) vcg viec red rac hoa PTHH doi vdi k^t c i u va m d hinh hda PT duoc thue hien tuong tif n h u trong bai bdo [ ! ] , t h e o d o moi PTthanhBDLTdUOcthay bdng m d t PT thanh nSm giOa 2 lien ket ODLT dat tai 2 dau cudi eua n. Trong qua trinh ehiu lue, PT thanh ludn luon iing x d dan hoi tuyen tfnh (OHTT), cdn lien ket d 2 dau cudi cCia PT cd the trdi qua eae trang thdi: bien dang dan hdi, bien dang ODLT hodc bj pha hoai d4o; theo do eae phan t d thanh ODLT nay se Iam viee n h u eac phan t d ttianh OHTT nhung vdi lien ket tai dau cufii PT tuong ling v * mot trong cde trUdng hop: ngam, khdp (khap dio), t u do (khdng lien k^t). Do dd, eae ma tran ciing loai cua mdt phan t d thanh
^DLTse CO gid tri khae nhau phu thude vao qua trinh chat t i i , Gia tri eac ma tran nay cCia phan t d thanh ODLTthd'm'h^ong he toa do cue b d (ma h 3 n d p cdng [ K ] ^ ma tran khdi luong [ M ] ^ ma
tran can [Cl_^ vec t o tdi trpng quy nut ffO) ^ d u q c t h i e t l d p t r o n g c d n g t r i n h [1]. ^
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Sd durtg eac ma trdn eua phdn I d thanh DDLT t r o r ^ he tpa d d da ndi d muc 2.2, ma tran bien ddi ehuyen vj vd lUe nut cua ph&i ht p h u o n g phdp PP PTHH [3], eae diSu ki&n bien cua ket cau. t i n h den ma t i ^ do eiing k d c ^ phu thude vao chuyen vj n d t BQ = [K{UI] do ma tran do cdng cda cac phdn t d thanh DDLT phu thudc vdo qud trinh chat tdi, c6 the nhdn Afet phucmg trinh chuyen ddng trong h$ toa do chung tai ti>di d i » n b ^ ky c i k k ^ c j u khung ODLT sau ddy:
[ M ] f i } + [ C ] f l } * ^ f , ( { U } ) = { R ) , ,5, trDr>gdd:f^({U))-vecto luc phue hdi cijakei eau,
f([Ul)=tK{UIKUl,^ (7) {Ui- vec t o ehuyen vj niit ciia ket cdu trong
he toa d d ehung ({U}, = IU, V Qy gdm ehuy&i M thSr>g theo F^uong t m c x, true y va chuy^ w xoay quanh true z);
[Ml, [Q. [K], {R} - t u o n g dng id ma trdn kha luong, ma trdn can, ma trdn d p cdng vd v k to tdi trong quy n u t cda ket cau.
Phiiong trinh (6) la phUcing trinh phi tuy&i ddi vdi ehuyen vj n u t {Ul cua khung.
2A. P h i A m g p h a p phftn tich p h i ho^lbi ti^ cda k h u n g DDLT kht ke den i n h hMlhg cda luc d o c d 6 i v d i m d m e n d ^
Phuong phdp giai bai todn phd hoai Itiytien eua khung phdng ODLT khi ke den dnh iwdng cua lUc dpc den mdmen dio eua tiet di$n hoan toan t u o n g t U n h u phUcing phdp gidi bdi toan khi khong ke den anh hUdng tr§n dd nghidi cdu trong [1]. 5if khac nhauchi dehA, sauma budc ti'nh ldp ngoai v i f c cdp nhat lai cdc malrin cua phan t d do s u xuat hi^n,pha hoai cic khdp d ^ va cac phdn t d trong he c d n p M i ^ ^ b i lat gia trj mdmen deo cOa cde tiet i ^ H ^ ^ gia tri mdi eua life doe N theo eae edng t h f t i m u e l .
Tieu chuan pha hoai c£ia tiet d i | n thaih (hay khdp ddo) d 2 ddu eudi PT van duoc Ihiia nhan nhU trong (1], theo do tiet dien se bj pha hoai khi chuyen vi xoay cCia tiet dien tai db, &
cd gid t r i :
6>e„ = ue, (B trong d d : 6 - gdc xoay tift dien khibdtfiu
chdy deo, 6,^ - gdc xoay gidi han cda tiet diSn sau khi ehay deo (tuong dng vdi thdi diem lite 'di dan - deo bi phd hoai), p - chi sd ptid hoaiifeD (hay cdn g p i Id do d e o ) cua tiet dien.
Tren eO sd eae thuat todn n w trfirb tdc gii iS lap chuang trinh d ^ phdn tfch ddng lUc hoc aJ phd hoai luy tien cda ket cau khung ddn khi ke den dnh hudng cOa life dpc d6i m e n deo. Phan mem tinh todn duac lap
ngdn ngCf Matiab. | 3 . T h { d w s &
Ket eau khung cd dang n h t i hinh S Idm tdos
4i(0
nw
(2)
W ,
0)i W i i i
3 0 8 (4)
i i I
2 (8) (3) 1
6 02)
i i i
5 (9) (5) 4
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i l l
8 (10) 11 TO 7 10
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vat lieu t h ^ p hlnh c h d 1 vdi t i ^ t di6n ed kieh thudc 1(200x100x5,5x8mm), m d d u n dan hdi E
= 2.1 e+5 MPa, dng suat chdy ddo =21 OMpa. Tai trpng ddng tae dung tren ket cau gdm cae tdi trpng tdp trung: P,{t) = 30f(t)kN, Pj(t) = 35f(t)kN vd edc tdi t r p n g phdn bfi deu: q,(t) = 15f{t) kN, qj(t) = 50f(t) kN, q,(t) = 25f(t) kN, trong do f(t) ed d^ng ngdn han hinh tam gide (hinh 5b), t h d i gian duy tri tac dung cCia tdi trpng T = 0,05(s).
TJ sd edn dUcte chon ^, = t , = 0,05. Chi sfi phd ho^i dio p=2
Thin gian phan tich t =0,12(s) De so sdnh da Uin hdnh phan tich ket eau dfii vdi 2 trudng htJp: ke d^n dnh hUdng cOa life doe ddi vdi m d men deo (EAL) va khi khdng ke din dnh hudng ndy.
Cdc ket qud t i n h toan bdng so dupe the hien trin hinh 6, 7 vd hinh 8. Tren hinh 6 vd 7 Id sa dfi ket eau va vj t r i edc khdp ddo (ky hieu bdng chdm trdn den) edn lai sau khi khung bi phd hoai luy tien duoc cdp nhdt tai thdi d i l m t ^ , 0 6 (s), theo d d tai t h d i d i ^ m trdn sfi PT trong khung cdn lai Id 9 khi khdng ke d^n EAL va edn lai Id 6 k h i e d k l d e n E A L .
Trdn hinh 8 Id do thi mdmen udn theo thdi gian tai niit 6 thude phan t d (11) eiia ket edu khi kd den vd khdng k^ ddn EAL.
ifinh 6. So do ket cau vd vj Oi cac khdp d ^ tai thcii die'm t^D,06(s)-khi khfing ked^n EAL
rt
Hinh 7 A r « ket ciu n t=0,06{s)-khik;denEAL
VIM cdc khdp dte tai thcA i^em Hhih 5. Sd do ket cau (a) va dang tai trong dong ngan han (b)
eua ket cau khi ke den vd khdng ke den EAL Nhdn xet .Td ket qua tfnh todn bang sd cd thd diia ra cde nhan xdt sau ddy:
- Qud trinh phd hoai luy tien ciia kit du khi ke den EAL xdy ra nhanh hOn so vdi khi khdng kd den EAL (hinh 6,7).
-TrUdc khi b; phd hoai gia tri tuyet ddi ciia m d men u6n trong tidt di^n c^a PT khi kd ddn EAL bang hoae Idn hon khi khdng ke ddn EAL (hlnh 8).
TAlLieUTHAMKHiO
1. Nguyen VSn Hoi, Vu Van Hoang, Nguyen Van Tli (2014), Phan tfch dong lOC hoc khung dan - dio co ke den sif pha hoai luy tien cia cac phan til ket cau,/Tap dli Xay difng (Bo )Cay dung), so thanglO, nam 2014.
2 Nguy«i Van Tii (2010). Tinh toan khung phing dan - dio chiu tic dung ciia tii trong dong ngin han, /Luan snTS, Hi noi
3.Bathe, KJ (1996), Rnite Element Procedures/ Prentice Hall International inc, Englewood Oiffe.
4.Chopra, A,K (2007), Dynamics of Stnjctures: Theory and Applications to Earthquake Engineering (3rd Edition)/ Prentice Hall International inc
S.Griengsak Kaewkulchai (2002), Dynamic progressive collapse of frame structure /EM.New York
6.lzadifard R.A (2010),Ductility effects on the behaviour of steel structures under blast loading/Iranian Journal of Science
&Technology,VDl 34
Hinh 3 So thj mo men uon tai nut 6 thuoc PT(11)