G^,o5. o r • ^ l i ' - r L
PHAN TiCH NOI Lu'e VA CHUYEN Vj KHUNG PHANG KHI HINH T H A N H K H Q P
DEO CHIU TAI TRONG TTNH
Ngay nhan bai: 10/8/2014 Ngay sufe bai: 10/11/2014 Ngay chap nhan dang: 28/11/2014
Vu Quoc Anh, Nguyin Hai Quang
TOM TAT
Trong bii bao trinh hky phtfong phap v i cac ket q u i tinh t o i n n6i liic va chuydn vi ciia khung khi hinh thanh khdp d^o. Ap dyng phiiOng phap phan tif hGu h ^ , sH dyng mo hinh dan - d^o de tinh toan. So sanh ket qua tinh ciia philOng p h i p khdp d^o li^n tiep v6i phifdng phap tinh toan khdp d^o tnic tiep de diia ra cic nhan x^t ve gia tri chuyen vi, noi life va sii phan phdi l ^ npi liic khi hinh thanh khdp deo.
SUIMMARY:
This article presents the method and results calculation of internal force and displacement of 2d frame when forming plastic hinge. Apply the finite element method and the elastic-plastic model in the calculation. Compare the result calculated between consecutive plastic hmge method and direct method to give comments on internal force and displacement result and the distribution of internal force when forming plastic hinge.
Vu Qu6c Anh: Tnidng dai hoc Kien Tnic H i Npi
Nguyin Hai Quang: Tnidng Cao ding Xay diing Cong trinh Do thi
1. Gidi thieu
Trong tinh toin ket cau, tfiong thu'dng quan ni&m ket cau lim vifc trong giai floan dan hoi.Tuy nhi&n, mot s6 cong trinh da nghien cu'u c6 ke den cic yeu to phi tuyen [1,2,3,4,5].
Cic cap do phan tich nhu sau:
-
pMiiDh^ah
p h a m f c h d t o i l i S i b a c l e d f c * den phi luyin hinh hoc
phan lich phi d ^ ii6i bic nhli cd kt d#n chay deo
I^Uii tich phi (Un bAi b i c , ImiiatdcfbHuyfa
hlnh h i ^ vi chay deo
Q i u y ^ VI ngojig Hinh I.Cic cap do phan Wdi
lii Ir^iiB gidl h|ll d b biS)
gliS l i p 6B dinb dia bi%
[UI vong gi& hon phi ^
gift hiin dn djnh phi din hi
", 1
•
Phantichainh6ituyenttnh(bacnhat). [ " • I W - C l r^ ^-,, , , ,_,„,
Phan tich dan hoi bae2 c6 keden phi tuy€n hlnh hoc: L''.*''.J)''*)-l'"^t ., Phan tich phi dan hoi bae nhit co ke den chiy deo cua tiet dien: [K, +/(.l(ii4) - ( * ! Phan tich phi dan hoi bae hai c6 ke den chiy d ^ tiet difen va phi tuyen hlnh hpc
Vdi:
K ] la ma tran do cijng dan hoi, K ] la ma tran do cilng phi tuyen hinh hgc
4 8 | B n i l B i a i 12.2014
chay d^o.
[l^r-l la ma t r i n giam d^o t h l hien sU thay doi d p ciJng do si
Trong hinh 4, EJ l i do cilng cua phan tCf dam, ' vh ' l i do cCmg 6 dau trai va dau phai ciia dam. Khi tiet di^n dau dam bl c h i y deo m d t phan ' M M „ , l „ _ M l
Hinh 2. Mo hlnh dan-deo
Bi dOn g i i n trong t i n h toSn, m o t s6 cong trinh nghidn CLfu sif lam viec cila ket c i u co quan he giCTa m o men v i gdc xoay cua tiet dl^n theo m6 hinh dan - d^o ly t u d n g [2,3] {hinh 2).
Khi khao s i t qua trinh chiu luc trong cua tiet dien chCf nhat (hlnh 3 a) chju udn (hinh 3.b), b 6 qua i n h hudng cCia li/c c i t , lUc doc d^n su phan bd Ong suat t h i y r i n g khi thay doi m6 men thi sU p h i n bd limg s u i t t r o n g dam c6 the t r i i qua cac gial doan sau:
- Giai doan mot, k l til khi tiet dien bSt d^u cd m o men, iJng s u i t tren tren c i hai t h d k^o va n^n deu nho hon ling suat c h i y <^p (hinh 3.c).
a) b) J)
cj=a^
e)
Hlnh 3. Phan bo liHg suat trong tiet dien
- Khi tang m 6 men cua tiet dien thi se t r i i qua mot thdi diem ma ilng s u i t 6 t h d bien cila t i l t di§n dat tdi cr^ (hinh 3.d).Th6i diem ay t h d bien cua tiet dien b i t dau bj chay deo.
- Giai doan hai, tiep tuc tang m o men cua tiet dien, su chay d^o cua tiet d i | n lan dan tir t h d bien vao trong giu'a tiet diSn va gia tri y (hinh 3.e) nhd dan.
- T i l p tuc t i n g m 6 men cOa t i l t dien thi se t r i i qua mot t h d i diem gia t r i y = 0 khi do t o i n b o tiet dien bi chay d^o.Ti/thdi d i l m d o m o men uon cua tiet dien khdng the tang dUdc nCia (hinh 3.f)
Trong bai b i o nay trlnh bay phuong phap phan tich v i cac ket q u i n h i n diioc khi t i n h toan ket cau theo quan he giCfa Lfng s u i t v i bien dang cd quan he d i n - d^o (hlnh 2) va su phan b d Ong s u i t trong tiet dien n h u hlnh 3.
2. Gicki b a i to^n dio h e thanh b£ng phydng phap phan tit huTu han.
2.1 M o h i n h tfnh
Theo p h u o n g p h i p phan tiJT hijtj han, md hinh t i n h cua p h i n tCr dam CO xet den sU hinh t h i n h k h d p d^o tai hai d i u n u t la-
H /''J-,.,,..-'
jLAa.
EJ. EA, m1
^ e , v
9 , ^ 5 ^ ^ ^
'
^^J \LS
\ "^
Trong do:
' ^ la gia trj m d men tai tiet dien dau dam
M = — ^ — la g i i tri m o men khi t i l t di&n b i t dau hlnh t h i n h khdp
abh'
M^ ^- ° • la gia tri mS men khi tiet dien bj c h i y d^o hoan toan (hlnh thanh khdp d^o)
Khi [ W J l H t i e t d i e n dau dgm chua bl chay d^o thi !< = ">.
Khi I H ^ ^ p t i l t dien dau d i m bj c h i y d i o hoan loan thi k=0 Sau khi tinh toan tadUOc ma tran d o cu'ng cila p h i n ti> dam l i :
K = 0 -ft, 0 -ft,
-T •
0 ft, 0 -h,
[ ' l _ ^ 4 ¥ l ^ 4 ' | ^ 2 2
!,£; lk,)[Ej'^lkJ^lk,lk/ ' 6 f ^ ^2^ 6
yK.
'-^
0
-K
" f t /
K
0 0 EA 1 0 0
[^^
^ -«.
0 0
-h, h,
\ -».
1 ^ 1
&**:,
hj[EJ Ik J " hJEj' ' I Vec t o tai trong nut quy doi cua t i i t r p n g p h i n b d deu tren dam:
Aql 2 /I,
Aql 2 -h 0
^ 4 Aql'
4 0
4 Aql^
Hlnh 4. M D hlnh t i n h cua phSn t U d a m
FT ^M^^i] ..=4^^^1.s.
sau khi bien ddi thay r i n g ma tran dp cufng, vec t d t i i trpng nut quy ddi tUdng Crng vdi lien k i t khdp.
Tir do ta duoc p h u o n g trinh c i n bang cho tCfng budc gia t i i cua dam
4ennffi[iQi|4g
/C„jiU = AP„
(6) 2.2. PhUOng phap khdp d i o trUc tiep
Trong tinh toan neu mudn nhan biet qua trlnh c h i y d^o dan dan cila t i l t di&n thl khong the ap dung phuang phap khdp deo lien tiep vi khi t i l t d i f n b i t d i u hlnh thanh khdp deo, do cLrng cua t i l t dien phu thuoc vao p h i n chua bj c h i y d i o Vi vay, phUong phap nay dapc gpi la phuong phap t r u c t i l p c d t r i n h t u tinh toan n h u sau:
Budc 1. Chia t i i trong thanh cac bUdc gia tai ^ , ^ 1 B u d c Z X ^ c d i n h c S c a a c t i n h c i l a l i e n k e t a l t h i e t lap ma tran do cOng ' ^ u v a v e c t o t i i t r o n g n i l t q u y d o i ^K
Budc 3. Giai he phuang trinh (5) Budc 4. Tinh sd gia cua m o men va tdng mo men 6 cac t i l t dien Budc 5. Bien luan 6e tinh cho budc gia tai sau
Neu trong qua trlnh tang md men (gia t n tuyet doi cua mo men d bddc gia tai trudc nhd hon hoac b i n g g i i tri tuyet dot cua md men d budc gia tai sau], so sSnh M vdi H N l u M<M, thi t i l t dien dd chUa c h i y d i o . NgUoc lai thl t i l t d i e n d d duac xem la chay d i o mdt phan, khi tinh cho bUdc gia t i i sau phai do cung cila tiet dien
6EJ\M„-M\
" r|M-M,| •
Oe tang dp chinh xac cOa ldi g i i i , kiem tra su chenh lech gia t n y d budc gia t i i trUdc vdi budc gia tai sau, neu chenh lech dd nhd thi ch^p nhSn, neu ch^nh lech Idn thl chia ddi bUdc tai de tinh
Neu trong qua trinh giam md men (gia tri tuyet ddi cua mo men d budc gia tai trudc Idn han g i i t n tuyet ddi cua mo men d budc gia tai sau). Khi tinh cho bUdc gia t i i sau p h i i coi tiet dien do chua bi chay deo d l tinh cho budc gia t i i sau.
Quay lai bUdc 2 de tinh cho bUdc gia t^i tiep theo cho d i n khi h i t tSi trong tinh toan h o i c he t r d thanh ca cau b i l n hinh thi bai toan ket thuc.
3 . V i d u tinh t o i n
Phan tich npi luc khung thep p h i n g tai [8] n h u hlnh 4
0.52Mp F ^ .'^.40M|VI
0,66Mr F = 6Mp/l
F/2
Hlnh 4 So do chiu lUc ciia khung phang
Vat lieu co mo duyn dan hoi E. (Vld men quan tinh t i l t dien cac cot v i dam la J. LUc tap trung F tai vi tri 3 - giu'a dam va F/2 tai vi tri 2 - d a u cdt.
Y#u cau: Phan tich ndi lUc va chuyen vi cua khung phang lam viec trong gial doan dan hoi va dan deo theo phuang phap khdp deo true tiep v i phu'ang p h i p khdp deo lien tiep va so sanh k i t qua gifla hai phuong phap.
K i t qua tinh toan theo phuong phap khdp deo lien tiet n h u sau [8]
So sanh k i t qu3 tinh toan theo phuong phap khdp deo lien t i l p vdi phUdng phap khdp deo true t i l p nhusau
Tir hinh 6 lap dUpc bang so sanh ket qua nhU sau:
+ Nhan xet: Khi t i l t dien 4 b i t d i u hinh thanh khdp d i o va moi t i l t dien khac d i u l i m viec trong giai doan dan hoi nen k i t q u i tinh toan d phuong p h i p khdp d^o lien t i l p va phuang phap khdp d i o true t i l p deu cho k i t q u i la gan gidng nhau.
- l a n g t i i t r p n g F i a m c h o t i l t d i e n S bat dau hinh thanh khdp d i o Tir hlnh 7 lap duac bang so sanh k i t qua nhU sau:
+ Nhan xet Khi tang tai trpng lam cho t i l t dien 4 hinh thanh khdp
Hinh 5. Ket qui phan tich bai toan bang phuong phap khdp dki lien tiep d&o den khi tiet tien 5 bat d i u hinh thanh khdp d i o . Ddi vdi phUOng phap khdp d^o lien tiep thi khong xac d m h dUdc dieu nay nhung ddi v6i phuong phap khdp deo true t i l p thi xac dinh dUOC. TCr dd k i t q u i tinh toan CO sU khac biet giCra hai p h u o n g p h i p (bang 2),
- T i l p tye tang tai trpng F d l den khi tiet dien 3 b i t dau hlnh thanh kh6p deo. K i t q u i t i n h toan nhU sau:
Tir hinh 7 lap dupc b i n g so sanh k i t qua n h u sau:
- T i l p tue tang t^i trong F de den khi t i l t dien 1 bat dau hinh thinh khdp dec. K i t q u i tinh toan n h u sau;
TU hinh 7 lap dupc b i n g so sanh k i t q u i n h u sau:
N h i n xet: Khi tang t i i t r p n g den khi t i l t dien 1 b i t dau hinh thinh khdp deo thi k i t qua t i n h toan dupc t h l hien 6 b i n g 4 co sU khic biSt dang ke gida hai phuong phap t i n h . G i i i thfch cho SLt khac bifet dd l i phuang phap khdp ci^o lien tiep khong x a c d m h dupe qua trinh chiy dio dan d i n cila t i l t dien ma chi eo p h u o n g phap khdp d^o true tiep mdi c6 the xac dinh duac dieu nay.
SOaWIEnOl 12.2014
0 36OMp 0.649Mp a. PhutJng p h a p k h d p d ^ o trUc t i l p
0.356Mp 0,64RMp b. PhKong p h a p k h d p d e o lien t i e p Hinh 6. Bieu do mo men Ung vfli net dien 4 bat dau hinh thanh khdp deo Bing 1 5a sinh bieu do mo men khi ttet 4 bat dau hinli thanh khdp deo
Tiet d i e n 1 2 3 4 5
PhacJng p h a p i c h d p d ^ o t r i / c t i e p ( d a n v i t i n h : Mpi
0 , 3 6 0 0 , 0 8 4 0 , 5 8 8 0 , 6 6 9 0 , 6 4 9
P h a o n g p h a p l c h 6 p d e o l i e n t i e p ( d o n v i t i n h : Mpi
0 , 3 5 6 0,085 0 , 5 8 9 0 , 6 7 0 0 , 6 4 8
Sai l e c h
(%)
1 , 1 4 5 % 0 , 6 8 1 % 0 , 0 8 6 % 0 , 0 8 4 % 0 , 0 9 0 %
4 . Ket luan
Qua cac vi du d i duoc khao sat d tren ed the dUa ra mdt sd k i t luan sau:
Khi tai trong nhd, chUa cd t i l t dien nao hinh thanh khdp d i o thi tinh toan theo phuong p h i p khdp deo lien t i l p , phuong phap khdp d i p true tiep va theo m o hinh dan hoi deu cho k i t qua tinh toan l a n h U n h a u .
Khi tai trpng Idn lam xuat hien khdp d i o tai mpt s6 t i l t dien thl k i t qua ndi lUc theo hai phUOng phap khdp deo lien t i l p va phuang phap khdp deo true tiep cho ket qua khac nhau. SU sai k h i c nay cang nhieu khi t^i trong tac dung cang Idn va CO nhieu t i l t diSn hinh thanh khdp deo.
0,373Mn (l.fiTOMp a, P h u o n g p h a p k h 6 p d i o trUc t i e p
0.1f>7Mp C1.66yMp b. P h u o n g p h a p k h d p d e c lien t i e p
!n dng vdi tiet dier 5 bat dau hinh thanh khdp deo
in ktii tiet 5 bat dau hlnh thanh khdp deo
Tiet d i d n 1 2 3 4 5
P h u o n g p h a p I<h0p d ^ o t r u e t i e p ( d o n v j t i n h : Mp)
0 , 3 7 2 0 , 0 8 7 0 , 6 0 8 0 , 6 9 0 0 , 6 7 0
P h u o n g p h a p IchOp d e c l i e n t i e p ( d o n v j t i n h : Mp)
0 , 3 6 7 0 , 0 8 7 0 , 6 0 8 0,691 0 , 6 6 9
Sai l e c h
(%)
- 1 , 2 4 2 % 0 , 3 5 7 % - 0 , 0 7 5 % 0 , 1 7 6 % - 0 , 0 9 1 %
i2.2oi4gnnKiiax!5i
l).4D7Mp 0,73SMp
a. Phuong phip khdp dio true tiep
0,4O4Mp 0,736Mp b. Phuang p h i p khdp d i o lien t i l p H"inh 8 Bieu d6 mo men dng vdi tilt dien 3 bit dau hlnh thanh khdp dio
B i n g 3. So sanh bleu dd mo men khi bet 3 bat dau hinh Hianh khdp deo
Tiet dien 1 2 3 4 5
Phuong phap khdp d§o tnic tiep (don vi tinh: Mp)
0,407 0,094 0,668 0,760 0,738
Phuong phap Ichiflp d^o lien tiep (donvi tinh: Mp)
0,404 0,096 0,668 0,760 0,736
Sai lech
(%)
-0,793%
2,034%
-0,050%
-0,050%
-0,322%
F = 5.570Mrrt
D,«97Mp 0.121M|i
0.95 5 Mp
n-iii7Mp a 9 W M p
a. Phuong phip khdp deo true tilp
F = !i.570Mp/l
0.998 Mp 0.l59Mp
0.987 Mp
O.607Mp 0.996Mp
b. Phuong phip khdp dio lien tilp
Hinh 9 Bieu do mo men dng vdi tiet dien 1 bat dau hinh tiianh khdp dJo
Bang 4: So sanh bieu do m d men khi tiet 1 b i t dau hinh thanh khdp deo
Tift dien 1 2 3 4 5
Phuong phap Ithdp deo tnic tiep (don vl tinh: Mp)
0,407 0,121 0,995 0,997 0,999
Phuong phap khdp deo hen tiep (don vj tinh: Mp)
0,607 0,159 0,987 0,998 0,996
Sai lech
(%)
32,954%
23,804%
-0,846%
0,050%
-0,301%
5.TAILI£UTHAMKHAO
t l ] , eang Ngoc Canh, Ngo Hdu Cirdng, PhSn ticli viing deo va phi tuyen hinh hoc killing thep nda dng hhfing gian, Tap chi Xay dUng, Vol.52, no.6,2013
[2] N g u y i n Van Tii. Tinh ! o ^ n he khung phing t h U md hinh d^n-d^o song tuyen tinh d i i u t i c dung cUa til trong ddng. Tuyen t | p cong t i i n h Hoi nghj khoa hoc d t nha nghien cdu tre (Hoc v i f n lOQS), so IV/2D09, trang S-15.
[ 3 ] . Nguyen Van Tu, Nguyen Van Hdi. Tinh todn kAdD khung phSng d a n - d ^ chiu tac dung eda tdi tning dfngid Ket den hieu ilng P-Delta v^ tinh phi tuyen hlnh hgc d a ket cau TapchiXay dutig, Bo );aydung,s6l1/2009,tiang 81-85.
14]L.Xu,Y Uu, D.E,Grierson,"Nonlineai3nalyslsof steel framevjorks through direct modification of memlrtr stiffness properties" Advances in Engineenng Software 3f ( 2 0 0 5 ) 3 1 2 - 3 2 4
[5] L Xu, y. U u , D.E. GriHsnn,'Compound-el(iiia»
modeling accounting for seni-rigid connections M member p l a s t i a t y ' Engmeeiing Structures 30 (lOOD:
1 2 9 2 - 1 J 0 7 .
[6] M. Sekulovic, M Nefovska - Danllovlc. " 9 8 1 ^ inelastic analysis of steel frames w i t h flexible coiuMdliinsI Theoret Appi. M e c h , Vol 3 1 , No.2, pp.101,134, B e W
2004 • * [71 N.S. Trahalr, M. A. Bradford, D.A. Nethertot anilL
Gardner,°TlieBehavlourand Design of Steel StiurtuiBtir
E G ' F o u r t h edition, pp.179 '*
[8] A Wouwenvelder Delft, (2003), Elatistit - p l W analysisof a portal frame, pp. 27.