Phan tfch phi tuyen khung thep phang dung ham chuyen vj da thiFc bac nam
Nonlinear analysis of planar steel frames using fifth-order polynomial displacement function
Ngay nhan bai: 24/01/2015 Ngay SLTa bai: 15/3/2015 Ngay chap nhan dang: 25/04/2015
Doan N g o c T j n h Nghiem, Le Nguyen Cong T i n , Nguyen Thj Thuy Linh,
N g u y i n Tan Hu'ng, Ngo Hu'u Cu'dng
TOM TAT
B^i bao nay trinh bay ni6t phan tii dam-cot co the mo phong tac dong bac hai va su chay dec ciia ket c3u khung thep phang chm tai trgng tinh. Ham chuyen vi ciia cau kien dam-cot chiu
!uc doc va momen uon d hai dau miit dugc gia dinh xap xi bang ham da thiic bac nam thoa cac dieu kien tuong thich va can bang tai hai dau miit va d chinh giiia cau kien. Tii do mgt ma tran dp ciing voi cac ham on dinh c6 xet dgn hiSu irng cung dugc thiet lap de gia lap chinh xac tac dgng bac hai. Cac he so chay deo dau miit dugc sir dung de mo phong su chay deo dan dan cua tiet dien hai dSu phan tii theo gia thiet khap deo. Mgt chuang trinh phSn tich phi tuyen cho kit cau khung thep phSng duac phat trien bang ngon ngii l§p trinh MATLAB dya trgn thu|t toin giai phi tuyen theo phuang phap chieu dai cung ket hgp vai phuong phap chuy§n vi dir nho nhdt vi ket qua phan tich ciia no dugc chiing minh la tin c3y qua cac vi du s6.
Tis khiia; Khiip deo, higu iing cung, ph§n tich phi tuySn, khung thep, ham da thiic bSc nam.
ABSTRACT
This paper presents a beam-column element capable of modeling the second-order effects and the inelasticity of planar steel frame structures under static loads. The displacement function of a beam-column member subjected to axial forces and bending moments at the ends is approximately assumed to be a fifth-order polynomial function satisfying the compatible and equilibrium conditions at the mid-length and ends ofthe member Then a stiffiiess matrix with stability functions considering the bowing effect is formulated in order to simulate the second- order effects accurately. The end plasticity factors are used to model the gradual plastification of two end element sections by plastic-hmge assumption. A structural nonlinear analysis program of steel frame structures is developed by MATLAB programming language based on the arc-length method combined with minimum residual displacement method and its analysis results are proved to be reliable through some numerical examples.
Keywords: Plastic-hinge, bowing effect, nonlinear analysis, steel frames, fifth-order polynomial ftmction.
ThS. Doin Ng9C Tinh Nghiim
Khoa x a y dung & Co hoc iing dung, Truang Dai hgc Su pham Ky thuat Tp.HCM NCS, Khoa Ky thuat Xay dung, Trucmg Dai hgc Bach khoa - Dai hoc Qu6c gia Tp.HCM KS. Lg Nguygn Cfing Tin
Khoa Xay dung, Trucmg Dai hoc Xay dung Mien Tmng ThS. Nguyin Thi Thiiy Linh
Khoa Xay dung, Tmong Dai hgc Cong nghe Tp.HCM ThS. Nguyin Tan Himg
Khoa Xay dung Dan dung va Cong nghiep, Trucmg Dai hgc Bach khoa - Dai hgc Da NSng PGS,TS. Ngfi Hfru CuoTig
Khoa Ky thu^t Xay dung, Tmang Dai hgc Bach khoa - Dai hgc Qufic gia Tp HCM; Email:
1 . Gidi t h i e u
Trong phan tfch phi tuyen k^t cau, phuang phap d i m - c o t dUOc xem la phUOng phap dOn glan va hieu qua trong viec mo phong tac dong phi tuyen ma van dam bao d o chfnh xie dn t h i ^ t cho phSn tich thiet ke thUc hanh n h u da duoc nghien cu'u va phat trien bcfi Lui &
Chen (1986) [1], Liew va cong sU (2000) [2], Kim & Choi (2001) [3], Ngo-Huu & Kim (2012) [4], ... Tuy nhien, viec sii dung ham on dinh chfnh xac t i f I6i giai gi3i tich ciia cau kign d i m - c g t gay kho khan trong viec khai t n l n cong thiic trong qua trinh thiet lap ma trSn 66 eilng phan tis. Nam 1994, Chan & Zhou [5]
da de xuat ham chuyen vi xap xi da thu'c bac nam cho cau kien dam-cot va thiet lap ma tran do cilng phSn t i i CO xem xet tac dong bhe hai bang phuong phap t h ^ nang toan p h i n diing. J u d i l m cua viec sii dung ham nay la sii dOn glan trong viec thiet lap cong thiic ma vin dcim bao do chinh xac nhU h^m on dinh lugng giac truyen th6ng.
Nghien ciiu nay sii dung dang ham chuyen vi da thirc bac nam cCia Chan & Zhou [5] de xay dUng ma tran do ciJng phan t i i co xem xet tac dong phi tuyen hlnh hoc theo \j thuyet dam-cot. Hieu iing cung dudc ke den de xem x^t su thay doi chieu dai phan t i i do sU uon cong cOa phSn t i i khi chju life. PhUOng phap khdp deo hieu chinh duoc sii dung d l mo phong iing x i i phi tuyen vat lieu. O l gi^i he phuong trinh can bSng phi t u y i n , phuong phap chieu dai cung (aTC-length method) k i t hop vdi phuong phap chuyen vj dU nho nhat (minimum residual displacement method)
5QSGSIS[iil!ia!13l
dugc lua chgn d ^ dp dung do c6 toe do hoi t u cao. Mdt chUOng trinh may t i n h dUOC phat trien b i n g ngon ngCr lap trinh MATLAB de tU dgng hda viec phan tich dng x i i phi tuyen cOa khung thep p h i n g chiu tai trong tinh. K i t qua phan tich dUOC so sanh vdi ket qud cac nghien cdu trudc do chdng t d do tin cay cua chuong trinh phat t r i l n .
2. Co s d i y t h u y e t
2.1.Cdc hdm dn Oinh khi xdp xl hdm chuyin vi ttdng da thirc bgc 5 Xet phan t i i d3m-c6t dan hoi chiu life doc true va md-men uon 6 hai dau phan t i i n h i i trong Hinh 1.
(la) ( l b ) Hinh 1. Phan tildam-cfil flien hinh
Phuong trinh vl phan cua phan tir dSm-cpt:
Ap dung eie diiu kiin hiin, ta dUOC quan he giiia mfi-men va gdc
(2) xoay
iM2r"r[s2 sijjejj
vdi s,, S2 duoc goi la dc hSm dn dinh, Ket q u i ldi gidi g i l i tfch ciia hSm c h u y i n vi A ( x ) v a cdc hhm dn dmh Si.sj duoc trinh bay nhu trong B i n g 1.
(v6l X ^ L J-U- cho c l hai trUdng hgp F s 0 va F >0) Oe don g i l n hoa cac phep b i l n dfii toan hoc, ham chuyen vi A ( X ) dugc xap xl bSng da thiic bac 5:
A ( x ) = asX^+a4x''+a3X^+a2X^+a,x + ao (3)
C I c h f s o a,{l = 0 ~ 5 ) dugc x l c djnh t i i v i ^ c c h o h S m c h u y i n v i g i l t h i l t 6 tren thoa c i c dieu kien tuOng thfch va d i l o kien can b i n g CIc p h u o n g trinh duOc trinh bay nhusau:
mi m.
C|'A{X
d=A(x) d A ( x ) ' | ( M , + W
(4) (5)
d ^ A ( x )
d ^ dx^
TCr cac phuong trinh (6) den (11) ta x l c dinh duoc de hi sfi a| (i = 0 ~ 5 ) , t i i day ta x l c d m h dugc cdc hSm 6n d m h Si,S2 theo q = X^ n h u trong B i n g 2.
Ket qua cac ham 6n d m h de xuat va h i m 6n d m h truyen thong theo ldi g i l l g i l i tich dugc trinh bay n h u t r o n g Hinh 2 cho thay h i m on dinh de xuat cd do chfnh x l c khd cao. Vdi c i c h&m dn dinh de x u l t , ta de d i n g xac djnh dugc cdc dao ham cua c i c h i m 6n djnh s^, $2 trong cic cdng thilc tinh todn ngi lUc nut phan t i l d p h i n sau
Bdng 1 Ldi gidi gidi tich cua h^m chuyen 1 A ( x ) v a cac ham 6n dinh s,,S2.
TrUdng h o p F < 0 A ( > . ) . a s i n C ^ ] + b c o s f ^ l + cx + d
( l - c o s > . - X s i n ? . ) e , + ( c o 5 J . - l ) 0 3 _
>.(2-2cos>.-A,sin?.) (sinX-A,cosX}ei + ( > . - s i n X ) e 2 ,
X{2-icosX-}.sinX)
(i-cos).)(eife2)
{ 2 - 2 c o s > . - X s i n ^ ) ( s m X - X c o s J . ) e i + (X-sin?L)e2
^ ( 2 - 2 c o s X - X s l n X )
>.sin?.-^^cosX ' 2-2cosA.-A.sin>.
X ^ - A s i n X
"•^ 2 - 2 c o s 3 i , - X s i n A
Truijfng h t f p F > 0 A ( x ) = asinh — U b c o s h — + c x + d
( l - c o s h A . + A , s i n h X ) 9 T i - ( c o s h A . - l ) e 2 , A.(2-2cosh>. + i.sinhX)
^ (sinh?.-A.cosh>.)ei+(X-sinhA.)e2, A.(2-2coshX,-(-XsinhA.}
^ ( l - c o s h A ) { e , + e2) (2-2coshA. + AsinhA.)
( s i n h A - > . c o s h A ) e , + ( X - s i n h ? i ) e 2 ,
^ ( 2 - 2 c o s h > . + >.sinhX.) )L^coshA.-?^smhX
^' 2-2coshX+X.sinhX, AsmhA-A.^
' ' 2 - 2 coshX + X, sinh^
132
Bdng 2. Ldi g i l l cua hdm c h u y i n vi A ( X ) v a c a c h a m o n d j n h s,,S2 khi xap xi ham chuyen vi bang da thdc bac 5.
TrUdng hdp F £ 0 A(x) = a5X^+a4x'' +a3X^+a2x^ -i-aix + ao ao = 0
a, =61
(6q^-512q + 7680Je,+(q^-64q + 3840]G2 L(q-48)(q-80) fl3q^-832q + 3840J6,+[5q^-192q + 3840)e3
L^(q-48)(q-80) 4q[(3q-160)e,+(2q-80)e2]
^*' L3(q-48){q-80)
^ 4q{9i + e2)
^ L''(q-80) 4(3q^-256q + 3840]
(80-q){48-q) 2(q^-64q + 3840J '' (80-q)(48-q)
Trirdng hcrp F > 0 A(x) = a5X +a4X +a3X +a2X -(-a|X + ao ao=0
a,-ei
(6q^+512q+7680J9, + fq^+64q + 3840)92
^^ L(q-i-48)(q + 80) (l3q^+832q+3840J9,+(5q^ + 192q-i-3840Je2
"* L^{q+4B)(q+80) 4q[{3q+160)e,+(2q + 80)e2]
"" L^(q + 48){q + 80) 4q(ei+e2) ' L''(q + 80}
4[3q^+256q + 3840J ' ' (80 + q)(48 + q)
2(q^ + 64q-H3840J
^^ (80 + q)(48 + q)
T
S, (F > 01
^ " ~ " * ~ * - - ^ 4 i ( F £ 0 )
*'*11^L«-—-^^
S ^ ( F > 0 )
— — — l y thuyet —S—Tac gia
" ^
- « ^
X
H'inh 2. So sanh cac ham on dinh
2.2.Qaan hi ndi lUc vd gdc xoay hai ddu phdn td Taed:
L J dx 2 J I, dx
EA^ E A f f d A Y
,l^6.!:lfi
L 2L J I.0
Theo Oran [6), luc doc duoc vi^t lai n h u sau:
F=EAri+b,(e,+62f+bj(e,-ejfl
Trong d d , b ^ . b ; la eae hSm hieu iing cung dUOc xde dinh theo ede ham dn dinh S|,S2 va q = A. nhUsau:
(14a)
{14b) 8(si + S2)
( s i + S 2 ) ( s 2 - 2 ) ^ ^ _ S2 8q ' ^ 8(si + S2) SCrdung MAPLE, tac gia chu'ng minh dUoc cdc quan hi sau:
s ^ = - 2 ( b , + b 2 ) ; s ^ - - 2 ( b T - b 2 ) k h i F < 0 {15a) s; = 2 ( b , + b 2 ) ; s ^ - 2 ( b , - b 2 ) k h i F > 0 (15b) Ggi EI va c; t u o n g iing la he sd chdy d^o mo t l mdc dd c h i y d^o d hai dau m u t phan t l i ( 0 < e , , e 2 < l ) ; trong do, ei va e j c d g i d tri bSng 1 n l u t i l t dien van edn hoan toan dan h6i, b i n g 0 n l u t i l t dien da e h l y d ^ o hoan toan va c6 gia t n ndm giOa 0 va 1 neu t i l t dien dang c h i y d^o.
Theo Liew va cong su [7], quan he mo-men vh gdc xoay duoc v i l t lai nhusau:
JMil Elpip 53plf9,|
\ ^ l \ L [ S 2 P S 3 p j l 9 2 |
Trong do, cac gid t n S]p,S2p,S3p dUOC x l c dinh theo cdc ham on d m h S|, S2 va cac he so e|, e2 :
S i p = e i s , - ^ ( l - e 2 ) ;s3p=e,e2S2,S3p=e2 s , - ^ ( l - e , } (17)
Tir (13), (15a), (15b) l U c d o c d u o c hieu chinh lai n h u s a u :
F = E A U + f | s ; p 9 j + s i p 9 i e 2 + ^ s ^ p e ^ j (18)
{ B i e u t h i J c l a y d a u " + " k h i f > O v a d a u " - " k h i F £ 0 ) . Vdi:
(16)
Bdnq 3. Ket q
L(mm)
1141.97 2283 95 3425 92 4567.84 6851.90 9135.78 11419.73 13703.67 15987.62 18271.56 20555.51 22839.45
u l ty so tdl tdl han [P/P,] cua cot hai dau khdp.
Vk
0.25 0.50 0.75 1.00 1 50 2.00 2.50 3.00 3.50 4.00 4.50 5.00
(P/Pv)
Euler
16 4 1.7778 1.0000 0.4444 0.2500 0.1600 0.1111 0.0816 0 0625 0.0494 0,0400
CRC Co xet
l/SD 0.9844 0 9375 0.8594 0.7500 0.4444 0.2500 0.1600 0.1111 0.0816 0.0625 0.0494 0.0400
Ngo-Huu 8i Kim Khdng xet
l/SD 0.9870 0.9870 0.9870 0.9880 0.4450 0.2500 0.1600 0.1120 0.0820 0.0630 0.0500 0.0400
Co xet l/SD 0.9870 0 9360 0.8610 0.7600 04450 0.2500 0.1600 0.1120 0.0820 0.0630 0.0500 0.0400
Tdc Khdng xet
l/SD 0.9960 0.9960 0.9960 0.9825 0.4371 0.2474 0.1587 0.1100 0.0817 0.0626 0.0498 0.0405
gia Cdx^t
l/SD 0.9858 0.9396 0.8604 0.7493 0.4371 0.2474 0.1587 0.1100 0.0817 0.0626 0.0498 0.0405
5 a i s 6 ( % ) Khdng x6t
l/SD
1 75 164 1 04 0 81 0.99 0.12 0.16 0.81 1.25
C 6 x 6 t USD 0.14 0.22 0.12 0 09 1 64 1 04 0.81 0.99 0.12 0.16 0.81 1.25
2.3.IVIa trdn dd cUng phdn tdddm-cdt
So dd liic v l chuyen vi dau mut eua p h i n t i i dlm-c6t dUoc trinh bay n h i / t r o n g Hinh 3.
9,=U3 L
(20) (21)
Trong dd, [7] I I ma trhn c h u y i n ciia p h i n t i i d l m - c 6 t khung p h i n g .
m-
Ma tran do eilng phan t i i trong toa do dia phuong v l toa d ^ tdng the dUOe xae dmh nhU sau:
Hinh 3. LUc vi chuy^ vi dSu miil phan til dam-cot
Ta cd quan h^ gida edc thong sd hinh hgc va cae ehuyen vj dau m i i t p h i n t l i n h u sau:
5 = ( U 4 - U , )
Ndi Iu'e nut phan til trong toa do dia phuong va trong he tga do tdng thi:
,_. r (M1+M2} (M,i-M,) f {Z}= -^ ^ ^ - L - ^ M, F - - ^ - ^ M J (23)
cosa - s i n a 0 0 0 0
sina cosa 0 0 0 0
0 0 1 0 0 0
0 0 0 cosa - s i n a 0
0 0 0 Since cosa 0
' hay k/| •
^"("1- (26)
[KT] = [ T ] " [ k T ] [ T ]
Khai tnln (26) bang phin mem MAPLE, ta xdc dinh du'gc ma tran do Cling tilp tuyen phan tCr:
Trong do:
(27)
(28)
( • i , * a 2 , * ' a i , ) ( • » * • » ) ^ ( i t < - " i | , * i i | , ) (=i,tsi|,)
T »
1 3 4
B
[•%]=£
T , ( T , . T , )
(30) {31a) (31b) T , = - ( s i p O , + S2p02j;T2=-^S3pei + s^p92J k h i F <
T , = ( s ^ p 9 i + s ^ p e 2 ) ; T 2 = ( s i p 9 i + s ^ p e 2 ) k h l F > 0
Ma tran do ciing phan til d i m - c o t de xuat d tren cd xet den dnh hudng bac hai va t i e d g n g phi tuyen vat lieu t h o n g qua ede ham on dmh Sip, S2p, S3p da dugc hieu chinh theo cdc he so chay deo va cac gdc xoay d hai dau phan t ^
2.4.Phdn tich phi tuyin vgt lieu
Bi ki d i n I n h hu'dng cua iing suat dU trong mat cat t i l t dien du'di tdc dung cua luc doc, tae gid sCr d y n g khai mem mo-dun t i l p t u y i n f , duoe dUa ra bdi Hgi dong nghi§n cilu cgt cua Hoa Ky (CRC - Column Research Council):
Ben canh do, de ke d i n tae d d n g ddng thdi cua lUc doc va mo-men udn, dudng eUdng dd Orbison [ S J d u o c s i l d u n g :
(33)
Theo Liew va edng sil [7], hi s6 chdy d^o e difoc xac dinh theo cong thilc e = h ( a ) = 4 a ( l - a ) , vdi cda t h d n g sd deo dUoc tfnh theo dd ldn c u a l U c d o c v l md-men 6 hai dau m u t eau kien.
2.S.Thudt todn gidi phi tuyen
Trong nghten eilu nay, tdc gia s i i d u n g phuong phap e h i l u dai eung k i t hop vdi phuang phap e h u y i n vj d u nhd nhat dugc Chan va Zhou [S]
d l xuat de gidi he phuang trinh phi tuyen.
Phuang trinh can bang gia tang dUoc trinh bay nhUsau.
{Au + AX,Au} - [ K T ] " ' | A P + AA.AP| (34) Trong do: AP I I vec-to lUC khdng can bang, Au la gia so chuyen vi,
AP I I v^c-tO song song vdi vee-to t l i , Au la vec-tO chuyen vj ket hop va Ak ih he sd d i l u chinh t l i .
d budc lap dau tien, lay AA.^ theo cdng thilc ciia phuong phap chieu dai eung'
are length
A?., = - (35)
6 bu'dc t h i l 2 t r d d l , AX, (i > 2 ) d u g c xae djnh t i i d i l u kien ehuyen vi d u nhd n h i t :
3 { A A . , A U + Au, }^ { A X | A U + Au, }1 ' ~ dAX, ~ Oon g i l n bieu thiie (36), ta dUoc:
AX,= ( , > 2 ) (37)
MM
3. V i du so
Mdt chuong trinh phan tich k i t c l u dugc phdt t n l n bang MATLAB de dp dung p h i n tfch phi dan hdi bac hai cho khung t h 4 p p h i n g chiu tdl trong tmh, Cac ket qud phan tich duac so sanh va danh gia vdi k i t q u i cOa cac nghien eilu trUde do qua eae v f d u so sau.
3.1.C6thaiddukhcV
Cot thep hai dau khdp chm lilc nen ddng t i m tai dau cot vdi cac t h o n g sd nhU trong Hinh 4 dUoc Ngo-Huu v l Kim [4] phan tfch bang phuong phap khdp t h d trong dc trudng hop cd v l khdng cd xet d i n dnh hudng eiia iing suat dU ban dau trong cau kien. 0 v i du nay, tac gid phan tich cdt bang 1 phan t i i de xuat.
= 200 GPa
= 250 MPa
= 51.2 mm
Hinh 4 Cot hdi dau khdp
K i t qud dudng cUdng do cot theo (P / Py)
At =^(L/ry] J o y / n ^ E dUoctrinh bay n h U t r o n g Hinh 5 va B i n g 3,
—•—Tac gia (Khons xel USD) CRC -e-TScgia (CA i^USD)
Hinh 5 €Jcing ci/cirg 36 cot hai flau khdp chiu ii/c doc t m c tai dau miit.
3.2.Khung 2 tdng 1 nhjp
Khung 2 tang 1 nhip vdi ede t h d n g s d n h u H i n h 6 duge Chan v l Chui [9] phan tich dan hdi va phi dan hoi va duge m d phdng b i n g m o t phan t i l d l xuat cho mgt eau kien trong nghien cilu nay.
Ket qua dUdng tdi trgng - chuyen vl dinh A trong p h i n tich phi t u y i n dan hdi va phi dan hoi ciia khung dugc t h i hien 6 Hinh 7 va Hlnh 8. Dudng t l i trong - chuyen vi ciia chuong trinh de xuat g i n nhU trung khdp vdi ket q u i cOa Chan & Chui. Gid t n tai gidi han trong ph^n tieh cua khung dUoc trinh bay 6 B i n g 4 vdi sai sd Idn nhat chi k h o i n g 2%,
io.20i5SSEB[3Ii{!IS|l35
ffl
W12
g
i
77?
P
1"
\
TT W14-48
W14>'48
E = 2900D ksi a , = 36 ksi
P
1 j
777
%
W12
g
i
Hlnh 6 Khung 2 tang 1 nhip li^n ket ngiim.
2250 S laoD
^ 900 45D
/ ^
1 1
( f C ^ r e - o - ® " ® "
Chan & Chui - O - T i c g i i
Bang 4 K i t qud tai qidi han eua khuna 2 tana Ket q u i i t l i g i d i h a n
Chan & C h u i T i e gid
Saisd
PhSn t i c h d a n h o i 2560 2558 0.08%
nhip.
P h i n t i c h p h i d a n h o i 480 470 2.08%
S 3
%
K S
O l
3 777 P
r r r
777
r'
W1EX40
r
W16X40
1"
W16X40
r'
w i e x t o p = eo kN H = 31 kN 9 15 m
S
%
^
%•
s
3
O l
3 2P
r
i"
r'
77^777
r"
W16K40
r
W16X40
1"
wieK4o
r'
W16X40 E = 200 GPa o^ = 250 MPa 9 15 m
V
'\
'\
'\
S
% .,
3 R 3
X
5
77^7 _ I Hinh9.Khuti94tarig2rhip.
Hinh 10 cho thay quan he hi sd tai trgng - c h u y i n vi ngang d dinh khung eCia tac gia rat sdt vdi k i t q u i trUdc d d cCia Kukretl v l Zhou. Sai sd glCra he sd t l i gidl han }„. cOa hai p h u a n g phap la 0.38% ( ^ i m 1.831, ^|lJcgUl= 1.8
Chuyen vi, A (in) Hlnh 7. Ouan h§ \ii trong - chuyen vi dinh J vdi phan tich dan hdi.
3.3.Khung 4 tdng 2 nhip
Khung thep 4 tang 2 nhip vdi cdc thong sd hlnh hoe nhu Hinh 9 duoc Kukreti va Zhou [11 ] phan tich b i n g phuong phdp khdp ddo hieu chinh. M6-dun dan hoi £ = 200 GPa, ilng suat e h l y d^o CT, = 250 MPa, P
= 60 kN va H = 31 kN 0 vi du ndy, khung dugc md phdng b i n g mgt p h i n t i l d l xuat.
0.04 0.0£
OiuyenviApn) Hinli 8 Ouan he tai trong - chuyin vi dinh A vdi phan n'di phi dan hoi.
ChuySn vL A (mm)
Hinh 10, Ouan he he so tai tiong - chuyen vi ngang dinh ben phli khung 4 tang 2 nhip.
3.4.Khung Vogel 6 tdng 2 nhip
Khung Vogel 6 tang 2 nhjp trinh bay 6 Hinh 11 vdi t i l t dien c l e cau kien dugc trinh bay nhU trong Bdng 5 dUOc Vogel (12] phan tich phi tuyen b i n g ed hai phuong phap khdp dio va phuong phdp vung ddo.
Bai t o l n nay dUoc chon lam eo sd d l kiem chiing edc phUOng p h l p p h i n tich don gidn khde. Trong vi du n l y , do dam ehiu tdi p h i n bd nen khdp dio ed thi hinh thanh d cle vi tri giCfa d i m , tde gid k h i o sdt vdi 2 trudng hop. chia dam thSnh 2 phan t i l , cgt t h l n h 1 phdn t d d l xuat (2B1C) va trudng hop chia dam t h l n h 4 phan t d , edt t h l n h 1 nhdn t d i t l xuat(4B1C).
136B
H,= 10.23 kN f i \ I "
E - 205 GPa ^ f , = 235 MPa X= 1/300 Hinh11 Khung Vogel 6 tSng 2 nhip.
T T T i r r T T T i r f t w
IPE330 ?trr I ) t MPT
u I M r r
7 ;_,
Binq 5. Kich thUdc cac cau kien khung Vogel 6 tang 2 Tiet dien
HEB260 HEB240 HEB220 HEB200 HEB160 IPE400 IPE360 IPE330 IPE300 IPE240
b l (mm)
260 240 220 200 160 180 170 160 150 120
tr (mm)
17.5 17.0 16,0 150 130 13.5 12.7 11 5 10.7 9.8
d (mm)
260 240 220 200 160 400 360 330 300 240
nhip.
tw (mm)
10.0 10.0 9.5 9.0 8.0 8.6 8.0 7.5 7.1 6.2
Ket qua chuyen v\ ngang tai dinh ben p h l i so sdnh vdi k i t qua cOa Vogel sil dung phuong p h l p vi^ng dio thi hien 6 Hinh 12 Ket q u i phan tich cho thay he sd tai trong gidi ban A. ciia hai phuong phdp la s i t nhau vdi sai sd 0.5% ( A , ( v o g 5 i ) = l . n i , ^ m t g H ) = 1.107). Vdi viec chia nho dam thanh 4 phan ti!r de xuat, bai t o l n hdi t u v l ket qua cua phUOng phapvung deo do Vogel phan tich.
4 . Ket luan
Ham c h u y i n vi xap xl dang da thdc bae nam da dUOC l p dyng de thanh Idp ma tran d d c i l n g cua p h i n t d d a m - e d t c o k e den tac ddng phi tuyen hinh hoe va vat lieu theo ly thuyet dam-cgt. l/u d i l m cCia ham nay la tinh don gian eho viee khai tnen eae edng thilc nhUng v l n dam bao do ehinh xdc can t h i l t CLia ldi g i l i de ed the ap dung trong phdn tich t h i l t k l thuc hanh. Ket q u i cua cac vi du sd chiing t d phUong phap d l xuat va chuong trinh dUOc phat trien cd the dU dodn khd chfnh xdc dng xd phi tuyen phi dan hoi eua cau kien va he ket cau khung p h i n g chiu t l i trong tinh.
TAI LIEU THAM KHAO
I, liii,LM.,Chei],V^f.{]%6),Analysisandbehaviouroftlexibly-joiniedframes,i.nqinee<ing Structures, 8(2), 107-18.
2 Liew, J V R, Chen, W F, Chen, H. (2000), Advanced inelastk analysis of frame structures, Journal of Constructional Steel Research, 55(1-3), 245-265,
3. Kim, S.E., Choi, S.H. (2001), Pradical advanced analysis for semi-rigid space frames, lntemationa!JoiirnalofSolidsandStruclures,38,9111-31
4 Ngo-Huu, C, Kim, S E. (2012), Second-order plaslic-hinge analysis of space semi-rigid steel frames, Thm-Walled Structures, 60(11). 98-104
5 Chan, S,L„ Zhou, Z.H, (1994), Pomtmse equilibrating polynomial element for nonlinear oiM(ysiso^frfl/nH,Journal of Structural Engineering, 120(6), 1703-17
6 Oran,C (WDJangentstiffnessmplaneframes,] Struct Div,99(6),973-985 7. View,iH.K^'r\iti\>>N.,C.hen'^.\.{Wl],Second-orderrefinedplastic-binge analysis for frflme(/es/'gn./'[jrt/,JournalofStriictural Engineering, 119(11), 3196-3216.
8 Orhison, J.G., McGuire, W, Abel, J.F (1982), Yield surface applications in nonlinear steel frame analysis. Computer Methods in Applied Mechanics and Engineering, 33,557-73.
9 Chan. S.L, Chm, PPT [1000], Non-linear static and cyclic analysis of steel frames with semi-rigid connections, Elsevier.
10. Balling, R. (2012), Computer Structural Analpis, Lecture notes, Brigham Young University, Utah,
I I , Kukreti, A.R, Zhou, F F, (2006), Eight-bolt endplate connection and its influence on frame behavior, Engineering Strudures, 28,1483-93.
12 Vogel,U (1985),fdAftrofrngframaStahlbau, 10,295-301.
ChiivfinvbA(iniii)
Hinh 12, Ouan he he so tai trong - chuyen vi ngang dinh her ph^i khung Vogel 6 tang 2 nhip.
