TAP CHI KHOA HOC TRUONG OAI HOC MOTP.HCM - S 6 2 (41) 2015
PHAN TICH PHI TUYEN KHUNG DAN THEP PHANG sty DUNG PHlJOfNG PHAP D A M - C O T
/
Ngay nhan bai: 11/12/2014 ^ ^ I f 0 ^ Bang Thj Phirang Uyin' Ngay nhan Iai: 02/03/2015 U Thanh Cudng' Ngay duyet dang: 26/03/2015 NgO Hiru Cudng^
TOM TAT
Phi tuyin hinh hgc Id ke din su sai lich hinh hgc ket cdu tgi timg thdi diim gia tdng luc tdc dung vdphdn tich phi tuyin vdt lieu la ke din su biin ddi cua vdt lieu khi luc gia tdng. Phdn iich phi tuyin hinh hgc sir dung phuang phdp ddm-cdt (beam-column method) dung hdm dn dinh vd phdn tich phi tuyen vdt lieu ke din sir ehay deo a hai ddu phdn tir di mo phdng su ldm viec ciiajjhdn tir cung nhir ciia todn bg hi kit cdu khung ddn khi chiu tdc dung cua ngogi lire. Phdn tu ddm-cdt ke din idc dung cua lire nen vd uon ddng thdi. diin td kit hgp suphdn tich vi sai lech hinh hgc cua ddm vd vdn di dn dinh cua cdt khi chiu luc tdc dung. Bdi bdo sir dung phuang phdp phdn tich ndng cao phdn tich mdi quan hi giira lire vd chuyin vi cua hi kit cdu khung ddn la dudng cong bgc hai, ki din su ldm viic ddng thdi cua hi khi chiu luc tdc dung, phdn tich mdi quan he giira luc-chuyin vi tgi tirng thai diim luc gia tdng vd tgi thai diim kit cdu dgt din trgng thdi gidi hgn. Su dung hdm dn dinh theo phuang phdp ddm-cdt giiip cho viic khai bdo sd phdn tir it han. gidm thieu dugc thdi dan phdn tich bdi todn vd gidm bd nhd dim mdy finh rdt nhiiu.
Tir khda: ddn thep. phi tuyen. hdm dn dinh, ddm-cdt.
ABSTRACT
Nonlinear geometric is mention of geometric error of structure at the point increasing force and the nonlinear material is mention of a change material. Nonlinear geometric analysis by using beam-column method and nonlinear materials thai including plastic hinge ofthe ending elements for simulation the working ofthe elements as well as the entire the trusses system under the effect of external forces. Beam-column including the effects of compression and bending that describes the combining analysis ofthe deviation ofthe beam geometry and stability issues ofthe load-bearing column. The article uses advanced analytical methods to analyze the relationship between force and displacement ofthe trusses system through quadratic cun>e which including the combination of effects. Analysis the relationship between the force-displacement at each increasing force point and the point reaching structure's limit. Using the stability of beam- column method enables to reduce the declaration of element, reduce analysis lime and reduce the problem of computer memorycache.
Keywords: Steel trusses. Nonlinear, Stability function. Beam-column.
1. Dat van d£ chu yeu chi chiu dgc trong thanh, khong ke tac T «„« «u;5„ +' I, A' t.^- L- u". ddng do luc keo (nen) va udn ddng thdi. Do Trong phan tich dan hoi bac nhat, quan ; ^ , . • u- ,- u .*- u^- L - U-^
. . •- i,r^ .,i ^v,.„-i • ' ! . - * • ' .u- - A-^- vay, phuang phap phan tich dan hoi bac nhat ha eiua lyc va chuyen vi a bat cu thai diem , ; , ^ ^ K ,. .. . ; , ,. '.
. ~ „ la. mAf A,^?^„ *u- r^- .V. 1. J ' khong xem xet su Iam vice dong that cua cac ndo cung la nigt duong thang. Cac thanh dan . . . , ' ,, .. l i , - • -
thanh. cung nhu sy lam viec dong thai cua ' Cong ty Tir Van Dien Mien Nam. Email: uyendangl [email protected]
- Trucmg EJai hpc Ma TP.HCM. Email, [email protected] -' Trirang 09' hpc Bach khoa TP.HCM. Email: nhc\[email protected]
KHOA HOC KV THUAT
toan bd he ket cdu dudi tae dung ciia tdi trgng.
Khi phdn tich khung ddn nau chi xet dan sy tdc dung cua nen (hay keo) dgc true thanh ma bd qua cac tac dung cua md men thi chua tha tha diln ta hat dugc su lam viec cua he ket cau khung dan. Khi six dung phuang phdp phdn tich tryc ti^p theo phuang phap phdn tich ndng cao cd thuan Igi ldn ciia phuang phap phan tich nay Id: (i) Phong doan dugc he sd chiau dai hiru hieu; (ii) cung cap ket qua ngi lyc todn bd ket cdu tai trang thai gidi ban sir dyng dugc chinh xac ban; (iii) Ap dung mgt each hgp ly va pbu hgp vdi tdt cd cac loai ket cdu khung phdng bao gom khung khdng giang, khung cd gidng va kliung ket hgp.
Theo phuang phap dam-cpt su dung ham dn dinh cd phuang trinh ham dan gidn nhung
dien ta tac ddng phi tuyen hinh hgc ctia phdn tu khi chiu lyc tac dung, md td dugc nhung ung XLT thyc te lam viee cita kat cdu, dac biet la cdc ket cau khung kbdng ddn. Sy dan gian trong phan tich, tdn it bd nhd mdy tinh nhung cho ra kat qua dang tin cay.
Bai bao nay tac gia str dung ham dn dinh trong phan tich phi tuyan hinh hgc kit hgp vdi phuang phdp khdp deo thd trong phdn tieh phi tuyan vdt lieu de dien td tac dgng phi tuyan cua khung dan thep phang khi chiu lyc tdc dung.
2. Co- Sff ly thuyet 2.1. Gid thuyet phdn tir
Xet phdn tu hiru han dam-cot phang dien binh nhu Hinh 1.
Hinh 1. a) Phan tir dam-cot dien hinh trong mat phang; b) Mo hinh vat lieu cua thep a,.
NhiJng gid thiat sau dugc SIJ dung trong viec thanh lap phan tu hiiu ban ddm-cdt:
(1) Phdn tCr ban ddu thang va cd tiat dien deu;
(2) Mat cat ngang trudc vd sau bian dang ludn phang va vudng gdc vdi tryc thanh;
(3) Khdng xet dan sy mdt dn djnb cue bg vd mdt dn dinh ngang;
(4) Khong cd tdi trgng ngang trong nhip cau kien;
(5) Mo hinh vdt lieu thep la dan-deo tuyet ddi.
2.2. Phdn tir dam-cot do sir tdc dpng cua PS
Be ke den tac dgng cua sy sai lech hinh hgc do tac dung cua lyc dgc true gdy ra. Theo W.F.Chen va E.M.Lui (P-E Austrell, O
Dablblom, J Lindemann va ede tac gia, 2006).
da dua ra dugc mdi quan he gi&a lyc va chuyln vi gia tang theo phuang trinh sau:
0 0
'',
s„
e
S.l
e.
(1)
Trong do, I,L,A, E la mo men quan tinh, chiSu dai phto hi, dien tich tiSt dien, mo dun dan h6i vat lieu; P , M ^ , M B l a luc doc true gia tang, mo men gia tang tai dau A va B;
e ,9^ ,83 la chuyln vi doc true gia tang, goe xoay gia tang tai hai d i u phin tit A va B; s„, s.jhay Sj, la ham 5n dinh eho phta tu dam-cot CO dang:
TAP CHl KHOA HOC TRJONG OAI HOC MOTP.HCM - S6 2 (41) 2015 105 fslpsm(,Tjp)-:r-pzmi!r4p) ^„ ,(,
2 - 2 cos(;r^) - 7i,[pim{n.[p)
"'Pmsht.njp) - Tljpsinhi^^) ^ ^ 2 - 2 cosh(ff 7F) + !T%lpsiab{!r,Jp)
(2)
7r-p-7r4p^H!^4p) , ^ , 0 2cos{jry[p) - ff.Jpsmiff.Jp)
ffyjpsinhiff-fp) - ff'p
(3)
2 - 2 cosh(.jr.^/^) + 7iJpsinh{ff.Jp) Vdi p
iJP>0 P
P: lyc dgc true cua phdn tir.
2.J. Phi tuyen vgt lieu do tdc ddng ciia ung sudt dir
Be dian td sy suy gidm do cung, gia tri md dun dan hoi E thay tha bang md dun tiap tuyen E, tbeo qud trinh lyc gia tdng. E, xdc dinh dya vao md dun dan hdi vdt lieu E theo phuang trinh:
E , - 1,0E khi P<0,5Py (4) p
= 4—Eil- P.
-)khiP>0,5P^, (5)
Vdi Py Id lyc chay deo ciia vat lieu thep.
2.4. Phi tuyen vgt lieu do sir hinh thdnh khdp deo
Ma trdn do ciing ciJa phdn tiJ phang suy bian til trang thdi dan hdi thuan tuy din trang thai chdy deo hoan toan dugc de xudt bdi Liew va cdng sy vao nam 1992 de xem xet qua trinh chay deo tai hai ddu cua phan tii' nhu sau:
AM, AM,
nj\s,-—0-iB) IAIB^:
Hi-ne)
(6)
\
A M A , A M B ia mo men tac dung gia tang tai hai dau phan tur A va B. A9A, AOB la goc xoay gia tang tai hai dau phan tir.
HA, HB la cac thong so vo huong eho phep mo phong qua ninh giam do cung piii dan hfii lien quan den su chay deo cua mat c5t ngang tai hai dau phan tu A va B.
n = 1: mat cjt ngang tai dSu miit dang xet van con dan hoi,
n = 0: mat cdt ngang tai dau miit dang xet da chay deo hoan toan,
0< n ^ 1 : mat cat ngang tai diiu miit dang xet dang trong qua trinh chay deo.
DS tinh toan su ehay deo mot phin, Liew et al (1992) da dua ra ba miic ehay deo hieu chinh nhu sau;
Khi 0,5<a<l ,0: ti=4a( I -a) ; (7) K h i a < 0 , 5 t h i r | = l ;
Khi 01=1 thi 11=0;
Ham chay deo cua mat cat ngang theo AISC-LRFD (2005) cho thep chu I hoae ehO H khi phan tu thanh dan chiu Iceo mat chay deo CO dang:
P SM, p a(,p,m,) = — + '- = lkhi—>0.2 ' P 9M„, P
P M„ p a(p,m,) = + — ^ = 1 W — < 0 . 2
^'^ -' 2P M,. P.
(8)
Mat chay deo trong mat phang cua Orbison:
a = U5p^+m^,+3,67 phnl (9) P M,
Voi p = — ; m_= —-—;
Trong do, Mpy la mo men cue han cua vat lieu thep.
Khi phin tii thanh dan chiu lue nen, thay
KHOA H O C KY T H U A T
Py = Per. Per thco tieu chuSn AISC-LRFD
(2005) dugc xac dinh theo eong thiie:
[:•]=[::][;]
(11)exp(-0.4!9/i;),4SI.5 0.877
,X>1.5 (10) 2.5. Chuyen doi he trtfC toa dp phan tur Ma tran chuyen doi he true toa do tu dia phuong sang he true tpa do tong the co dang nhu sau:
Hinh 2. Sa do khSi phan tich he
Trong do, c=cos(\j/). s=sin(i|/); voi y la goc hgp boi true toa do Oxy voi he true tga do Ox'y'.
2.6. Phirffng phdp gidi vd thu^t todn
Khca ddcur ket
tao ma tian ngtiep : i . K .
Tiyen K ,
3. Ket qua so
Tac gid khdo sat ba ket cdu khung dan thep phang da chting minh dugc tinh khd thi ciia phuang p h ^ so vdi nhimg phuang phdp phdn tich khde nhu sau: Bai toan cdt hai ddu khdp chiu tdi trpng tap trung, bdi toan khung dan thep phing ba thanh chiu tdi tap trung va bai toan khung giang thep phang chiu tai tap trung.
3.1. Bdi todn cpt hai ddu khdp chiu tdi trpng tap trung
Bdi todn cdt thep cd mdt ddu ngdm, mdt ddu khdp dugc cho nhu hinh 3. Cdc thdng sd ve vat lieu va hinh hgc dugc cho nhu sau:
Module ddn hdi vdt lieu thep £ = 200GPa;
U'ng sudt chay deo a^. = 250MPa; Tiat dien cdt W8x31;
Hinh 3. a) Scr do cot hai dau khdp cfaiu tai trong tap trung;
b) Bieu do quan he giira he so tai trong-tham s3 do manh cot hai dau khdp
I :
- ElUei
^ .
TAP CHI KHOA HOC TRUONG OAI HOC MO TP.HCM-SO 2 (41) 2015
Ban kinh quan tinh cdt ry = 51,2 (mm).
Theo ly thuylt Euler lyc tdi han cua cgt chiu nen dung tdm dugc tinb nhu sau:
xl
Voi A--
(12)
thong so do manh true yeu, K=l (cgt hai d i u khop).
Theo ket qua nghien ciiu ciia Hgi d i n g Nghien eiiu Cpt CRC, P „ eho cpt thep chii I, hai dau khop, dugc tinh theo cong thiic:
1-0,25/1',/l^.
<-J^
(13) Tir cong thiic va ket qua dat dugc, tac gia CO bang so sanh sau:
B a n g l L (mm)
0 3.500 7.000 10.500 14.000 17 500 2L000 24.500 28.000 31.500 35.000
So sanli iiet qua phan tich ciia CQt 1 p
(MV)
0 1.353 1.168 813 463 298 205 153 118 93 75
Tac P/Py
1,00 0,92 0,79 0,55 0.31 0,20 0,14 0,10 0,08 0,06 0,05
gli U
0,00 0,45 0,89 1,34 1,79 2,23 2,68 3,13 3,57 4,02 4,47
Euler
P/Py 1,00 0,92 0,79 0,55 0,31 0,20 0,14 0,10 0,08 0,06 0,05
Xc 1.04 1,12 1,35 1,78 2,22 2,68 3,10 3,54 3,99 4,43
ai dau CRC
P/Py 1.00 0,95 0,80 0,55 0,31 0,20 0,14 0,10 0,08 0.06 0,05
chop chiu tai tap trung LRFD
P/Py 1,00 0,95 0,80 0,55 0,31 0,20 0,14 0,10 0,08 0,06 0,05
ic 0,00 0,35 0,73 1,19 1,67 2,09 2,51 2,93 3,35 3,76 4,18
Ty If sai lech CRC
(%)
0.00 -3.17 -0.80 0,24 0,37 0,88 0.10 1.35 2.00 1,62 1,72 Nhdn xet:
Dya vdo Bang 1 va biau do so sdnh kat qua phdn tich cua tac gia vdi cac ket qud Euler, CRC va LRFD, tac gid nhdn thdy rdng ket qua phdn tich dat dugc Idia gan vdi dudng CRC vdi ty le sai lech Idn nhat Ja 3,17%, kha nhd.
Kat qud cua LRFD cd ke dan dp sai lech hinh hgc ban dau ndm dudi ket qua phdn tich cua tdc gia Id bgp ly.
Tae gia da nio phdng mdt phdn tir cho cdu kien cgt hai dau khdp chiu tdi trgng tdp trung tai ddu cdt co xet dan su thay d6i kich thudc chieu ddi cgt vd da cd ket qud kha tdt.
Ddy chinh id uu diem cua phuang phap ddm- cdt dung ham dn dmh de md phdng tac ddng phi tuyen hinh hgc.
3.2. Khung ddn thep phang ba thanh chiu tdi tap trung
Bai todn khung dan thep phang ba thanh chiu tdi tap trung dugc md td nhu Hinh 4. Cdc thdng so ve vdt lieu va hinh hgc dugc cho nhu sau: Module dan hoi vat lieu thep E = 200GPa
; U'ng suat chay deo a^ =250MPa; Sir dung tiat dien thep W14x82 cho tat cd cac thanh; ha sd poisson K ^ 0 , 3 ;
KHOA HOC K? THUAT
Hinh 4. Sff do cgt hai dau khdp chiu tai trong tap trung
Bdi toan nay dugc Seung-Eock Kim, Moon-Ho Park, Se-Hyu Choi (2001) da phdn tich sir dung phuang phap ndng lugng. Tdc gia sir dyng chuang trinh cua minh vd ddnh so
phdn tu cac thanh nhu trgn Hlnh 4. Ket qua phdn tich lyc tdc dung-chuyan vi dugc the hien nhu hinh sau:
Hinh 5. Quan he giua lure tac dung - chuyen vi diem A khi P hydng len
SfunE-EodcKin. Moos-Hu Pailt. Se-Hyu Qioi Arinj 1
—*— Seung-EtJckKuB, Moon-Ho Park Sf-Hyu Cboi Arlms 2 Ket qua tic gii
Hinh 6. Quan he giira lire tac diing - chuyen vi diam A khi P hvdng xuong
PfliW)
TAP CHl KHOA HOC TRUONG OAI HOC MO TP.HCM - S6 2 (41) 2016 Bang 2. So sanh tai trong giffi han P„ bai toan khung dan thep phSng ba thanh
Idii P hu-ffng xuong
STT
1 2 3
PhUtfng ph j p phan tfch
Phuang phap nSng lugng - Seung Eock Kim va cac cong s\r (2001) duong 1
Phuong phap nSng luong - Seung Eock Kim v^cdc cgng su (2001) duong2
Tac gia (2014)
P . (kN) 7097 7060 7350
Sai s6 (%)
3,43 3,93
Bang 3. So sanh tai trong gioi ban Pu bai toan khung dan thep phang ba thanh khi P hirdng len
STT
1
2 3
Phirong phap phan tich
Phuong phap nSng luong - Seung Eock Kim v^ cac cong su (2001) duong 1
Phuong phap n5ng luong - Seung Eock Kim va cac cong su (2001) d u o n g 2
Tac gia (2014)
P . (kN) 5768 4273 5810
Sai s6 (%)
2,12 2,64
Qua xem xet Hinh 5 vd Hinh 6 md ta mdi quail he giGa luc tac dung-chuyen vi tai dilm A khi P hudng ian vd khi P hudng xudng, tac gid nhdn thay rang tmg xir cua kat cau khi chiu tai tai diam A trong ca giai doan dan hdi vd giai doan chdy deo hoan toan triing khdp vdi kat qua phdn tich theo phuang phdp nang lugng cua Seung-Eock Kim khi lyc P hudng xudng vdi sai sd ve tai tdi han la 3,43%
va 3,93%; vd khi luc P hudng len thi sai sd vk luc tdi ban giiia kat qua tac gid vdi.ket qua phdn tich theo phuang phap ridng lugng cua
Seung-Eock Kim Id 2,12% va 2,64%.
3.3. Khung gidng thep phiing chiu tdi tdp trung
Bdi toan khung giang thep phang ed lian kat hai ddu khdp cd dinh d gdi tua va chiu tai tap trung ngang tai nut duge md ta nhu Hinh 4.
Cdc thdng sd ve vat lieu vd hinh hgc dugc cho nhu sau: Module ddn hdi vat Heu thep E = lOOGPa ; U'ng suat chay deo a^. = ISOAdPa;
Sir dung tilt dien thep W14x82 cho tat cd cdc thanh; he sd poisson v = 0,3;
Hinh 7. a) Sff d6 khung gidng thep phang;
b) Quan he giua lire tac dung - chuyen vi diem A.
(ij A P (0 ' (5) i2)
2,54m ^ p
no
KHOA HOC KYTHUATBdi toan nay duge Seung-Eock Kim, Moon-Ho Park, Se-Hyu Cboi (2001) da phdn tich su dung phuang phap nang lugng. Tac gia sir dung chuang trinh cua minh va danh sd
phdn tir cdc thanh nhu tran Hinh 7. Ket qua phdn tich Iuc tac dung tdi ban cua tac gia so vdi Seung Eock Kim nhu sau:
Bang 4. So sanh tai trong gidi han P^ bai toan khung giang thep phdng
STT 1 2
Phirong phap phan tich
Phuong phap nang luong - Seung Eock Kim va cac cpng su (2001) Tac gia (2014)
P . (kN) 6078 6160
Sai so (%) 1,34
Nhdn xet:
Qua xem xet Hinh 4 md ta mdi quan he giua lyc tdc dung-chuyan vi, tac gia nhdn thdy rang iing xu ciia ket cdu khi chiu tai tai diem A trong cd giai do?n dan hoi va giai doan chay deo hoan todn triing khdp vdi ket qud phdn tich theo phuang phdp ndng lugng ciia Seung- Eock Kim vdi sai sd ve tdi tdi ban Id 1,34%.
4. Ket luan
Tir cac ket qud cua bai bdo, cac kat ludn dugc the hien nhu sau:
Sir dung phuang phap phan tich ndng cao da phdn tich dugc nhirng img xu ciia he ket cdu khung ddn khi cd luc tac dung md khdng cdn phai sir dung be sd uon dgc vd ke den sy khdng tudng minh thdng qua viec kilm tra do mdnh. tai tdi han Euler cho timg trudng hgp thanh. Va tdt cd nhixng viec kiem tra nay da dugc ke den trong phuang phdp phdn tich nang cao sir dyng phuang phap ddm-cdt, va day cijng la diem thuan lgi Idn nhdt cho ngudi
thiet ke, da cd the nhin thay dugc kha ndng chiu tai cyc ban ciing nhu chuyen vi ciia toan bd he khi kat eau dat dan tai tdi ban-
Sit dung phuang phdp ddm-cdt da diln ta tdc ddng phi tuyen hinh hoc cho kat qua gdn gidng vdi nhiing phuang phap phdn tich phi tuyen khde. Nhung viec sir dyng phuong phdp ddm-cdt giup cho viec chia nhd sd phdn tir it hem, it tdn bd nhd phan tieh, giam thiau dugc thdi gian phdn tich bdi toan.
Doi vdi bai toan cgt, ket qud sir dung phuang phdp cua tac gid so vdi phuang phap ASD va AISC-LRFD sai khde khd nhd. Vi vdy, khi sir dung phuang phdp ddm-cdt dimg hdm dn dinh ciia tdc gid cd the chdp nhdn dugc.
Sir dung phuang ddm-cdt dung ham dn dinli da phdn tich dugc nhiing ung xix cua he va xdc dinh dugc tai tdi han ciia toan bd he kat cdu khi chiu lyc tac dung gia tang. Va ddy ciing Id diem (quan trgng) ndi bac ciia phuang phdp nay.
TAI LIEU THAM KHAO
Chu Qudc Thdng. (1997). Phuang phap phdn tu hiju han. Nha xudt bdn Khoa hgc va Dai hgc Ky thuat.
W.F. Chen, E.M. Lui. (1987). Structural Stability - Theory and Implementation, Elsevier.
P-E Austrell, 0 Dahlblom, J Lindemann va cac tac gia. (2006). Calfem - A finite Element Toolbox (version 3.4). The Division of Structural Mechanics.
Cuong Ngo-Huu, Seung-Eock Kim. Jung-Ryul Oh. (2006). Nonlinear analysis of space steel frames using fiber plastic hinge concept. ScienceDirect.
TAP CHi KHOA HOC TRITONS OAI HOC MOTP.HCM - S 6 2 (41) 2015 111 McGuire and H.Gallagher, D. Ziemian. (2000). Matrix Structural Analysis. John Wiley & Sons,
Inc.
^eung-Eock Kim, Moon-Ho Park, Se-Hyu Choi. Direct design of three-dimensional drames using prctical advanced analysis. Journal of Constructional Steel Research 57 (2001) 907-923.
Cho Suk Han. (2006). Second-order analysis and desin of Angle Trusses and Frames. Thesis.
P-E Austrell, O Dahlblom, J Lindemann va cac tac gia. (2006). Calfem - A finite Element Toolbox (version 3.4). The Division of Structural Mechanics.