SOrdung phiftAig phap ma tran chuyen cai tien trong phan tich ket cau dam lien tuc
Using modified transfer metliod to analyse straight continuousbeam
Le Dung Bao Trung
Tom tat
Bai bao trinh bay phifdng phap ma tran thuyen cai tten (PP MTCCT) phan tich noi lire, chuyen vjhe ket cau dang dam lien tuc. Ket qua nghien cilTu du'dc kiem chutig qua vi du t i n h tay bang phuang phap phan tilr hiilu han(PTHH) va chay may vdi phan mem SAP 2000.
Ji(kh6a:Phan t&ddm thong lien tuc, Phuang phdp ma trdn chuyen cdi tien
Abstract
This paper presents IVlodified Transfer (i^elhod in analysis internal force anddisplacement of straight continuous beam. Results are verifieci with SAP2000 programe.
Key words: Straight continuous beamekmentModified Transfer Method
THS. LeDungBdo Trung B6 mon Ket cdu Thep Gd, Khoa Xdy dUng Email: [email protected]
Ngiy nhan bar 02/5/2019 Ngay siia bai-23/5/2019 Ngay duy?t dang: 8/01/2020
1. Gidi thieu
Trong cae lai lieu[3]. [4], [5j. [6], [8] va [9] tac gia da trinh bay phuang phap ma Iran ehuyen cai tiln phan tich thanh eong phang hinh trdn, thanh eong xoln 6c 3D hinh trdn, thanh cong phing hinh elip chju tai trgng long quat, g i i lua dan hdi bd Iri tai vi tri bit ki Bai bao nay trinh bay phuang phap ma trgn ehuyin cai liln phan tieh ndi luc, chuyin vi he thanli thang dang dim lien luc, ehju udn trong mat phang tai trgng.
K i t qua nghien cuu ung dung Irong linh loan cae he k l l elu nhu dim hen tuc dd elu true, cong true trong cac nha cdng nghiep. nha may ddng tau; c l u vugt trong cdng trinh giao thdng; d i m doc, d i m phu nhilu nhip trong kit c l u khung dan dyng,.v.v 2. T h i l t lap ma tran dg cdng cua phan t d dam thang iis p h l n ti> thanh cong Phuang phap ma Iran chuyin long quat xetphin tu thanh eong m cd hai dlu mut la 1 va 2.Quy udc dng iyc va ehuyin vj nut la duang khi ciing chiiu vdi he tga do (HTD). Ki hieu {P}, {M}, {U}, {0} la cae vee ta ung luc, mdmen, chuyin vj thing va xoay tai nut. Vee la ung lue va chuyin vj nut tong quat cd dgng {^i}={Pi M i } \ {'?l^}={Ui Oi}"^, {5^2}={P2 Ms^, {'^}={U2 Oa}^ mdi vee ta nay ed 6 tlianh phln dng luc hoae ehuyin v!. Bieu thde ca ban eda phuang phap ma tran ehuyen giua hai dau 1 va 2 cua phln tir thanh m, [1], nhu sau:
i;i- [4i] [-4']"j[^]^4^r'
(1) Trong dd [^2^], [Az']' 1>^1 va [ ^ ] , kich thudc 6x6, la cac ma Iran dac trung cua m. Bliu thuc (1) la he phuang trinh dai s l tuyln tinh cd an sd la cae chuyen vi nlm d ca hai v l eda phuang trinh. cai lien Bieu thuc (1) dua an sd ve cung mgt v l , ta cd:
'12 '11 '12
"T22T12T11 hi'ii.
1^21 ^22]
-^Mm
(2) Biiu thuc (2) la bilu thuc tong quat ciia phuang phap ma Iran ehuyin cai tiln, ed dang luang ty bilu thire cda phuang phap PTHH. Irong dd [W^U la ma trgn do cung trong he loa do ehung eda phln tu m thill Igp tu phuang phap ma Iran chuyin.
Ngi dung ehi tiit phuang phap ma tran ehuyin cai tiin trinh bay trong [4], Phln tu dam la irudng hgp dge biet eua phln Id cong, khi ehiu udn phing tgi m i l dlu phln tu ung luc ndt ehi gdm hai thanh phln luc P^ va momen My, tuang dng ehuyin vj thang U^ va xoay uiy He toa dp cd true x = x', y ^ y' va z E Z', chiiu duang ciia dng Iyc nut (va ehuyin vj ndt) quy ude nhu Hinh 1.
Do chi edn hai thanh phln ung Iyc va ehuyin vj niit nen trong cac ma trgn dac trung ta ehi gid Igi eae hang va edt luang dng vdi cac thanh phln nay.
Cac ma Iran dae trung hinh hoc long quat (dugc thiit lap trong [1], biln dii sang PP MTCCT trong [4]), ap dyng vao trudng hgp thanh thing linh duge nhu sau:
: :i-Hr
0 1 1 0,[.41 11
23
KHOA HOC & CONG NGHE
VIvl O
4 —
\Iv2
'CD
?i2
—k
A
( d l , d > ) ( d 5 , d . | ) ((!•, dn) X
A H l i EJC
Hinh 1. Quy i/dc dau u'ng lu'c Hinh 2. Sd do t l n h va ki hieu chuyen vj tai cac dau phan t t f nut phan t u ' thanh dam
Do he tga 66 rieng cung chieu va song song vol he tga dp Chung nen ta xac djnh tiep cac thanh ph§n cua ma Iran bi§n doi tga do nhu sau.
vd[ff„] = [ffJ = [cOSy>] = [/]
Khi khdng k l d i n biln dang trugt, ma tran dp eung t i l l dien ed dang:
[M,] = [0];[M„] =
12 1'
6
6 "
1^
2
Cac ma tran thanh phan ciia ma tran [^ dugc tinh nhu
[.A] = [ff„][M,][//,r=[0];
Q = [H,][M,][H,f =
4,]M =
•Q + [Af
X
ytu
1 EI^.
; M'K.] = ]M =
EI X•
X
1 [ « ] « - - ^ j
[?;.]=[.< T'1M*WI
X '
1
ds = EI^\fi
3 I' _2'"1 2
1 ri -n
•/,Lo iJ
[''
3 1-
L2
'"1
2
/ ;l
Va tinh dugc cac ma tran thanh phan cua ma tran do ci>ng:
" 12 6 "
[K,MT„T[TuhEI,
I' t6_ 4_
"/' /
12 (T I' I' 6_ 2 I' I
[K„h-[T„] + [Tn][T„r[T„] = E,,
12 6
6"
2
"12
6
L/-
6 '
4
_ Ghep cac ma trgn khoi ta duac ma tran dp cung eda
/ J
phln tu thanh thing trong he tga dd chung:
2 4 TAP CHi KHOA HOC K l i N TRUC - XAY DUnO
Bang 1. Ket qua pt
Joint
A B C
U1 (UJ m 0 0 0
an tich chuyen vj nijt.
U2 (U,) m 0 0 0
U3 (U,) m 0 -0.00053
0
SAP2000, (m R1 (U),) Radians
0 0 0
-rad) R2 (Ul,) Radians 0 0.000107
0
R3 ( u j j Radians 0 0 0 Bang 2. Ket qua phan tich li'ng IUc nut, SAP2000, (kN-tn)
Frame (thanh) 1
2 Jgint (nut) A B B C
F1 (PJ KN
0 0 0 0
F2 (P,) KN
0 0 0 0
F3 (PJ KN 6.4604 -6 4604 -3.5396 3 5396
Ml (MJ KN-m
0 0 0 0
M2 (My) KN-m -7.1510 -5.7698 5.7698 4 8490
M3 (M J KN-m 0 0 0 0 Bang 3. So sanh u'ng IUc nut tinh dUdc theo cac phu'dng phap
Thanh
1
2
Nut
A B B C
PP IVITCMR P;
6.4795 -6.4795 -3.5195 3.5195
IVI, -7.1990 -5.7599 5.7598 4.8001
PP PTHH
P j
6.4795 -6.4795 -3.5202 3.5202
M, 7.1996 5.7593 -5.7604 -4.8002
SAP2000 P,(F3) 6 4604 -6 4604 -3.5396 3.5396
M, (M2) -7.1510 -5.7698 5.7698 4 8490
/'
6 12 6 1-
f
4 6 2/ /'
6 12 fi 6
1 2 6 4
/
Ldi giai
Rdi rac hda va ki hieu phln td thanh nhu Hinh 2, he tpa do va ehilu duang cua ehuyin vj, ung lue nut thing nhlt nhu l\^ue 2. Phln tu dim ch!u udn phang tai mdi nut cd hai bac l u do tuang dng hai chuyen vj thang va xoay. Vec la chuyin vi niit trong he tpa dp chung {dJ cd dang;
(3) Ma tran nay ed dang tuang ty mg Iran dp cung phln Id dim chiu uin phdng trong phuang phap PTHH, [7], nhung cd mdl sd sd hang trai dlu do hat phuang phap khdng cung quy ude dlu.
Ap dung cae budc giai tuang tu phuang phap PTHH Ihu dugc kit qua phan tich.
3. Vf du kilm chu'ng 3.1. Vidu1
Sd dyng phuang phap ma Iran chuyin md rdng tim chuyin vj thing va gdc xoay lai eae diem A, B va C cua thanh tren Hinh 2, cae so lieu tinh loan nhu sau
Lue tgp trung tgi B: P = -10.0 (kN) Vat lieu thep, E = 2.1e+08(kN/m^).
Chilu dai 1, = 2,0 (m); I2 = 3.0 (m). Till di$n thep I to hap 300x120x10x6(mm).
Su dung Bilu thuc 3 tinh dugc ma Iran do edng eda hai phln tu la:
[*J,=
19359 -19359 -19359 -19359 25812 19359 -19359 19359 19359 -19359 12906 19359
-19359 12906 19359 25812 ' 5737 -8607 -5737 -8607"
-8607 17214 8607 8607 -5737 8607 5737 -8607 -8607 8607 -8607 17214_
Lip gtiep hai ma tran thanh ma tran do cCfng tong the,
S O 3 7 - 2020
25
m KHOA HOC & CONG NGHE
xd ly dieu kien bien cd cac thanh phln chuyin vi tgi nOl A va C deu bang khdng. thiit lap vdc ta lai trgng nut, lap va giai phuang trinh can blng thu dugc vec la ehuyin vi nut:
Tien hanh cac budc giai bai toan tim ndi luc.
theo phuang phap PTHH thu dugc:
Vec to chuyen v
{d, rf4'=1.0.-0.003*1-0.4462 O.lUsf ^ rf,}^ =1.0.'-0.003.{-0.4463 - . 1 1 1 6 ^
va cac vee ta dng lue nut trong he toa dd neng:
P h l n t u i , kN-m:
{^}i ={6.4795 -7.1990 -6.4795 -5.7599}'"
P h l n l u 2 , kN-m'
{^}^ ={-3.5195 5.7598 3.5195 4.8001}''
va vec ta dng Iyc ndt trong he tga dg rieng- Phan l u 1 , kN-m-
{^}, ={6.4795 7.1996 -6,4795 5.7593}'"
Phln td 2, kN-m:
{,3?}^ ={-3.5202 -5.7604 3.5202 -4.800:
Su dung phuang phap PTHH de giai he thanh trong Vi d u i .
Ldi giai
Sa do tinh nhu Hinh 2, Ma tran dd cdng va quy uac dlu eda phln td thanh dim nhu trong tai lieu [7]. Thye hien cae phep tinh ta thu duac:
[^.V
[Kl
19359 19359 -19359 19359 25812 -19359 -19359 -19359 19359 19359 12906 -19359
19359 12906 -19359 25812 5736 8604 -5736 8604 8604 17208 -8604 8604 -5736 -8604 5736 -8604
8604 8604 -8604 17208
Su dung phln m l m SAP 2000 dl giai he thanh trong Vi dy 1.
Ldi giai
Xay dung mo hinh tinh trong phln mlm SAP (vdi dly dii cac dac trung vat lieu, lilt dien, tai trgng, hen kit) d i phan lich la thu duac kit qua nhu Bang 1,2,3.
Nhu vay kit qua tinh toan giua cae phuang phap lech nhau khdng qua 1%.
4. Ket luan va k i l n nghj
Bai bao trinh bay phuang phap ma trgn chuyin cai tiln phan tieh k i t c l u thanh dim thing, lien tuc, chiu udn trong mat phang tai trong. Day la phuang phap tinh loan tin cay, la edng eu huu ieh gidp tinh loan thiet k l , kilm chung, nghien cdu dang kit c l u nay, cung nhu la ca sd cho cac phan tich nang cao./.
T a i l i d u t h a m k h a o
1. Nguyin'Vrdm, Lj) thuyit tinh todn tSng thi khong gian kit cdu nhip cau, Ludn dn Tim si Khoa hgcMaxcCva, LienXo, 1982.
2. Bqng QuSc LUdng, Phuongphap tinh trong ky thu^t,NXB Khoa hoc vdKy thudt, mn0i, 2001.
3. Xdy difng ma trdn chuyen cda phdn td thanh cong blending trong mat phdng tdi trgng cd xet momen xodn. Tap chi xay di/ng, B6 Xdy Di/ng so thdng 2/2009.
4 Le Diing Bdo Trung Nguyin Hong Sdn, Phiidng phdp mdi phdn tich thanh congphdngliin tuc chiu tdi trong khdnggian.Tuyen tgp cong trinh hgi nghi khoa hgc todn qu6c Ctf hoc vd V^t ran bign dang lan thii XII, Dgi hoc Duy Tan, TPDd Ndng 145S-1465.2015.
s. Li DUng Bdo Trung Phuongphdp mdi phdn tkh tuyen tlnh chuyin vi, ndi lite vdm trdn liin tuc chiu tdi trong khdnggian, Tgp dti khoa hoc Kiin trdc vd Xdy dung TrUdng dai hgc kiin trdc Hd Ndi, 7/2016.
6. Phdn tkh kit cdu vdm Ebps liin tuc chiu tdi trong tdng qudt bang phuang phdp ma trgn chuyin cdi tiin. Tgp chl khoa hgc KiSn trdc va Xdydi/ng Trudngdqi hoc kiin trdc HdNdi, 12/2016.
7. Phgm V&n Bat, Tinh todn kit cdu hi thanh theo phifdng phdp phdn tHhUuhgn, Nhd xudt bdn Xdy DUng Hd ngi, 2017 a. PhAn tkh thanh cong ghinh hinh trin tdi trong tdng qudt, goi tUa
ddn hoi, H8i nghi cd hoc todn quic ldn thiiX, Hoc viin kf thudt qudn su. 12/2017.
9 sa dung phUdng phdp ma tr^n chuyen cdi tUn diphdn tich ihanh cong ehp cd gdi tUa ddn hSi chiu tdi trgng long qudt. Tap chi idioa hoc Kiin trdc vd Xdy dung TrUdng dai hoc kiSn true Hd Noi, 62-66.
2017.
26
TAP CHl KHOA HOC K I ^ N T R U C - X A Y DITNG