Anh hu'O'ng cua khoi lu'O'ng nen len iFng XLP dong cua dam ch|u tai trong di dong
Ngay nhan bai: 20/7/2014 Ngay su^ bai: 5/8/2014 Ngay chap nhan dang: 10/8/2014
Pham Dinh Trung, Nguyen Thanh Do, Nguyen Trong Phu'dc
T O M TAT:
Anh hitdng cua kh6i luong n^n \in i3ng xii dpng cua dam chiu tai trong di dpng ddoc trinh bay trong bii bao nay. Do cdng nln dUOc m6 ta bang cac 16 xo dan hoi tuyen tinh di^a tren mo hinh nen dan hoi Winlder va khoi luong nen tham gia dao dong ty le v6i bign d^ng cua 16 xo va mot thong s6 khong thil nguyen duoc sif dung de mo ta miic do anh hifdng cia khoi lifcfng nln. PhilOng trinh chuyen dong ciia he diloc thiet lap di(a tren nguyen ly cin bang dpng va co sd ciia phifong phap phan tii hiiu han, va giai bang phifOng phap tich phSn so tren toan mien th6i gian. Anh hudng cua thong so do cilng, khoi lupng nen tham gia dao dpng va van toe chuyen dong cua tai trpng len iing xii dpng cua dam dUpc khao sat.
TH khoa; Nen dan h6i Winkler, LUc di d^ng, Khoi lUpng nen, Phan tich dpng lUc hgc cfia dam.
ABSTRACT
The influence of foundation mass on dynamic response of beam subjected to amoving load is studied in this paper. The foundation is modelled by hnear elastic springs based on Winkler model and the foundation mass is direcdy proportional with deformation of the springs and parameter dimensionless is used to describle effect of the foundation mass. The equation of motion is derived by principle of dynamic balance and finite element method, and solved by numerical integration method in the time domain. The influence of parameters such as stiffness of foundation, foundation mass and velocity of moving load on dynamis response of the beam are discussed
Keywords: Winkler elastic foundation. Moving load. Foundation mass. Dynamic analysis of beam.
Pham Dinh Trung
To Ket cau, Khoa Xay dUng, TrUdng DH Quang Trui^ Binh Dinh Email: [email protected]
Nguyin Thanh Do
TrUdng Sy Quan C6ng Binh, Thu Dau Mot, Binh DUOng Email: [email protected] Nguyen Trpng PhUorc
Bp mon Siic Ben Ket C5u, Khoa Ky Thuat Xay DUng, Trifdng Dgi Hoc Each Khoa - Dai Hpe Quoc Gia TP.HCM Email: [email protected],vn
1. Gidi thieu
Mot trong nhClng mo hinh nen diTcrc gicSI thieu tif rat sdm va da dUoc ap ciung rat nhieu trong cac mo hinh phan tich ting xCr cCia ckc dang ket cku tuang tac v6i nen chfnh la mo hinh nen Winkler. Trong mo hinh nay, docClng cua nen dUoc mo tk bSng dc 16 xo dan hfii tuyen tinh tuang tac hoan toan v6i ket cSu va ap IL/C len nen ty le thuan v6i bien dang cCia 16 xo [1-6]. Ngoai m5 hinh nen Winkler truyen thong, mot sd mo hinh nen khac cung da dUOc de xuat de mo ta gan diing hon v6i Clng xCr that cua ket cau tUong tac v6i nen nhU nen hai thong so, nen ba thong so, nen dan nhdt, nen bien thien hoac mo hinh tuong tac khong lien tucgiCfa ket cau vdi nen... [7-11].
Trong hau het cac mo hinh nen da va dang duoc u'ng dung trong cac nghien cilu trUdc dSy thi deu bo qua anh hUdng cCia khoi luong nen trang qua trinh phan tich Cmg xCrdong luc hoc cua ket cau tuong tac vdi nen. Nhung bein chat that cua dat nen la co khoi luqng, vi vay khoi luong cisa nen dat se co sU anh hudng nhat dinh den u'ng xCr cua ket cau, dac biet la trong bai toan phan tich Cmg xCr dpng cua ket cau tren nen chiu tai trpng dpng. Do do, van de phan tich anh hudng cua khoi luong nen len iJTng xCr dong cua ket cau co tUong t^c vdi nen la can thiet va dang duoc quan tam. NhUng trong hau het cac nghien cuU thi chua that sU chiit trong den dieij nay va vi vay co rat it cac cong trinh dupe cong bo trong nhu'ng nan gan day. 0 6 vk Khdng [12] da phan tfch cinh hudng cua khdi luong nen ddi vdi tan sd dao dpng rieng cOa tam tren nen dan hoi, ket quk thUc nghiem cCia nghien cuU nay cho thay khoi luong nen tham gia dao dong la co anh hudng dang ke den dac trUng ddng hoc cCia tam va ty le vdi chieu day cua Idp nen ben dudi nhung cung chi tang d^n mpt gidi han nhat dinh.
Dua tren su tim hieu va tiep ndi sU quan tam den anh hudng cua khoi lupng nen len u'ng xCr cCia ket cau, bai bao nay phan tich knh hudng cua khdi luong nen len dng xCr dong cua dam chiu tai trong di dong vdi van tdc
khong ddi. D o cCmg nen dupc mo ta bang cac 16 xo dtin hoi tuyen tinh dUa tr^n mo hinh nen dan hoi Winkler. Khoi lUong nen tham gia dao ddng t;J' le vdi bien dang cCia 16 xo va mot thong sd khong t h i i nguyen dUpc sCr dung de mo tei mCic dp knh hudng ciia khdi luong nen. Diem kheic biet trong bk'i bao nay la' (i) anh hUdng cOa khdi luong nen trong qua trinh dao dong dUCJc xem xet nhU 1^ sU ^nh hudng cCia ngoai lUC do khdi iuong nen gay ra; (ii) thdng sd khdng thCr nguyen ke den anh hUdng cua khdi luong nen tham gia dao dong dac trUng cho dp nhay cCia dat nen cung dupc de xuat, Phuong trinh chuydn ddng cua he duoc thiet lap dua tren nguydn \'i can bkng dong va cP sd cua phuong ph^p phan tCr hitu han. Phuong trinh chuyen dpng tdng the cua he duoc gi^i bang phudng phcip tich phan sd Newmark [13] tren toan mien thdi gian va mdt chuong trinh may tinh dUOC viet bSng ngon ngu' lap trinh IVIATLAB de phan tich knh hudng cua thdng sd len ijtig xCr ddng cCia dam.
2. Ctfsofly thuyet 2 . 1 . Mo hinh ket cau
Xet ket cau dam Euler-Bernoulli cd chi4u dai L, hi rong b, chieu cao h, md dun dan hoi E, m^t dd khdi p dat tren nen dan hdi cd do cdng k^
m | t d d k h d i p , v & c h j u tai trong di ddng vdi van tdc \k h3ng sd v, the hien tren Hinh 1. Mo hinh nen duoc md tk bSng cac 16 xo cd khdi lUpng phan b d dpc theo chi^u dai dam va do ciJng 16 xo \k dan hoi tuyen t i n h dac trUng cho do cdng n4ndUatren mo hinh nen Winkler.
L ' J 4
Hinh 1: Mo hinh dam tren nen dan hoi Mpt thdng s6 khong thCr nguyen c6a d6 ciJng K^ [6] va \Sf sd mat dp khdi M cCia nen va dcSm duoc djnh nghTa n h u sau
k,bL' -£L
2.2. Ma tran phan Xii dam va vecttf t&i 2.2.1 Ma trdn d^ cCfng vd khoi luang cua phan tUddm
Cac ma tran do cdng va ma tran khdi lupng cua phan tCr dam Euler-Bernoulli hai nut, moi nut CO hai bac t u do, gdm m6t thanh phan chuydn vi thang vu6ng goc vdi true dam va mot theinh phan gdc xoay (Hinh 2) dupc trinh bay k h i nhieu va chi tiet trong cac ly thuyet phan tCr huu h^n [14], the hien n h u sau.
'12 61 -12 61 61 41' -61 21' -12 -61 12 -^1
61 21' -61 41'
m-'i
(3)131 156 -31' -221
A;:f
Hinh 2: Mo hinh phan t i l dSm tren nen flan hoi 2.2.2.Vecta tai phan til 2.22.1 Vectataiphdn tiilucdidong 0\k sis rang trong sudt qua trinh tk\ trong di chuyen tren dam cd m bUdc thdi gian va gia tri cua moi bUdc thdi gian la At, khi nay khoang thdi gian ma tai trpng di chuyen het chieu dai dam la T = m.At. Tai thdi diem I. vi tri lUc la x^
= v.t va toa dp cua nOt trai cua phan tCr trong h6 true tpa do tong the cung dUoc xae djnh x^
= lnt(xyi}.l. Tir do, t h d tU phan tCr i va niit phan tCr I vdi 1+1 tai t h d i ^ e m t iing vdi vi tri lUc kich thich duoc xae dinh i = lnt(xyi)+l. Khi nay, tpa dp t trong he tuc tpa dp dia phuong eCia phan tCr cung duoc xae dmh E, = x^-i.l Vi vay, veeto tai phan tCrdo thanh ph^n luc kich thich gay ra theo t h d i gian cung dUpc xae djnh thong qua ma tran ham dang [N], dupe the hien nhU sau
{ F : } = [ N ] ' F ( t ) (5) trong do, [N] la ma tran ham dang phu
thuoc vko toa do dia phuong ^ va dUoc trinh bay kha ehi tiet trong cac tai lieu ve phuong phap phan tCrhOu han [14].
2 2.2.2 Vec tatai phan tif do phan lUc nin DUa tren ly thuyet phan tCr hCfu han, chuyen vj Ui(^) va gia tdc ddng ^.(s) tai mdt vi trf bat ky tren phan tCr t h d i dUpc xae djnh tCl vecto ehuyen vi va gia toe eua nut tuong isng dupc the hien nhusau
H ( a = [ N ] ' K } . H ( 0 - [ N ] ' f c } ,6) Vdi gia thiet giu'a dam va nen khdng c6 hien tuong mat tuong tac trong sudt qua trinh dao dong va khoi lupng nen tham gia dao ddng t y le vdi bien dang 16 xo, khi nay khdi lUpng nen don vi tham gia dao ddng duac md ta n h u sau (Hinh 3)
m „ { ^ ) = K p , b H ( ^ ) 4 ( 4 ) (7) trong do K > 0 la thdng so khdng t h d nguyen ke den anh hUdng cua khdi luong nen tham gia dao dpng ma no dac trung cho d p nhay cua nen, H(0 = 1 neu u (Q > 0 va HIQ = - 1 n ^ u u ( 0 < 0 .
U ( ^ ) = ' ^ i , f ( ^ ) 4 ( 0 (8) Bang 1^ thuyet phuong phap phan tCr hiJu
han, vectcj tai cua phan tCr dSm do anh hUdng cCia khdi \u<3ng nen tUcJng tac vdi dam trong timg bude ttidi gian cung duoc xae d m h nhU sau
{ F , ' " } = | [ N ] X ( ^ ) d 4 (9) 2.3. PhUoing tr'inh chuydn ddng cCia h^
D6ng ky thuat ket ndi cac chi so bac t u do tuong ling cCia cac ma tran va vecto tcii cua phan tCrdam tren nen dan hoi chiu tai trpng di ddng trong he toa do tong the trong tiSng budc thdi gian, p h u o n g trinh chuyen ddng khdng cein tdng quat cCia he ket c^u dUoc bieu dien nhUsau
[ M ] { z } + [ K ] { Z } = { P ( t ) } ,,Qj trong dd [M], [K] va {P{t)} ISn luot la matron khdi lupng, d p ciing, va vec tP tai tdng t h i c6a ck he trong tCmg budc t h d i gian. PhUdng trinh chuyen dong sau khi thiet lap dupc gidi bSng phuong phap tfch phan sd Newmark tren t o i n mien t h d i gian di,fa t r ^ n chuong trinh m^y tinh dupe Viet bang ngon ngCi lap trinh MATLAB.
S . C a c v i d u s o
3.1 Kiem chuTng chUcmg trinh tinh Trong vi d u sd kiem chdng dau t i ^ n , bk\ bao kh^osatchuyen vl ddng cua dam don g i i n tr4n nen dan hdi Winkler va chiu tcii trong di ddng vdi van tdc h i n g sd. Ket qua ^huyen vj dong theo thdi gian tai vi t r i giCfa diirn dUde k h i o sat vk so sanh vdi ket qua cCia IMguyen va Le [6], the hien tren Hinh 4.
TCf eae ket qua khao s5t so k i l m chdng tren cho thay ket qua sd t r o n g bai bao la tUong ddi CO dp ehinh xae so vdi cac ket qua eua [6] dUOC neu trong t^i lieu trich dan. Td do cho thay chuong trinh may t i n h da viet bang ngdn ngii lap trinh MATLAB la cd d p tin cay nhat dinh va lam CO sd de tiep tuc phan tich anh hudng cua khdi luong nen len u'ng xCf ddng ciia dam chiu t i l trpng di dong.
Hinh 3. Phan to khoi lifting nen
Do do, luc tuong tac don vj giOa phan t d d a m vdi nen trong tCftig budc thdi gian do i n h hudng cua khoi luong nen duoc xae dinh n h u sau
Ty I? t/x
Kmh 4: Qiuyen vl dong chuan hda theo thiH gian tai giiia dam
3.2 K^t quS k h i o sat s6
Trong phan k h i o sat sd n^y, bai bao k h i o sat u'ng x d d p n g eua dam d o n g i i n tren nen dan hoi cd cac dac trutig hinh hoc va vat lieu nhU sau: chieu dat L = 2 m , be rdng b = 0.1m, c h i l u cao h = 0.02m, md d u n dan hdi E = 206x10' N/
8 4 | B i n n i I [ i B l 09.2014
" ~^~\ -^ Ko=5 I - I -i^Ko=50 I- -
-^-i-mftZ^^'ft*'
< 0,5
1
, • Ko=l ---- Ko-5
* f l ° " I ' ^ ' ^ a
Hinh 5; Chuyen vi dong tai vj t r i giQa dam, v = lOm/s (a) n = 0.5, K = 1.5, (b) n = 0 5, K = 1.5, (i = 0 25
0 0.2 H=0 25 - n=Q5
^ H=0 75
0 4 0 6 Ty IS l/T
0 8
1 °
S 0.5
0 0 2 0 4
Hinh6.Chuydn v\dong chu^n h 6 a t a i v t t r i g i i J a d a m K „ ^ 20,v = lOm/s (a) K = 1, ( b ) K = 1 5
Hinh 7 Chuyen vi dong chua'n hoa lai vi t r i giu'a dam K, = 25, v = lOm/s: (a) K = 0 5, (b) K = 0.7S
Hinh 8: Anh hi/iing thong s5 dp Cling ciia nen len he so dong DMF, t i = 0 5,K = 1,5:(a)bj = 1 , f b ) K j = 5
a--. 1 - OS -^ !M
^ " " " ^ 9 ^ 0
Hinh9.AnhhifSngt#s6matdokhoicuanenlenhgsoa6ngDIWF, Kj=5,K = 1.2,(a)|i=O.25,(b]|j = 0.75
m^ mat do khot p = 7860 k g / m ' chiu tai trpng di ddng F = I k N . Bai bao k h i o sat anh hUdng cCia cac thdng so len iSng xis ddng cua dam cd xet den anh hUdng eua khdi lUOng nen tham gia dao ddng (IM-lnfluence of foundation mass) va ket qua dupc so sanh vdi Idi giai truyen t h d n g bd qua anh hUdng cua khdi luong nen (OS- Ordinary Solution).
Trong khao sat sd d^u tien, bai bao k h i o sat anh hudng eua do cCmg nen len Clng xCr dpng cCia dam. Ket qua ehuyen vi ddng theo thdi gian tai vi tri giQa dam dupe xem xet va the hien tren Hinh 5 TCr ket qua cho t h % , khi dd cdng nen tang thi lam giam ehuyen vi dong eua dam.
Anh hudng eua t y sd mat dp khdi cua nen len dng xCf ddng cCia dam cung dUpc k h i o sat va the hien tren Hinh 6. Khi ty sd mat dp khdi cua nen tang len dong nghla vdi viec lam gia tang knh hudng cua phan nen tham gia dao dong va tCf do lam tang sU khac biet eua Cmg xCr ddng trong dam so vdi md hinh nen bo qua i n h hudng cCia khdi luong nen
Tiep theo, sU anh hudng ciia thong so cua khdi luong nen len u'ng u'ng xif ddng cua dam duoc the hien tren Hinh 7 Tir ket q u i cho thay rang khi thdng so anh hudng tang thi ciing ddng nghla la lam gia tang miic do i n h hUdng cCia khdi luong nen tham gia dao ddng, tit do lam gia tang sU khac biet trong Cmg xCr dpng eua dam sovdi mo hinh nen truyen t h d n g .
Hinh 8,9 va 10 trinh bay anh hUdng cCia cac t h o n g sd dp edng, ty sd mat dp khdi va t h o n g sd anh hudng ciia khdi luong nen len he so dong DMF cua dam dng vdi cac thdng sd van tdc khac nhau. Hinh 8 cho thay rang khi dd edng nen tang thi lam g i i m su khac biet giOa hai md hinh.
D o n g thdi cung eho thay trong mien van toe be thi i n h hudng cOa khoi lUpng nen tham gia dao dong lam tang dang ke u'ng x d dpng eua dam so vdi m d hinh nen truyen t h d n g , ngUpc lai trong mien van toe Idn thi anh hudng eua khdi luong nen tham gia dao ddng la khong dang ke.
Hinh 9 va 10 eung cho thay rang trong mien van tdc be thi anh hUdng cCia khdi lUong nen tham gia dao dong lam gia tang dang ke dng x d dong trong dam ii'ng vdi sU tang cCia t^ sd mat d p va thong sd anh hUdng eua khdi cua nen.
4. Ket luan
Bai bao da phan tfch i n h hUdng eua khdi lUOng nen len Cmg x d cua d^m chiu tai t r p n g di dong bang phuong phap phan t d hCTu han, Khoi lUOng nen tham gia dao d o n g dUpc m o t i t h d n g qua t h d n g qua thong so anh hUdng dac trUng cho dp nhay, mat do khdi va t y le vdi bien dang cua nen. Ket q u i k h i o sat s6 cho thay eae t h o n g sd do cu'ng nen, t y so mat do khoi va thdng sd i n h hudng eua khdi lUpng nen cd anh hudng dang ke d i n u'ng x d ddng trong d a m , lam tang dng xCr dong so vdi viec bd qua i n h hudng khoi lupng. Do do, i n h h u d n g eua khdi lupng nen tham gia dao ddng can p h i i dupc xem xet trong cac bai toan phan tich dng xis
09.20^4WmVBSR\SS
Hinh 10 Anhhuiingcflaheso lenhes6d6ngDMF,K„-5,ii=0i:(alK„=07S,(b):
ddng ciia ckc loai ket cau tren nen.
Hudng phat tnen t l l p theo cila vSn de nay la t i c g i i se t i m ra quy l u i t ciia t h d n g sd i n h hudng v i d6ng thuc nghiem kiem chdng.
TAILIEUTHAMKHAO
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10 Nguyen Trong Phudc, Pham flinh Tmng, Luong Van Hai, PhSn dug dong ciia tam phSn Idp chu'c nang tren nen dan nhdt d i m tai trong ph^n bo dieu hda di d o n g , Tap chi X^y DuUg, 12:
70-73,2013.
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14 Chu Quoc Thing, Phuong phap phan tii' hitu han, Nha xuat ban Khoa Hocva Ky Thuat. 1997
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