KHOA HOC-CdNG NGHE -S6 12/2015
P h a n tich a n h htfofng cua thong so' goi cao su l e n tfng xi d6ng cau cong dtfng chiu tai trpng di dpng bang phtfofng p h a p p h a n ttf httu h a n
• ThS. PHAM DINH TRUNG Trddng Dgi hgc Quang Trung
• PGS. TS. HOANG PHl/ONG HOA
• ThS. N G U Y I N H O A N G VTNH
Trddng Dgi hgc Bdeh khoa - Dgi hgc Dd Ndng
Tdm tit: Mgc dieh cua bdi bdo Id phdn tich inh hddng eua cdc thdng si gii eao su trong kit du cau dim cong ddng cMu tde dgng da tii trgng di ddng. Md hinh tai trgng di dgng ddtfc md ti bing h$ hai khii Idtfng d$e trung cho phin thdn vd bdnh xe, kit cau cdu vdm ddtfc rdl rgc dtfa trdn nin ting eda /y thuyit phin td hdu hgn. Phddng trinh vl phdn chuyen dgng eOa h$ kit du cMu phddng tl$n di d^ng ddtfc thiit ldp dtfa tren nguydn /y dn bing dgng vd glil bang phddng phip f/c/r phdn soNewmark theo tdng bdde thdi gian. Anh hddng eua de thing so gii eao su, dd cong cua dam du vd dc thdng si dae trung cua dc phddng ti$n dl ding cdng ddtfc khio sdt m0t cich chi tiit vd kit qui cho thiy de thdng si cd inh hddng ddng kidin dip dng ddng Itfc hgc cua du vdm.
Ding thdi, kit qui phdn tfch cung eho thay vin di dang quan tdm cda bdi bdo id thgt stf cd y nghia vd hdu ich trong vi$c thtfc hdnh tinh todn dng xd trong bii todn tddng tde eua md hinh du - phddng ti$n di ddng.
Tif khda: Gii cao su, phdn tieh dgng Itfc hge cUa ciu vdm, phddng ti$n di dgng, tddng tde ciu - phddng tidn.
Abstract: The purpose of this paper analyze the Influence of rubber restraint parameters in curved bridge subjected to a moving vehicle.
The model of moving vehicle Is descritxdby two masses characteristic for body and wheel, the curved bridge structure is disjointed based on the finite element theory. The equation of motion of the system is derived based on dynamic balance principle and solved by Newmark method in the time domain. The influence of rubber restraint parameters, the curvature of the curved bridge and moving vehicle parameters are also Investigated detail and the results showed that the above parameters have a significant Influence on dynamic response of curved bridge.
At the same time, the analysis result also shows that the paper Is truly meaningful and useful In
the practice of calculating behavior of interactive problem of Bridge-Vehicle.
Keywords: Rubber restraint, dynamic analysis of curved bridge, moving vehicle, Interaction of bridge • vehicle.
I.Datvande
Mdt trong nhOng giii phip nham hgn chd i n h hudng do tic dgng cilia t i i trpng ddng trong cic dgng kfl't ci'u ciu dam l i dung he thong cic gdi din hdi lifln kdt giOa dim ciu v i md, try c i u . Gdi cao su la dgng gdi din hdi m i dUpc sis dyng khi rflng rai hien nay, vdi uu dilm l i de chd tgo, cd die die tfnh cd ly rd rang v i die bidt l i dd bio tri v i sijfa ChQa (Hinh 1.1).
a) - Chi ti0t gdi, b) • dng dicing trong g6i cdu
Hinh 1.1: Gii cao su Chfnh vi cic uu dilm trfln, md hinh gdi cao su d i thu hut dupc nhieu sg quan t i m cua cic nha khoa ligc v i cung da cd khi nhidu cae nghidn cUu v^ Ung xii cua gdi cao su trong eae b i i toan ptiin tieh dap Ung ddng lgc hgc cija cac dgng kdt cdu ciu dim trong thdi gian qua, ddng thdi md hinh gdi eao su hifln ciJng dang dupe Ung dyng trong hiu hfl't cic ciy cdu nhjp nhd v i vUa 6 Vidt Nam v i trfln thd gidi. Bfln cgnh dd, viflc nghidn cUu, phin tfch Ung xilf cilia kdt cau c i u dam tUOng t i c vdi phuong tien di dflng cung da cd kha nhidu eie nghidn cUu [1-9], do dd, d i y l i van de thit sg thu hut duoc khi nhilu sg quan t i m cua c i c nhi nghifln cUu c i trong va ngoii nude.
D l tidp ndi sg quan t i m ddn Ung xijf cua md hinh gdi cao su trong bii toin phan tfch dip Ung dflng lUc hgc trong cac md hinh bai toan tuong t i c ciu - phuong tifln di ddng, bii bao t i p trung phin
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KHOA HOC - CONG NGHE
tich i n h hudng c u a cac thdng s d gdi cung n h u cac thong sd dac trUng cua m d hinh kdt c a u cau dam cong dUng v i dgc trUng eua cac phUdng tien di ddng len dap Ung ddng lue hgc c u a dam c a u mpt each chi tidt hdn.
2. C d s d ly t h u y e t 2.1. Md hinh kit du
Xet md hinh cau dam d a n g v d m (dam be t d n g cdt thep d g Ung lgc) t u a trfln cac gdi cao su chju t i e dpng cua mo tiinh phuong tidn di d d n g vdi v a n tdc h i n g s d , the hidn tren Hinh 2.1.
Hinh 2.1: Md h'inh du vom chiu phddng tidn di d^ng
Mo hinh gdi cao su dUOc dgc t n ^ g bdi ttidng s d do ctTng dan hdi trUpt k^ va thdng s d dd eUng dan hdi chiu nen k. dgc triing cho dac tinh cO ty c u a gdi cao su. D o n g thdi, md hinh kdt c d u dam cdu cd b i n kinh cong dUng R n h i m d a m bao y d u td d d cong t h o i i c u a d i m c i u sat vdi thuc t d cau tgo iiinh hgc eua d d m , khi dd nhjp Z.^eua cau dupe t h i hifln nhu sau:
Z, = 2 f l s i n ^ . L,=^R
( I ) Trong dd: R - B i n kfnh cong va 4 la gdc chan cung cua dam cau (Hinh 2.1J.
2.2. Ma trgn phan tddam
Md hinh t<dt edu cau d i m duoe rdi rgc t h i n h n phan tCi, mdi phan ttf cd hat nut ij, moi nut cd ba bgc t g do gdm c d hai chuyen vj thang va mpt c h u y i n vj gdc xoay [10], the hifln trdn Hinh 2.3.
Hinh 2.3: Md hinh rdi rgc kit du du vdm Vdi g i i thiet r i n g : S d phan tiT chia la du de xem c i c p h i n tijf d i m cau cd chieu d i i / l a phan tLl thanh t h i n g trong hd true tpa dp tdng the, the hidn trdn Hinh 2.4.
Hinh 2.4: Md hinh ptian tddu vdm Dga tren quan he hinh hgc, c h i l u dai mdt p h i n tiJr dam c a u / d u o e x i c dinh n h u sau:
' = <••« , ( 2 ) Trong d d : ^'=4/n - Gdc c h i n eung cOa phan
tLf d i m cau dupe x i c djnh dga tren sd chia phan tLf d i m v i gdc nghidng a giiJa true phan t i l thU / vdi t n j c X c u a hfl tryc tga do tdng the, bidu didn bdi c d n g thUc:
" ( i - * - ) " " ! ' - " - " " ' ] (3)
arrSD ^ Dga tren ly thuyet p h d n til hOu hgn cOa p h i n tLf d i m Euler - Bernoulli, cac m a t r i n dO cUng [ K T
^ v i m a trgn khdi lupng [M T cOa p h d n t i l d d m cdu trong he t n j c tpa d d t o n g ttid dUpc xac djnh v i ttil hien n h u sau:
:K 'l =[Ti:[KL[n- [M"L = X ML[T! (4) Trong dd: [K]^ v a [M\ - Ldn lUpt l i c i c ma trdn phan td dam c a u trong h d trgc t p a dp dja phuor^, x i c dinh theo cac c d n g tliUc:
(5)
(6)
va n \ l i m a tran chuyen trong hd trgc tga dp tdng the, xac dinh n h u sau:
(7)
Trong dd: a - Gdc nghieng giOa trgc cHa p h i n tijt dani eau vdi t n j c X c i j a he t n j c t p a dfl tdng t h i . Ddng thdi, dudi t i c dgng cCia phUdng ti^n di dgng, cac gdi cao su p h i t sinh p h i n ige d i n hdi t i c dung ngupc Idn kdt c i u ddm cdu trong hd trgc tga dp tong the,Jchi n i y dd cOng tdng t h i do i n h hudng ciia thdng sd gdi cung dupc x i c djnh n h u sau:
*^.!.^='*«f*. - . " - * . < >1 (8)
^ Do d o , m a trdn do cUng t d n g t h i trong tUng phan tilr se do i n h hudng d o n g thdi d d cijfng ciia phan tis dam c a u v i dp cUng do i n h hudng cija gdi cao s u , xac dinh b d i :
(9) - Ma *
„ ,- „ .,'do oua pAdn 1? 1} . tran d d cUng p h i n tis thU / d o i n h h u d n g c u a gfflf cao su tUdng Ung vdi ch? s d b i c t g do c u a p r a n l
t d dang xet. | 2.3. Md hinh phdtaig tiin di ding
Md hinh phUdng tidn di d d n g dupe m d t i nhU he hai b i c t u do g d m cd hai khdi luong ndi vdi nhau b i n g Id xo d a n hdi tuydn tinh k^vd c i n nhdt c^ tuong Ung vdi m d hinh nhip x e ' Khdi IUdng j i phan dudi l i m^ vd khdi lupng p h i n trdn l i M^j) tuong Ung vdi khdi IUdng c u a b i n h xe v i t h i n x e , | j ian luot cd c h u y i n vj dUng l i z , v i zjt 11, t h i hidn
[KL=[K,1-
Trongdd:[K^X=[W
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KHOA H p c - C d N G N G H l
t r d n Hinh 1.1. PhUdng trinh c h u y i n dflng cua khdi lupng v i t t h i trong trudng hop bd qua i n h hudng cOa Igc h u d n g t i m v i lgc Coriolis dupc bieu di§n n h u sau:
l-k *JkH/=-(A^v^«JgJ
(10)Trong dd: f^ - Lgc tuong t i e v i g l i gia tdc trgng t r u d n g . _ _ _ —
G i i i thidt rang t o i n bd c i c thong s d ci^a v i t t h i l i x i c djnh tai thdi d i l m f v i do Idn eCia bUdc thdi gign Af l i du be. Phuong trlnh vi p h i n c h u y i n ddng c u a khdi lupng M^tgi thdi diem f+Af dupc vidt lai n h u sau:
Trong dd: \
D g a trdn ly thuydt c u a phUdng p h i p Newmark vdi h$ s d p=0,25 v i y=0,5, c h u y e n vi z^ tai thdi d i l m f+Af dugc xac djnh bdi [10]:
-A.
(13)Trong dd:
9., -W.{6|i„ +6,z.J+c.{6,r„ + V . . ) - * ^ „ (14) v i c i c hfl s d b^dUpc x i c djnh n h u sau:
. J- . _ J _ 4 ± ,
T h d phuong trinh (14) v i o phuong trlnh vi p h i n c h u y i n ddng cua khdi lupng m^ trong phuong trinh (10), lgc tuong t i e f^ tgi thOi d i l m f+A/dugc x i c djnh:
/ „ . ^ =>",/-,..„+'XA=-+M,J.»+/>.,.-+*,, (16) Trong dd:
i f.) y f.) (17) vdi:
•iC^-K.^w,, =-c,(ftti,j+V..)+Vvj (18) T r u d n g hop g i i thidt r i n g khdng cd hifln tuong mdt tUdng t i c gii^g phUPng tidn di ddng v i b i m i t kdt edu d i m , khi n i y c i c g i i trj chuyen vj, v i n tdc v i gia tdc dUng eda khdi lupng m^ chfnh l i g i i trj c h u y i n vj, v i n tdc v i gia tdc dUng cCia kdt edu d i m tuong Ung vdi vj tri cCia phuong tifln di dflng, duoc x i c djnh thdng qua ma trfln h i m dgng v i vflc to c h u y i n vj nut p h i n tis n h u sau:
^»,..=[Nj[TLM„.,cos« (19) Trong dd: [N ] - G i i trj cilia m a trgn h i m dgng c h u y d n vi c u g p h i n t d d a m chju udn tUOng Ung v d i vj trf c i i a phuong tifln di d f l n g , duoe trlnh b i y k h i nhidu trong c i c t i i ll@u vd phUOng p h i p p h i n t i l h i J u h g n [ 1 0 ] .
So 12/2015
2.4. Phddng trinh ehuyin d^ng D g a trfln nguyfln ly c i n bang d f l n g , phuong trlnh vi p h i n dao ddng khdng c i n c u a phdn t i l d d m c i u tgi thdi diem t+At dUpc bidu didn b d i phUPng trinh:
|w|.{<il.*(fK'l+]KI,=-[Tr[N.]',/; (20) Dung ky thuat kdt ndi c i c ch? s d bgc t g do tuong Ung c i j g cae ma t r i n va vectO t i i eCia p h i n tCf trong h§ tga dd tdng t h i trong tUng bude thdi gian, phUdng trinh e h u y i n ddng tdng q u i t c i l a he kdt c a u dupe bidu d i l n n h u sau:
[W]{«V[K-]M = fF-) (21) Trong dd: [M'], [K'] v i {F'} - Lan luot la m a trfln
khdi luong, dfl cUng, v i vdc to t i i tdng the eCia c i hd trong tUng budc thdi gian.
Phuong trinh chuyen ddng sau khi thidt l i p dupc g i i i bang phuonq p h i p tfch p h i n s d Newmark [12] trfln toan mifln thdi gian dua tren chuong trinh may tfnh dupc vidt bang ngdn ngO l i p trinh MATLAB.
2. K d t q u i k h i o s i t s d 2.1. Kiem chdng chddng trinh tfnh Mgc dieh eua p h i n n i y l i k i l m tra s g phu hpp cua chUPng trinh m i y tfnh da vidt bang ngdn ngU ldp trinh M A T L A B , c i c kd't q u i s d dupe so s i n h vdi c i c kdt q u i cilia p h i n mflm SAP2000 v a c i c kdt q u i khac dupe trich d i n trong cac tai liflu tham k h i o .
Trong v i d y k i l m chUng dau tifln, bai bao k h i o s i t tan s d rieng khdng thU nguyfln v i c h u y i n vj tmh cCia c i u v d m hai d a u gdi c d djnh, vdi lUdi chia 40 phan t i l va c i c thdng sd d i e trung n h u sau:
b=0,4m, h=0,4m, E=2,4x10» N/m^ p=2.500 kg/
m ^ v i *=90°, R=10m v i P =1.000N, t h i hifln trfln Hinh 2.1.
a)-SAP2000: bJ-n^ATLAB Hinh 2.1 :Md hinh du Kfl't q u i chuydn vi dUng c u a c i u vdm dUpc x e m xet v i so s i n h v d i kdt q u i p h i n tfch b i n g phan m e m SAP2000, dupe thd hifln trfln Hlnh 2.2.
Hinh 2.2: Chuyin vj ddng trong md hinh du Trong phan k i l m chUng tiep theo, b i i bao k h i o s i t Ung x i l dflng eCia kfl't eau c i u d a m dgng p h i n g chiu phuong tifln di d f l n g , kdt q u i c h u y e n vj ddng c i l a diem gi(7a d i m v i cQa khdi iupng phUOng tidn dUOc xem xet v i so sanh vdi kdt q u i c i i a Neves [13], t h i hidn trfln Hinh 2.3.
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KHOA HOC - C O N G N G H £
sr^
Hinh 2.3: Dap dng dgng da du TU cac kdt qua khao sat sd kiem chUng tren cho ttiay ket qua trong b i i bio la tuong ddi cd do chinh xac so vdi cac kdt q u i cda cic t i c gia dugc ndu trong tai lieu trich dan. TU dd chuong trinh da xay dung tren may ti'nh bing ngdn ngQ lap trinh MATLAB CO dp tin cay nhat djnh v i lim cP sd tie tidp tgc phan tich anli hudng cua cac thdng sd len Ung xi^ dpnp cua dam.
2.2. Kef qua kliao dt so
Trong phan khao sat ket qua sd, t)ii bao khao sit md h'nh ciu dim vdi hidi chia 100 ptian tH va CO cac ttwng sd dac tnjng nhU sau [13]: L=25m,
&=2,87x10^ Wnf, fc2.9 m*, pA=2.303 kg/m va *=90P;
chiu md hkih tai trpng di dpng co thdng sd dac trung M,=5.750 kg, /c,=1.595x103 N/m (c,=0, m.=0). Cac ttidng sd gdi cao su dupc xac dmh tir thuc nghiem
^,=1716,8x10* N/m va ^^=81,34x10* N/m.
Trong phan khao sat sd dau tidn, tiai bao khio sat anh hudng cua cac thong sd dp cting gdi idn dap Ung ddng lgc hpc cua cau vdm va mpt thdng K dac tning ctio ty; ie thay ddi dp dng cua gdi cau dupc si^ dgng. Anh hudng cOa thdng sd dp cdng fc^ va k^ ldn chuyen vj dpng theo thdi gian cua diem giOa cau vdm Ung vdi cac gia trj van tdc ktiac nhau cua phUPng tidn di dpng tan lupt dUOc xem xet va the hien tren Hinh 2.4 va 2.5.
TiJT ket qua ttie hien tren Hinh 2.4 cho thay ttidng sd dd cijrng chju nen cua gdi cao su Ac^ thi anh hudng ddn chuyen vj ddng trong cau vdm la ttiat su khdng ding ke, nhung thdng sd dp ben truot c u a ^ i cao su Ic^ la co anh hudng dang ke ddn chuyen vj ddng trong cau vdm, vdi sU gia tang gii tri k^ thi ddng nghia vdi vide lim gia tang dp cUng tn/dt cua gdi v i lam giam ding ke chuyen vj ddng trong cdu vdm. TU do cho thay, cac thdng sd dp cdtng gdi la cd i n h hudng ddn Ung xd ddng lgc hpc cua ket cau dam cau v i kha phu hpp vdi ban chat md hinh v i t ly cua kdt cau dgng vdm trdn cac gdi tpa dan hdi khi chju tai trpng.
sy\j^h
Hlnh 2.4: Anti hudng cua thong so li^ ten chuydn vi dumg cua diem giQa dam: (a) V=ldm/s, (b)2Sms,(c)50m's
Trong phan kh4o sat so tiSp theo, bai b ^ khao sat i n h hifdng cua thong so dac triing h'ml) hgc cua du dim len dap Otng dong Wc hoc d y he, ket quk chuydn vi dong cua diem giBa d M va goi cao su duoc xem xet va I4n luot the M B tren Hlnh 2.6 vi 2.7. Til ket quS kh4o sat cho I M | thong so dac trong hinh hoc cua d^m cau b& tdn cot thep dM ling lyc CO i n h hi/dng den ilng m dpng li,rc hoc cua he. dac biet ia dnh hudng ro i ^ den chuyin vi truot cija g6i cao su, khi dd cong ciia vom cang ldn dong nghTa vdi su gia tdng gia tri c i a gdc chan cung ^ thi lUc truot chan vdm cang ldn, do dd lam gia tang chuyen vj truot cua cua gdi cao su.
Hinh 2.S: Anh hudng cua thong s6 if lot vi dijtng cua diSm giOa dam: (a) V=lAa/s, chuyen ^
(b)2Sm/s,(c)50m/s
Hinh 2.6: Anh hudng cua thing so ^ Iki chuyin vidtJfng cua diem giffa dim: (a) V=10mls, (b)2Sm/s,(c)50m/s
Hinh 27: Anh huang cua thdng so i let chuyen vi ngang aia goi cao su ftin tr^i- (i V=10m/s, (b) 25m/s, (c) SOm/s
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KHOA H p c - C d N G N G H l
C u d i c u n g , b i i b i o khao sat i n h hudng c u a thdng s d d d cUng gdi len ty s d dflng DMF ciia chuydn vj, dupe djnh nghTa l i ty s d giUa c h u y i n vj d d n g Idn nhat vdi c h u y i n vj ttnh Idn nhat trong c i u . Kdt q u i ty s d ddng DMF Ung vdi c i c gia trj c u a v i n toe c h u y i n dflng c d a phuOng tien di d d n g dupc x e m xet v i t h i hifln trdn Hinh 2.8 vd 2.9.
Hinh 2.8: Anh hudng cda thdng si k^ Idn ty si dgng cua chuyin vj trong du
Hinh 2.9: Anh hddng cua thdng si k^ len t^
siding cua chuyin vj trong du
Tis kdt q u i k h i o s i t thd hifln trfln Hinh 2.8 vd 2.9 cho thdy, thflng sfl dd c d n g ciia gdi l i cd i n h hudng d i n g k l ddn t^ s d ddng eug c i u , dac biflt l i thdng sd dfl b i n trupt k^ l i cd i n h hudng rd rflt, Ung vdi s g gia t i n g eCia thdng s d dfl b i n trugt ciia gdi thi ddng nghtg vdi vide lam g i i m chuyen vj ddng d i m c d u , vi khi n i y s g gig t i n g dd edng trUpt eua gdi thi eijng dong nghtg vdi vlfle l i m tang dfl edng ciig gdi tid v i t d dd l i g i i m lgc truot ngang trong k i t cdu dam c i u .
3. Kdt lu#n
B i i b i o da trinh b i y tidn trinh p h i n t d hdu hgn dd phan tfch dap Ung dgng lgc hpc cua md hinh ket c i u nhjp cau cong ddng tga trfln gdi cao su chju t i i trpng di ddng. Anh hudng ciia cac thong s d d i e trUng cOa gdi cao su dupe mfl t i mdt each chi tidt v i he phuong trinh vi p h i n chuyen ddng cua c i hd kdt c i u dupe thidt l i p dua tren nguydn ly can bdng dflng trong tdng bddc thdi gian. Kdt q u i k h i o s i t s d cho t h i y c i c d i e trung eiia thdng s d dd cdng gdi cao su c6 i n h hUdng d i n g k l ddn Ung xijf dflng lgc hpc cua he ket cdu c i u , dong thdi b i i b i o cung cd the dugc xem l i cd y nghTa thge tidn trong vide thge hanh, tfnh toan dng x d eua c i c dgng kdt c i u c a u dam bfl tong edt t h ^ d g dng lgc chju t i e d y n g cua t i i trgng di dgng
T i i lidu tham k h i o
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