KHOA HOC - C O N G N G H E l l l l l
MO HINH DAM THEN NEN DAN HOI AP DUNG TRONG TOAN TOAN KET CAU TANG TREN DU&NG SAT
TS. NGUYEN HifU THIEN Tnfomg Pgi hpc Giao thdng Vgn t
Tdm d f ; Bdi viit trinh bdy md hinh dim tren nen dan hdi, m^ trong nhirng md hinh phd biin nhit ip d{/ng trong tinh todn thiit ki kiin tnic tang trin dirdng sit Md hinh di c$p den trudng hqp dd/ toin mdt Idp vdi mdt ho$c nhiiu tai trqng tip trung tdc ddng ddrtg tiidi trin dim dai v6 h^n thich fiqp cho ray hdn liin dt/pnc dung trong dudng sit dd tiij vd dudng sit cao tdc. dim cd khdp ndi (^10 dudng ray cd mdi nil Ngoii ra cdn de cqp din bdi todn dim kip khi xit din dnh hudng cua tim d$m ray fio$c dudng ray d^ng tam ban. Vl dyi tinh todn minh hoa xet din tdc ddng anh hudng cua nhiiu tai trqng.
Tir khoa: Dim trin nen ddn tidi; Ray hdn liin; Tai trqng banh xe.
Abstract: The article presents a beam on elasb'c foundatic^ model, one of the most popular models in calculation of railway superstructure. The model refers to tiie case of a one layer problem with a concentrated or multiple loads that impact simultaneously on the infinite lengtii beam suitable for continuous welded rails are used for urban railway and high speed raSway. beam wi^ hinge for Jointed track. Also mentions in double tyeam model if considering the impact of rail pad or slab. A calculation example to illustrate the impact of multiple loads.
Keywords: Beam on elastic foundation model; Cotinuous welded rail; Wheel load.
I.DATVAND6
Trong xdy dyng dudng sdt cd rit nhilu d l i tupng, vin d l ky thu^t phdi quan tdm nhu cdc tieu chuln thilt k l binh d l , mgt d t dpc, mgt d t ngang, ga, depot, cdc rong trinh phy trp dpc tuyin, kiln true ting trdn, ting dudi cua dudng. Trong tinh todn kit d u ting trdn dudng sit thi viflc mfi hinh hfia tinh todn sao cho ngdy cdng phdn dnh sdt dilu kign lam viflc thyc t l cua kit d u tu dd cd dupc lya chpn thilt k l dam bdo khd ndng chju lye, dfl ben vdi chi ph(
hpp ly ludn Id mflt ydu d u co bdn. Bdi viit nay trinh bdy mfl hinh dim trdn nin ddn hoi, mflt trong nhijng mfl hinh p h i biln nhit dp dgng trong tinh toan thilt k l kiln triic ting trdn dudng sit, gfip phin ddp ung ydu d u xdy dyng cdc logi hinh dudng d t ngdy cdng phdt triln hifln nay.
2. M O HlNH D A M T R £ N N £ N D A N Hdi 2.1. Tnffimg hpT) mflt tdi trpng tgp trung Xdt mflt thanh ray ddi vd hgn Id trudng hpp ray han liln dien hinh trdn dudng sit cao tic hay dudng s i t dd thj cd dd cung ching uin Id Ei. Ray dupc ke do lidn tgc bing mflt nin ddn hli cfi hd sd nin Id k, Iyc tde dflng ldn ray Id Q. nhu so do hinh 1 dudi ddy.
Hinh
w(x)
Md hinh dam dai vd hqn trin nin din hdi Zimmermann Id ngudi d i u tidn de d P den md hinh ndy. Xdt dilu kifln cdn bing cua mflt phin tu dim nhu hinh 2:
q(x)dx
Hinh 2. Md hinh phan tir dim
I s l 3 ndm 2017
l l l l l KHOA HOC-CONG N G H E
TO di4u vain can tjdng ta cb phirong trinh can tiang ii,rc:
qdx^i — d x = hvdx dx PhiKrng trinh cdn bdng m6 men:
Ddx dM ,
= ax Phucmg trinh cc bdn bieu thj quan hi giOa dx u6n vd bi^n d^ng:
W = -Ei'-^
dx-
m
(2) mo men
(3) TO cde phuang trinh trdn rut ra phuang trinh vi phdn:
El^ + kw = q(x) (4) Oo bdi todn dang xdt chl c6 iyc tdp trung (q = 0) ndn
£ / ^ + t w = 0 (5) dx'
Xdt dilu i<i$n bidn d6i v*i dean ddm x > 0 ta co:
H'(OO).0;IV'(0).0;M'"'(0) = - ^ (6) 2 EI
Thay do vdng dang hdm mu ta thu duvc \d\ gidi:
,^U).9^,,lx)—^,,lx)
^ ' BEl ^ ' 2kL ^ ' TO (7), phdn ivc phdn b6 cua n4n ray id:
(7)
p{x).k.ix)-f^r,{^) Tu (3), xdc djnh mfi men uin cCia dim:
M{x)-fn(x) Trong d6:
- Q: Tdi trgng bdnh xe (N);
- El: OO cOng ch6ng u6n cua ray (Nm');
- K: Hi s& n4n: (N/m/m);
- W(x): Si v6ng cOa ray tai toa dO x(m);
- L: Chi^u ddi ddc trung cua duang ray (m);
r I ^ l 1
- Cdc hdm dgng:
7 7 W - e - ' ' 4 c o s ^ + s i n - j x^O
DO v«ng tuong ddi ilM iMnNnudnMaigM | M
Hinh 3. Dq vong vd md men udn tuong ddi trong ray hdn lien do mdt li/c t$p trung giy ra Nhung dudng ndy eung cd t h l dupc dCing nhu cdc dudng anh hudng d l xdc djnh dd vong vd md men u6n khi dilm dgt tdi trpng bdnh xe ngay x = 0. Bigu thuc (11), (12) the hifln cdc sdng dilu hfia mgnh tit d i n vdi chilu dai sfing bing 2JIL. Cdc dudng ndy giup ich trong vi^c udc lupng cde d i m ddi hOu hgn vdi tdi trpng bdnh xe t$p tmng, l i y ehilu ddi dim Idn hon 2nL.
2.2. Trudmg hp'p n h l l u tdi trpng t$p trung Khi cd nhilu tdi trpng tdc dgng nhu trong trudng hpp tai trpng d cdc gid chuyin hudng thl dfl vfing vd mfi men dupc tinh theo nguydn tac eflng tde dgng. Tgi dilm X = 0 ta cd:
(8)
(9)
1
" 2kL Po=kWg
l.QM'.)
"'-^IPA'.)
(13) (14) (15) Trong id \ id i<hodng cdch tO dilm ddt tdi cua bdnh xe Q, td'i dilm X = 0. Anh hif&ng san ph^ng eua cdc tdc trpng dugc minh hpa nhui hinh 4 dudi ddy.
cos—sm— x^O L i l
(10)
(11)
(12) Cdc hdm ii(x), n(x) xdc djnh hinh dang duwng ddn h6i vd phdn b4 m6 men, dupe bleu thj tren hinh 3.
M™« = 100*'/.QL
M_„ = 0.79*y/3L
M™, = 0.70*'/.QL Htnh 4. Xem xit inh hudng cua nhiiu tii trpng
KHOA H O C - C 6 N G NGHE l l l l l
• TnKmg hpp chi cd mOt tai trpng Q tdc dyng, momen dat gia tri idn nhdt
M „ - i Gi- (16)
- Trudng hpp eb hai tdi trpng Q tae dung, i<hoang cdch!, theo do momen dan dgt gid tri nhd nhit id: 1 = O.SjiL. Nho vay gid tri ldn nhit cua mo men tong id:
M „ . ^ [ , / ( 0 ) + , . ( ; r L / 2 ) ] . 0 . 7 9 ^ (17) - TrLTdng hpp efi ba tal trpng Q tae dgng, khoang cdch I = 1.12L, gia trj Idn nhit cua mdmen tong la:
M „ . ^ [ M ( 0 ) + 2 / . { 1 . 1 2 L ) ] - 0 . 7 ^ (18)
Cfi t h l nfii ring trong trudng hpp cd nhieu tai trpng tdc dgng thl md men uin Idn nhit cua dam nhfi han ddng k l so vdi trudng hpp tai trpng dan Q. Tuy nhidn ddi vdi dfl vong vd ung suit ndn trdn nin thi tn/dng hpp nhilu tdi tn?ng chf gdy tdc dflng nhd va dupc xdc djnh thflng qua hdm s l r\{x).
2.3. Dd vdng dm
Dudng dfl vdng tuong ddi t h l hifln tren hinh 3 cho ta thiy ung suit ndn cd t h l dgt gid trj dm b-en dogn 2.36<x<5.50L. Oieu ndy la khdng phu hpp vdi dudng cfi ba Idt VI ba Idt Id logi vdt liflu ty nhidn khfing cd kha ndng ehju kdo. Cfi t h l gid djnh rang tai trpng bdn thdn cua dudng ray efi t h l khu dupc dp vong dm ndy. v l ly thuylt ed the xdc nhgn dilu kifln can bdng tCF trpng lupng trdn mpt dan vj chilu dai dudng:
, . ^ 2 . 0 . 0 2 2 ^ (19) Vdi dudng dOng td vpt be tfing de thfia man dilu kifln ndy. Qua phdn tich ly thuylt vd thyc nghipm cung chi ra dnh hudng cua dfl vdng dm d i n md men uin vd dfl vong tdn nhdt Id rit nhfi.
2.4. Dim cd khdp noi (dudmg sdt moi noi) Anh hudng cua m l i ndi ray din dfl vdng vd md men uin dupc kilm tra bing ly thuylt dam chju uon trdn g l i ddn hdi.
Cho tdi trpng Q tdc dflng Idn dudng ray tgi cho cfi m l i nli. X = 0 nhu hinh 5 dudi ddy.
MAm nu6n
- >
•3L
o^^*ngy
Vmi.
>WL ,
-Y^
\A.
'
>
.— ^j-cwnw
/ N Khdpn6i
y 2n
W.M
Hinh 5. Dp vpng, md men duong ray mii nil
Cic dilu kidn bien doi vdi phan dam x > 0 g i m :
e
«•(»:).0;iv"(0)-0; ii"'(0)- 2EI Thay ham dO vong dang hdm mu ta thu dope idi gidi:
w(x)-^—e '"-cos—.^-c'cos—(20)
^ ' 4EI L kL L^ ' Op vong idn nhit g i n nhy g i p hai l l n so vdi ray ddi ding nhit. Tai khdp n l i , cdc d i u ray tae thdnh gde nghidng Idn nhat bing 2a.
2 « . 2 K ( 0 | . 2 ^
Mfi men Idn nhit cyc hgn dgt tgi x = JiL/4:
(21)
\MJi = ~^e''^'QL = 0.\6\QL (22)
3. Md HlNH D A M K ^ P
Nfii Chung mfi hinh dim tren nin ddn hoi eua Zimmermann du d l mo td ung xu cua dudng ray.
Tuy nhidn trong mflt s l tafdng hpp d n dupc md ta chi tilt han nhu khi d n ddnh gid ung xu cua cdc t i m dflm ray, hodc khi ddnh gid dnh hudng n i n ray dgng t i m ban.
Md hinh mang tinh thyc t l dfi Id mfi hinh dim kdp.
D l i vfii cdc g l i tya rdi rgc ed khodng cdch gdi tuang doi Idn. mfi hinh hai idp cfi t h l dupc si> dgng dya tren phuang phdp phan tu hi>u hgn. Vdi cdc tuyin dudng d t dupc ke dd lidn tgc mfi hinh Zimmermann suy rflng trd ndn huu ich. Cd hai mfi hinh dupc t h l hifln trdn hinh 6 dudi ddy.
I sd 3 ndm 2017
l l l l l KHOA HOC - C O N G N G H E
w, (mm]
ittdoiiefitvic
Hinh 6. Md hinh dam kip d cd hai md hinh, dim trdn tupng trung cho ray, dim phia dudi bilu thi kit clu kd dd lidn tgc chu ylu Id tim bdn ho$c kit clu be tdng d t thdp khdc.
Cdc thdng s l cin bilt id cdc dO cOng ching u6n Ei,, Et^, cdc hd s l nin k,, kj d l i vdi ke dd iidn tyc, cde hdng so ddn hii kd, (K,), kd, (K,) d l i vdi kd dd rdi rac.
Vdi trudng hpp ke dd lien tye, khing ed iyc phdn b l tdc dyng trdn ray, phuang trinh vi phdn:
^*,(|
El, dx'
d'w.
- 0
• dx' ^ ' -' - ' ' (23) Gidi phuang trinh vi phdn trgn thu dupc d | vdng eua ray id w, vd d | vong cua ket elu kieu nhu t i m bdn ldv»,.
Hinh ve 7 dudi ddy bieu thi m|t m|t vi dy dupc tinh todn vdi cac s l lidu Q, = Q, = 35kN, Ei, = 549kNm^
Elj = SG.OOOkNm'.
Hd s l nin tuang duang:
1 1 1
Treng vl dv trfin, gid trj hfi s l nin tuang duang dupc gii> khdng dli va bdng 34.483kN/m'. Oing thdi xem xdt hai trudng hpp cue han bdng x dli vdi k vd k,. Cdch thOc ndy da dope si> dyng trong cdc thi nghidm d l tinh ngupc cdc thing s l tu cde s l lieu do gpi Id ky thudt tlnh todn theo dudng cong dilu chinh.
-0.4 •
-0.8 •
-1.2^-
1 1
!
1
\\ \ 1 1
" 1
!<, = -
i<2=n -2 0 2
i
[ml
Hinh 7. Quan hi di vdng ray-hi si nin
4. Vl Dg TlNH T O A N
Cho tardc cde thdng s l thilt ke cua kit c l u dudng nhu sau:
- Ray U1C54 hdn liln;
- Chieu ddi dSc trung eiJa dudng ray: L = 98em;
- Gid chuyen hudng hai tryc, tai trpng bdnh xe Q = 120kN
- Khodng cdch hai tryc gid chuyin hudng I = 2.5m;
• — - O
0 .
k A i
sn ^
B C w(x)
Hinh 8. So di tii trpng gii chuyin hudng Yiu ciu:
- Xde dinh md men uin vd d l vdng Idn nhit gdy ra bdi tryc dan.
- Xdc dinh md men u i n vd dd vdng tai dilm ddt luc A.
- Xde djnh md men u6n vd d | vong tgi dilm giOa B cua gid chuyin hodng.
Ldi giii:
- Md men uin vd dp vong idn nhit gdy ra bdi tryc dan.
Ray UIC54 ed md men qudn tlnh dli vdi In^c y id 2.346cm*. Hi s l ddn h i i cua thdp ray iiy bing 210kN/mm' = 21 .OOOkN/cm'.
Gid tri dp cung ching u6n El = 2.346 x 21.000 = 49.266.000 = 49.266 x 106 (kNem')
KHOA H O C - C O N G NGHE l l l l l To (7), tai x = 0, T)(x) = 1 ndn
QI^ 120x89' ^-0.29(cm) SEI 8x49.266x10' TO (9). lai X = 0, |i(x) = 1 nen
M(x).Qf^J-^^ = 2940kNcm 4 4 - M l men u i n vd dp vdng tgi diem A, x = 2.5m Tinh i / ( c ) . e - ' " c o s - + s i i i - . - 0 . 0 2 1
Tinh u(c) = e""' cosi-sin-L—0.108
L i L\
» ' W - ^ ( l + '7c)-0.29(l-0.02I).028(cm)
M ( A ) . ^ ( l + , j ^ ) = 2940(1-0.108)-2622(HVcm) - Md mem u i n vd dd vdng taidilmB,x = 1.25m Tinh rj{A)-e-"- [ c o s - + sin - 1 - 0.348
Tlnh ; j ( A ) - e - " " c o s - - s i i i - l — 0 . 1 8 6 w(B) - 2f—n^ - 2 X 0.29 X 0.348 - 0.20(cm) OI'
8 £7
M(B) = 2 ^ ; / ^ = 2 x2940x(-0.186) =-1094 W\^cm Qua tinh toan trdn ddy ta nhfln thiy ring mo men dm cfi t h l dgt tdi 40% gid tri md men duong Idn nhit trong ray.
5. KtT LUAN
Tfnh todn k i t d u ting trdn dudng d t theo mfi hinh dim bdn nin dan hdi cfi co sd ly thuylt ch^t che td ly thuylt ddn hli qua thyc te chung tfi Id mdt mfi hinh tin d y . chinh xde. Viflc tfnh todn khd ndng chju lyc nhdm tdng dfl bin. tuoi thp eua cdc thdnh phan kit d u dudng nhu ray, t i m dflm, td vpt, t i m ban, tu dudng d t p h i thflng d i n dudng d t hipn dgi nhu dudng d t dfl thj. dudng s i t t i c dfl cao Id nhi>ng bdi todn phuc tgp dupe phdt triln theo nhilu hudng vdi
nhieu md hinh khac nhau. trong dd tinh todn theo md hinh d i m trdn nin ddn hdi nhu dupc trinh bdy d trdn la mdt hudng gidi quylt hidu qud. Mfi hinh cho phdp tinh todn nhilu dgng bai todn thyc t l nhu ray hdn lien dgt trdn be dor, t i m ban doi vdi dudng s i t dd thj, duomg d t cao tdc trdn chi'nh tuyin cung nhu dufimg ray cd mli n l i cho cdc tuyin dudng s i t p h i tfidng hodc tror>g khu vyc depot dudng d t do thj.
Hifln nay k l hogch ndng d p hfl thong dudng d t hipn tgi cung nhu xdy dyng mdi mgng ludi dudng d t do thj, dudng d t tdc dfl cao dupc nhd nufiv uu tien d^c bipt. Vi vgy nghien euu hodn thipn mfi hinh tinh se gdp phin dua ra cdc giai phdp k i t d u hpp ly cd dfl bin cao, ddp i>ng yeu d u md ede dy dn xdy dyng dudng d t ddt ra •
TAI U^U THAM KHAO
^ [1]. Modem Railway Track - Coenraad Esveld - 2001. MRT Productions.
[^. Quy phgm thilt k l Metns Trung Qude GB- 50157-2003.
[3]. Metropolitan Rapid Transit Authority- Kingdom of Thai Land-Office of the Prime Minister-1997.
|4]. Introduction to Urt>an Rail Transit - China Communications Press, 2012.
[51. Ttdu chuln DSDT - TCVN-8585:2011.
[6]. Thilt k l vd xdy dyng kit d u DSDT - tilng Trung, 2010.
[7]. Track Design Handbook for Light,Rail Transit - National Academy Press - 2000.
1
18]. Quy tilnh thO- nghiflm td vpt bd tfing dy ung lycTCCS-02-2010-VNRA.[9]. Tfnh todn nin ray vdi viflc ung dgng hfl sd Idiuldi dgi dflng - Nguyin HiJu Thifln, Tgp chf C l u dudng Viflt Nam s l 1+2/2016.
[10], Tinh todn Cmg suit ray vdi viflc (mg dgng hfl s l khulch dgi dflng - Nguyin Huu Thifln.
Tgp chi Clu dufing Viflt Nam s l 12/2016.
[11]. Tinh todn ung suit Ifip ba Idt vd n i n j dufing vdi viflc ung dgng hfl s l khulch dgi r dflng - NguySn Huu Thifln. Tgp chf C l u dudng
Viflt Nam s l 1+2/2017.
[12]. Td vpt bd tdng d t thdp dufing s i t dfi thj - Nguyin Huu Thifln, NXB Khoa hpc vd Ky thudt 2016.
I s6 3 ndm 2017