84 NIL)J^ X6T CACK ^Q UAT RONG CHITON GU
1.076E-02 1.214E400 1.140E-02 1.227E
6.302E-05 4.999E-01 8.731E-06 4.998E-01
Hinli III 1.2 Bilu đ quy dao bi^n dang
(tinh theo he thuc biên dang vdi dO cong tning buili
4.027E-01 1.145E-01 1.145E-01 3.3I3E-02 5.452E-0I 3.120E-01 1.031E-02 Ị029E-02 1.406E-04 ) 1 2 2 2
ttẹ TRi)j^GTHAi D A N D ^ O C U A L\J6I DXM C O N G C O D ^ N G V O TRV
Nghien cuu b&i t o ^ v^ he tlidng ludi d ^ i cong cd dang vd tru duoc
c^c Dhh ky thuM v^ xfiy dung r^t quan tam. TInli todn b^i tôn n&y trong
gidi han d^n h'di da duoc xet dén trong [44]. Trong muc n^y nghien ciiu
trang thdi dhn - deo cua he thdng ludi d'&in cong khi chiu tdc dung cua luc m$t phan bd tily ^.
2.1 DijTvXNDfevAcACGlATmfil^
xet he thdng d ^ cong, cd dang vd tru, l&m bang vSt lieu khdng n^n dugc. Cdc true cua diLm ludi n^y dfeu nam tren mdt mat tm trdn ( goi ,15 mat trung binh hay 15 mat giira ). Mat vd tru trung binh cd bdn kinli 15
R, đ d5i dudng sinh 15 ẹ Gdc d tSm cung cua tliift dien ngang mat
trung binh 15 2/?^ . True cua cac d"am cong n5y dfeu ISp vdi dudng sinli cua mat trung binh mdt gdc cp .
He thdng d5m ludi nay tua tu do tren cac bien cong, cdn cdc bien doc dudng sinh : tua tu do hoac bi ng5nị Tren mat cdc di^n chiu tai phanbdtiiy ỵ
Gia Ihiet r5Dg : + Cac d^n du day d^ trang thdi ung su^t trong cdc d^m (d ph^i ngo5i cdc niit) chi k^ dên th5nh ph^i ung su^t tlieo liucmg doc true d ^ , cdn c5c th5nh ph^n ung su^t khdc 15 nhd nen bd quạ
+ Mat vd trung binh cd đ cong nhd (tlida man lieu chu^n cua vd thoai).
2.2 cAc H$ TII6NG Ki ra$u:
ct , 6 , z - Cdc toa đ tlieo cdc hudng : doc dudng sinh, tiêp tuyffn vdi cung cua thift dien ngang cua mat trung binh, tlieo hudng phdp tuyén ngo5i cua mat trung binh. Gdc toa đ dat tai di^m giira cung cua bien ngang .( Trong đ : a = x/R, 0 = y/R ).
Ct ^ P - Cdc toa đ hudng doc theo cdc true cua cac d ^ i
w, V, w - Cdc tli5nh phlln chuy^n djch trong he true toa đ: a , 9 , z
W,V - Cdc tli5nh p h ^ chuy^n djch trong he true loa đ:
^í^2'^i2»<^í<^2><^i2 - Cdc th5nh pli^i bi^n dang , utig su^t trong he tmc toa đ : a , 0 , z
^1 '^2 J ^1 > ^2 " Bién dang , ung su^t cua d^n tlieo hudng :
a - Chifeu cao cua dUm .
E , G - Md dun d5n hdi v5 md dun trugt cua vSt lieu dSm.
^\jQ\i^\^^2yQ2^^2 " Lilc phap, luc cat, md men udn tucfiig ung tlieo hudng a yP .
- Luc phdp, luc tiêp, luc cat, md men udn v5 md men xoan tucfng ung theo cdc hudng a , 0 , z X, Y , Z : Cdc th5nh p h ^ tai ngo5i tuong ung vdi c5c tpa đ : a ,0 , z
2 ^ T m ^ I J J P CAC QJUAN 11$:
Vdi he tlidng k^ hieu tren, tlieo 1^ thuyêt vd tlioai ta cd dugc c5c quan he :
^i = ^r - ^X\ 1 ^2 = 4 - ^X2 ' ^12 = ^n - ^/i2
trong đ ê ^ê ,^,2 1^ cac bién dang cua mat giiia, nd dugc lien he
vdi cdc chuy^n dich theo 1^^ tliuy^l vd tlioai:
. _ I du ^ _ \ dv w ^ _ \ ( d^ ^ du
^1 "" ~r^~^ ' ^2 ~ TT n^ ^ TT ' ^12 ~
• y^ Xi = 1 d^w R^ dá ' ^' " R' dÓ 1 d'^w . X 12 1 d^ M' 7?^ dadO Do a CO v6c to don vi trong he toa đ a,0 \h (cos^,sin^} iiCii tor bidu didn : e,j = C,,„C^„ê„ ta co
e, = e,cos^ ^j+^jsiii^ cp + 2ê2 c o s ^ s i n ^ .
Tliay cdc chuyin djch v&o ta durcrc :
^1 =
T dii . , Á ^ sin 2cp( COS'' 0 — + sin^ cpi— + w) + —
da ^ de 2 \da d0
d\' dii
— + —
R
d" w c^hv
cos ^ cp + sin ' ^ + sin 2 cp
da de d^w dadO ^1 -^X\ • Tucnig ty : 1 e, = — ^ R , du . T ,dv ^ sin 2ả cos '• cp — + sin ^ cp( — + w) — da de 2 ( d\' <?it y,~d^ 'de R cos '• cp dhv_ dá + sin •^ (^ d^w dé sin 2 cp d^ w dade = ^2 ~ ^Xl
Vdi cdc gia lliiêt da neu tlii trang tliai ung suffl, bidn dang d cdc d5in se tuan tlieo 1^ thuyft biên dang d5n deo nlid :
by = 3G?| - 3G<2^i va ^2 = 30^2 - 3G(oe2
Do gdc cua cac d ^ cong l$p vdi dudng suili mot gdc (p , ntn nCu goi
k 15 đ cong cua cdc d^n thi A: = sin^^
a/1 al2
Â,= \b\\'k.z)iz- , Â2= \c2[\-Lz)iz
-a/2 al2
A/, = jâyl-k.zj.z.dz , A/2 = jb'2[\-k.z).z.dz
-a/2 - a / 2
Do đ xdc dinh dugc Ny,N2,MiyM2 • ^ ^ ^*^ ^^ ^^^ ph^^ gi^o
nhau cua d^m (m5 ta goi chiing 15 cdc nut ludi) se cd ;
7^,2 = Â2,= 0,5(7^1-7V2)sin2^,
M| = ( A / , + A / 2 ) c o s ^ ^ , M2 = ( M I + Mjjsm^ ^ ,
A<f,2 = -Â2i = 0 , 5 . s i n 2 ^ M , - M j ) .
Cdc luc phdp, luc tiêp v5 md men tren c ^ thda man he phucfng trinh vi phan can bang :