1 1. , , F (. 1). . 1 , , , ( ). , . ,, d) z ( A) z ( N) z ( = , . . 2 . , . ,: () ( ). ,, . . , ,,, ,,., , . , , , . .. . , , . . , , , . - , , . , ( I2 = I min ). ., (..2). 3 ..2 (.2-),(..2-) (.2-). , : - , , ,- , ,- , . , , . . . (. 3) (2, 3, 5 6 ) . . 3 4 , F1 F2 (. 4-). F1 F2 . C C B B = (.) , . . 4 B C (. 4-), C C B B = , , , . ,, , . , ,, , . : - ,-( , ). . 5 , . . . . . , . . ( , ...) . .

,F=Fkr, - . , , , u = u (z). , . . , F = Fkr(. 5). . 5 6 , ) z ( M ) z ( u I Ex min = (1) z, , ) z ( u F ) z ( Mx = , 0 ) z ( u F ) z ( u I Emin= + , 0 ) z ( u k ) z ( u2= + (2) min2I EFk = . (2-) , z k cos C z k sin C ) z ( u2 1+ = .(3) C1C2 : 0 ) z ( u; 0 ) z ( ul z 0 z= == = ,(4) 0 C; 0 kl sin C2 1= = . .:C1=0( 0 ) z ( u = ). (sin kl = 0) :kl = n ,n = 1, 2, 3, . . . k2 l 2= n2 2,(4-) ,(2-)(4-), 2min2 2krlI E nF= . (5) 7 n = 1,, 2min2krlI EF F= =(6) kl = n u = u(z), zlnsin C ) z ( u u1= = . (7) C1,,, 0 C f ) z ( u1 max2 l z = ==, fmax , . n=1 . (.6-). n = 2, 3, 4, . . . (.6-, 6-). . 6 , ) 1 n (krF= ) n (krF , Fkr. . 8 () . , (.7-). , 2 l, (. 7-). . 7 (6), 2min2kr) l 2 (I EF= . (8) , . () . (. 8). B, C D - , l / 2 . , CD,()l/2 (. 8-). AC DB 9 ()l/4, (. 8-). . 8 (6) 2min2kr) 2 l (I EF= , (7) 2min2kr) 4 l 2 (I EF=. , 2min2kr) l 5 . 0 (I EF= . (9) . () . . 9. 10 z,,z Y ) z ( u F ) z ( MA + = , z Y ) z ( u F ) z ( u I EA min = . (10) (10) , A minY ) z ( u F ) z ( Tdz) z ( dM) z ( u I E = = = , ) z ( u Fdz) z ( dT) z ( u I Evmin = = ,(11) 0 ) z ( u k ) z ( u2 v= + (12) : min2I EFk = . , : ; 0) (M 0 ) z ( u; 0 ) z ( uA0 z 0 z= = == = (, ) 0 ) z ( u; 0 ) z ( ul z l z= == =(, ) (13) (12), 4 3 2 1C z C kz cos C kz sin C ) z ( u + + + = .(14) (13), ,(14), :0 C C4 2= = , (12) : z C kz sin C ) z ( u3 1+ = . (15) (13), , (15) : 0 l C kl sin C3 1= +0 C kl cos k C3 1= + .(16) 11 , (15), C1 0; C3 0,,(16), 01 kl cos k1 kl sin== , tg kl = kl . (17) (17):kl4.493, , (6), ( )2min22min2min 2krl 7 . 0I ElI E19 . 20lI E493 . 4 F = = (18) . ,(.10). (6,8,9 18)., l k lr= ,(19) k, 2min2rkrlI EF= (20) . 10 12 minilrr= (21) AIiminmin=- . , , , (20) (21) 2r2krkrEAF = = . (22) (22) (1), kr , . (22) PP2krE = = , P-, PPE =(23) P .,r>P, , (20). r 10 0,2820,2910,2990,3070,3130,333 0,2810,2910,2990,3070,3130,333 0,7450,7440,7430,7420,7420,742 76 10.1b/>10Wt/t . t.(. 10.7) t / b < 1 / 10 b / t > 10

10.7 ( ), - 331t b It= , (10.11) - tIt bt= =2t31W .(10.12) ''1/3''(10.11)(10.12) (10.8)(10.9) b / > 10 ( 10.1). (10.6)

tt tI GMt b GM' = =33 , (10.13) tt tzy max zyWMt bM tx = = = =232 . (10.14) 77 , ,t, , = + + + + + =i t n t i t t t tM M ... M ... M M M2 1. (10.15) , .. , ,(10.2),' I G ' I G Mi t i i t i t = =(10.16) , (10.15) ( ) ' I G ' I G ' I ... I ... I I G Mt i t n t i t t t t = = + + + + + =2 1. (10.17) (10.15) (10.5) = + + + + + =i t n t i t t t tI I ... I ... I I I2 1. (10.18) , tti ti tI GMI GM' = = , 78 , (10.6) (10.16) ti tt i tIIM M = .(10.19) , (10.4) (10.19), i ti tttti ti tti ti ti maxWIIMIIWMWM = = = ,(10.20) ti tiW / I ttmaxi ti ttti ti tmaxWMWIIMWM== = . (10.21) ( )maxi t i tttW / IIW= . (10.22) 79 , ,. . , ,,, ,(.10.8). ,, . . . (.10.8) . ) ) 10.8 () , : 10151lb,la,(10.23) , , , 80 101bt,at,101minmaxbt. (10.24) ,, , . (. 10.8). , : (. 10.9), 9. 9 (.10.10),(. 10.10) 10.10 - (. 10.11) . 10.11- : - , - , - . () . , () . , . 81 1. . ., ,, . 2. . , . , . (.10.12), (), B. 10.12 (. 10.12 ) - ( - ), 82 ) ) )) 10.13 , 331i i tit b I = , (10.24) =331i i tt b I , =ib B .(10.25) (. 10.14) . 10.14 bi, ti,(10.24), (10.25). t, i- t, , (10.16) (10.24), 83 't bG Mi iit33= ,(10.26) ' t b G M Mi i i t t = =331,(10.27) = =33i itttt b GMI GM' .(10.28) i-,(10.20) (10.12), 23i ii ti ti ti maxt bMWM= = , (10.29) , (10.26) (10.5), itti i maxtIMt ' G = = . (10.30) ttmaxttmaxWMtIM= = .(10.31) , (10.31) (10.4), maxtttIW= . (10.32) 84

(10.25) /t, , =331i i tt b I (10.33) 10.2 . 10.2 (*) (1)(2)(3)(4)(5) (6) L0,86 - 1,100,9910,831,00 U0,98 - 1,251,121,121,101,12 0,92 - 1,251,121,151- 1,13 - 1,451,121,17-- 1,21 - 1,471,29--- 1,16 - 1,441,311,201,301,20 ---1,70- +----1,17 (1) A.Foppl, (2) C.F.Kolbrunner, N.Hajdin, (3) N.M.Beljaev, G.S.Pisarenko,(4) J.Pawlowski,(5) M.E. i T. Niezgodinski, (6) N.W.Murray. , (2). 85 ,,, () , . ,, , , (. 10.15, ), (),, , (. 10.15, ). 10.15 . , . , , (10.3),, ( ) It, max . 86 10.3 , , It max 4d 2 32d4 3tdM 16 4td GM 32 o tI I =4) d D (2 2 32) d D (4 4 ) d D (D M 164 4t ) d D ( GM 324 4t o tI I =t D 4t D3 t DM 22t t D GM 43t b a 2 23 3b ab a+ 2tb aM 2 3 32 2tb a G) b a ( M+ max b a3a b 2ta bM 3ta b GM 1 i it b3i it b31 3i imax tt bt M 3 3i itt b GM 3 max 2a 433 . 04a803 3taM 20 4ta GM 2 . 46 2a 598 . 24a 034 . 13taM 09 . 1 4ta GM 967 . 0 max 8411. : - (, ) - - - . ( 5, 6) : - - , - . ,, . .

5. 6. 85 . ANz = wM0tz = Mx My wMxxz = ,wMyyz = , . y x SITxyxyzy = ,SITyxyxzx = , .2zy2zx z + = y x ATyyzy = , ATxxzx = , xA ,yA - , .2zy2zx z + = . , : wMtitzi = , wMmin ttmax z= ,3t bI3i it = , ittitIw= ,tIwmaxtmin t= ,biti -. . z z z x y z z y zy 86 , : wMtitzi = , wMmin ttmax z= ,tbA 4Iii2 *t= , t A 2 wi*ti = , t A 2 wmin*min t= ,* e,biti-. . . E : 32xy2z ekv + = . ., . . . I : yyxxzwMwM AN+ + = pojastitxxzwM AT+ = B: xxzwM AN+ = )] )AT( )AT( ( ),wM AT( ),wM ATmax[(2yy2xxrebrotityypojastitxxz+ + + = : xxzwM AN+ = rebrotityyzwM AT+ = B: yyzwM AN+ = pojasi ttxxzwM AT+ = C: ANz = )] )AT( )AT( ( ),wM AT( ),wM ATmax[(2yy 2xxrebrotityypojastitxxz+ + + = 87 T : AxxzwM AN = rebrotityyzwM AT+ = B: yyxBxzwMwM AN+ + = pojastitxxzwM AT+ = C: BxxzwM AN+ = )] )AT( )AT( ( ),wM AT( ),wM ATmax[(2yy 2xxrebrotityypojastitxxz+ + + = U A: yyxxzwMwM AN = )] )AT( )AT( ( ),wM AT( ),wM ATmax[(2yy 2xxrebrotityypojastitxxz+ + + = B: yyxxzwMwM AN+ + = pojastitxxzwM AT+ = O A: yyxxzwMwM AN+ + = )] )AT( )AT( ( ),wM AT( ),wM ATmax[(2yy 2xxrebrotityypojastitxxz+ + + = A: yyxxzwMwM AN+ + = 0z = B: yyzwM AN+ = BtityyzwM AT+ = C: xxzwM AN+ = CtitxxzwM AT+ = D: ANz = )] )AT( )AT( ( ),wM AT( ),wM ATmax[(2yy 2xxDtityyCtitxxz+ + + = 88 89 90 91 92 93 8712. ,, , . ( ), (.10.1) . 10.1 s-s . M1 (z) Mu (z) = - M (z) cos M2 (z) Mv (z) =+M (z) cos . 1 (z)2 (z) (1,u)(2,v). (1,u) . . (s - s) (.10.2). (.10.2), , . 88 10.2 (1) (2) (.10.1). , . : ) uIcosvIsin( ) z ( M uI) z ( MvI) z ( M) z , v , u (2 12211 + = + = =. (10.1) (u, v). (10.1) u v .

, . : 020 210 10= + ==uI) z ( MvI) z ( M) z , v , u (z z ,(10.2) (. 10.3) : ctgII) z ( M) z ( MII, u k vuv = = =210021k . (10.3) 89 10.3 : - , - , - . (.10.3). :-I1I2, ,- M1 = M1 (z) M2 = M2 (z), ,sin , cos ctg , (10.4),- , Mmax,- ,-u,v- A( uA, vA )B( uB, vB ),- de dp ,- . 90 . (.10.4) : A

dp ; Bde , (10.4) Ade; B dp .(10.5) 10.4 () (T(z) Tu = Tu (z) Tv = Tv (z)), . . : , 1 2 uu vzvvv uzu) z ( SI) z ( T ) z ( SI) z ( T = = .(10.6) (. 10.5) : 2 2zv zu + = .(10.7) 91 10.5 (u=0, v=0), . . . , , . (. 10.6). 10.6 0 = dA ) x y ( Mzv zuAt .(10.8) 92 , . . ., eu Mt = 0. .eu :

TdA ) x y (evzv zuAu = .(10.8) , . S (eu, ev) . ., . 93 ( ) . (, , , ...). , . . . . . , .

/ (). , (,) . ( ). 10.7 . 10.7. , () .N0 (u,v). u0 v0. 94 10.8 . 10.8. F ( ).() (u,v): o 1 uMu = F vo, o 2 v Mv = F uo. ( , ) . 95 : o , o 1 o 2. Iu, Iv iu, iv. + + = = uiuviv1AFuIFuvIFvAF2v02u0v0u0,(10.9) u v . u v. . ( 10.9) 0 uiuviv1 02v02u0= + + = (10.10) 1bvau0 0= + .(10.11) : 02u002v0vib ,uia = = . (10.12) :o, , ,o ,o N0 . 96 . 10.10. 10.9. 10.10. , . () ,. .,, . 10713. 14. : - - , a . : n) , ... 3, 2, 1, (i , SA, ASi*diidi== = . , : ji ijj id2jiij jjij iji ijj id2jiij jjij ik k ,A Sk,n) , ... 3, 2, 1, (i ,k S,S SAS,n) , ... 3, 2, 1, (i ,S= = = = = = = = = = . ij i Sj . ijk i . : ) 0 ( Soi in1 jj ij i= = + = = ) 0 ( S S k Soiqin1 jj ij i= = + == : n n nn 2 n 2 1 1 n2 n n 2 2 22 1 211 n n 1 2 12 1 11S S S............S S SS ... S S = + + + = + + + = + + + n n nn 2 n 2 1 1 n2 n n 2 2 22 1 211 n n 1 2 12 1 11S k k k............S k k kS k ... k k= + + + = + + + = + + + : = n21n21nn 2 n 1 nn 2 22 21n 1 12 11.S.SS.... ... . ....... =n21n21nn 2 n 1 nn 2 22 21n 1 12 11S.SS.k ... k k. ... . .k ... k kk ... k k, [ ] [ ]1k = . [ ]{ } { } = S [ ]{ } { } S k = , [ ] k[ ] . 108 .-., . ,,,, : - , , , , -,,,, -() , , , , - () , , , , . : - , - (, ),- ( , ), - , - . ,, . , . . 5. . . 5. i- 5 : { } { }T T4 3 2 1 i, , v , u , , , = = { } { }Tx z y xT4 3 2 1 iM , M , F , F F , F , F , F F = =x , Ay , Ix(t) , Iz , wx(t) , wz E , G , 109 . . u. u=1 . 6 . uLEAF Fk uLEAF Su 0 SEAL,u SB A1 11 B 11 1 1 11 1 = = = = == + = + = 6. .. . ux=1 . 7 . = = = = = = + = + = LGIM MkLGIM S0 SGIL,StB A4 44tB 11t1 1 44 4 7. 110 . . . v . v=1=1 . 7 . 2 23 23 2z22 22 22 3z12 2 33 1 32 31 2 23 1 22 2k v k vLEI6 Sk v k vLEI12 S 0 S S,v S S = = = = = == = + + = = + + = 3 33 33 2z23 23 23 3z12 2 33 1 32 31 2 23 1 22 2k kLEI4 Sk kLEI6 S S S,0 S S = = = = = = = + + = = + + = 7. . , . . . . . . , . 111, , . , 8. 8. , : [ ]==22 2112 11ek kk k1 11 1LEAk, { } { }T2 1T2 1 eu , u , = = { } { }T2 x 1 xT2 1F , F F , F F = = . . : [ ] { } { }e e eF k = ,=2 x1 x21FFuu1 11 1LEA. /L . : =F0u01 11 1LEA2, = =EAFLu2 . , 9. 9. , : [ ]==22 2112 11tek kk k1 11 1LGIk,{ } { }T2 1T2 1 e, , = = { } { }T2 x 1 xT2 1M , M F , F F = = . 112,,. : [ ] { } { }e e eF k = ,=2 x1 x21 tMM1 11 1LGI. GIt/L . : =t 2tM0 01 11 1LGI,tt2GIL M= . , 10. Slika 10. , () : [ ][ ] [ ][ ] [ ]= =22 2112 112 22 23zek kk kL 4 L 6 L 2 L 6L 6 12 L 6 12L 2 L 6 L 4 L 6L 6 12 L 6 12LEIk, { } {} { } { }T2 2 1 1T2 1 e, v , , v , = = { } { } { } { }T2 z 2 y 1 z 1 yT2 1M , F , M , F F , F F = = . ,,. : [ ] { } { }e e eF k = ,= 2 Z2 y1 Z1 y22112 22 23zMFMFvvL 4 L 6 L 2 L 6L 6 12 L 6 12L 2 L 6 L 4 L 6L 6 12 L 6 12LEI. 113Iz/L3 . : = 0F00v00L 4 L 6 L 2 L 6L 6 12 L 6 12L 2 L 6 L 4 L 6L 6 12 L 6 12LEI222 22 23z,EI 2FL ,EI 3FLvz22z32= = . (11),, . . 11. . . ,() (. ). : [ ] { } { }e e eF k = ,[ ] [ ][ ] [ ]{ }{ }{ }{ }=212122 2112 11FF k kk k = 2 x2 z2 y2 x1 x1 z1 y1 x22221111xz2z2z3zxz2z2z3zxz2z2z3zxz2z2z3zMMFFMMFFvuvu LGI0 0 00LEI 4LEI 600LEI 6LEI 1200 0 0LEA|LGI0 0 0| 0LEI 2LEI 60| 0LEI 6LEI 120| 0 0 0LEALGI0 0 0LEI 2LEI 600LEI 6LEI 1200 0 0LEA|LGI 0 0 0| 0LEI 4 LEI 60| 0LEI 6 LEI 120| 0 0 0LEA . . 114 ,, , . ( ) . , : - - - - . (12) . Fx3=F Fy2=F 1=2, A1=A2 , Iz1=Iz2

12. , , : []{ } { } F K = ,[ ] [ ][ ] [ ] [ ] [ ][ ] [ ]{ }{}{ }{ }{ }{ }{ } { }== =+xiziyixiiiiiii321321) 2 ( 22 ) 2 ( 21) 2 ( 12 ) 2 ( 11 ) 1 ( 22 ) 1 ( 21) 1 ( 12 ) 1 ( 11MMFFF, vu,FFF k k 0k k k k0 k k. 115= + 3 x2 x1 x32122 222 222 222 211 111 111 111 1FFFuuu | || || |LA E|LA E|| || || |LA E|LA ELA E|LA E| || || ||LA E|LA E = + 1 x1 x1 x32122 x 222 x 222 x 222 x 211 x 111 x 111 x 111 x 1MMM LI G|LI G|| || || |LI G|LI GLI G|LI G| || || ||LI G|LI G| || || | 116 + + + + 22 z 2222 z 222 z 1212 z 2222 z 2322 z 2222 z 2322 z 222 z 1222 z 222 z 211 z 1222 z 2211 z 111 z 1211 z 1212 z 2322 z 2222 z 2211 z 1322 z 2311 z 1211 z 1311 z 111 z 1211 z 111 z 1211 z 1211 z 1311 z 1211 z 1311 z 1| |LI E 4LI E 6|LI E 2LI E 6|LI E 6LI E 12|LI E 6LI E 12|| || |LI E 2LI E 6|LI E 4LI E 4LI E 6LI E 6|LI E 2LI E 6LI E 6LI E 12|LI E 6LI E 6LI E 12LI E 12|LI E 6LI E 12| || ||LI E 2LI E 6|LI E 4LI E 6|LI E 6LI E 12|LI E 6LI E 12| | , . e: = F00uu01 11 2 11 1LEA32 ,F ) u u (LEA0 ) u u 2 (LEA3 23 2= + = ,EAFLuEA 2FLu32== e: =000F000v0L 4 0 L 2 L 6 0 00 0 0 0 0 0L 2 0 L 8 0 L 2 0L 6 0 0 24 L 6 00 0 L 2 L 6 L 4 00 0 0 0 0 0LEI32212 22 2 22 23z. 117 : ( 13). 13. ( , ) . , . . . . : [] [ ] [ ] [ ] { } [ ] { } { } [ ] { }eTe eTe eTeF T T,T k T K = = = x-y [ ] ==yx

Cos SinSin CosyxTYXTT, X = xCos + ySin Y = -xSin + yCos. X Y x y 1 2