Mechanics Gr

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1. . :) , .) . , . , , , ., - ( ), .2 , . , . . 3 . ., 4 . , . , - , , ...12. 2.1. 2.1.1. . , . : 1. . . , .2. , . , , . . . . , . , , , . . , , , . , , . , . , . , , . . - : 1(), ( ) 2 (), , 1.2, , . W(), . ( ) W. , . (, ), . . . , , . . . , , , . , .2.1.2. (...) , , . ... . . A,B,C . , ... : C, ( ). 4 .3 4 , , . C A B .2.1.3. 1 2 . , " R1() 2() (), 1 2 ". ( ) ( ). '' (R) 1 2. , , ., 1, 2, 3 . R .4 , R , . , , . , , . : , , , . 2.1.4. 12 . 1 2, , , , R, 1 2 , :5 R , . , 90, : 1 2 R. , , 180. () ., , . :" ".6 , . :,, () . , y. 1,2,3 . R, . 1,2,3 R y. , , (1,2,3,...,i,...,) RX = i = icosi Ry = iy = is

R : R, 72.1.5. : R x,y , R FxFy, . . R . , R , . , :Sin R FyCos R Fx . , , : F1, F2, ..., Fn. Oxy, , OxF1x,F2x,...,Fnx yF1y,F2y, ...,Fny. R Rx= F1x+ F2x+ ...+ Fnx Ry= F1y+ F2y+ ...+ Fny. 2 2y xR R R + .8 , .2.1.6. :" , ". . . , - ( ). - . . ( ) . , ' , .2.1.7. n 2 1P P P ,... , , , :01niiP , , , , . , , , , , ( ). 9, , . n:n 2 1P P P ,... ,( ) n i P P Piz iy ix... 1 , , , , Oxyz. , , :000111 niiz zniiy yniix xP RP RP R . , . .2.1.8. n 2 1P P P ,... , . ... , . , . ( ). () , : . . ..., , . , . 1,2,3. , , . R.10 , , , ,, . , 1,2,3., . , . , , . 1,2,3. . R. R. , (R = 0) . ' :') .') ( )., , ., " , , ".2.1.9. 1: , =140. P=80KN. , .11 . :KN Cos Cos P P P P RO72 . 54 ) 140 ( 80 80 2 80 80 22 22 12221 + + + + KRP, : 70 93 . 012 . 54) 140 ( 80 OSinRSin PSinPSinRSin 2140270 . , ( ). .2: cm r 12 N W 250 cm l 20 . R .12AKB BT AWRKrxy . : W, . . . R . () , . , ... . , . ( , ). ( ), :0011niiyniixPP(1) , . xR y W. :13) () (00Sin T TCos T TW WWRR Ryxyxyx (2) :8 . 0 ) ( 13 . 53 6 . 02012) ( SinKAKBCos (3) (2) (3) (1), :';' + +;' + + + +;5 . 312 5 . 1870 8 . 0 250 00 6 . 0 0000011TRTT RT W RT W RPPy y yx x xniiyniix3: 3 2 1P , P , P , . .PPP1233P2P1PROABCDabcdabcdR , , ,3 2 1P CD , P BC , P AB . AD R . R, : . ,OB,OC,OD, d c b a , , , . 14 1P b a , , . , , . a a. 1P , a b. bb, 1P , a . , c 2P b, d 3P c, ., R d a , , , . . . R a d. , , R, a d.2.1.10. 1. 12,5 . SCA SC. .2. 25 C, . , ) ) , S R .3. 20 cm 20 , - . S R .154. F , 100 , .20. W .34 . W =120 . C .2.2. . .2.2.1. ., , . ( ).F1-F116 , , .F1-F1 . , ., , . , , .2.2.2. . P . :P r M 2.2.3. Vari gnon . n 2 1P P P ,... , . R . Varignon R .172.2.4. , . . R = 1 + 2 1, 2 Varigno, R, 1,2. , 1, 2 2 ( ). , R , .2.2.5. . 1, 2,. . . ,i,... , Oxy. ') ') , .18 i = 0 iy = 0 , . ' , . = 0. , : :, - , . , . . , . , - , 19 .2.2.6. 1: R 2 1 P P , KN P 2001 KN P 5002 20m.xyPRPOr r12R P2 y 1P . :2 21 12 10P PP PP Pyyx x , :KN P P P P RP P Ry y yx x x70002 1 2 12 1 + + + y( ). R . .VarignonR 2 1 P P , 2 1 P P , . . , :20m rSin Sin Sin rSin P r Sin P r Sin R rRO O ORP P R29 . 147100700500 20) 90 ( 500 20 ) 90 ( 0 0 ) 90 ( 700) ( ) ( ) (2 12 1 + + + 2 P 1 P RP r P r R r2 1 KN R 700 , 2 1 P P , 1Pm rR29 . 14 .2. : ') = 80 .') . = 3 m, -- 50.') Varignon, ,y . . , ( , ), =y3 =Psin3 -80sin50" 3 = 183.9 Nm ') , 2.3. . , n 2 1P P P ,... , , :2100001 1 1111 + + niiz izniiy iyniix ix Aniiz zniiy yniix xP r P r P r MP RP RP R , ( xy), . :0001 111 + niiy iyniix ix Aniiy yniix xP r P r MP RP R A,B,C, :0001 11 11 1 + + + niiy iyniix ix Cniiy iyniix ix Bniiy iyniix ix AP t P t MP s P s MP r P r M r,s,t A,B,C .2.3.1. 1: 5 P=10KN C, 2m . . .22AB=60 V VHxyACBPPA BBCO , . , x ., ... , , : . AV . ( ). , . x,y B B H , V ., P x,y :KN Sin Sin P PKN Cos Cos P POyOx7 . 8 ) 60 ( 10 ) (5 ) 60 ( 10 ) ( , x y .';' +; + + + KN VKN VKN HKN VKN V VKN HP V H VP V VP HBABBB ABy B B Ay B Ax B48 . 3 22 . 5 55 7 . 8 27 . 850 2 5 0 0002.4. , , . .23 , , . . , , , , . , " ". , :') ,,,IV ...') 1,2,3,4 ...') S, . , 4 S4 .') () . , :1) , .2) 3) , . :' ) .' ) - Rtter.' ) w - Cremona. , .2.4.1. 241: 20. , : N P N P 900 8002 1 . O60 . . . S . .. 1 S1. y x,, x . :0 ) (1 Sin S VA(1)0 ) (1 5 Cos S S(2) :0 ) ( ) (2 1 Cos S Cos S (3)0 ) ( ) (6 2 1 + S Sin S Sin S (4) :0 ) (4 7 5 + + S Cos S S (5)0 ) (1 7 6 + P Sin S S (6)25 :0 ) ( ) ( ) (2 3 7 2 + P Cos S Cos S Cos S (7)0 ) ( ) ( ) (3 7 2 + Sin S Sin S Sin S(8) :0 ) (3 4 + BH Cos S S (9)0 ) (3 Sin S VB(10) ( ). : . 2 1, P P . . :90058 . 2094 . 506 . 44488 . 91188 . 1188 . 1190071 . 78929 . 107654321 SSSSSSSHVVBBA 4S . 2.5. 2.5.1. . , , , (.28.). , Coulomb :') .') . , W . , ,26 () . , . R W. (.28.) , , ' . =t. . . , . ' . . . :27" ". - = 30, W=4 (.). =6 , , = 0.30. , . (.). , (). . , : mx=4.3 . =6.0 > max , .2.5.2. . , , R. R . = 0, 28 , = r. f/r= fr f . . :' )fr = 0.02 ' )fr = 0.006 . : r=2cm W, (.). f = 0.12 mm. . (.). , , . W :, , 292.5.3. 1: cm l 20 W=4KN 30 , . (30 . 0 f).1WNT2PTAWW21 ... o : . 1T , . , . 2T , . W . , 1W 2W . :KN Sin Sin W WKN Cos Cos W WOO2 ) 30 ( 4 ) (46 . 3 ) 30 ( 4 ) (21 :30KN W f T 04 . 1 46 . 3 3 . 01max1 , . y x . . : + 0 01 1 x x xN T P F(1) + + 0 01 2W T N T Fy y y y(2) + + 02) ( )) ( 1 (2) ( ) ( 02lN Cos SinlW Sin l T Cos l P M A (3) ( N P T T , , ,2 1). . 1T :KN T 04 . 11 (4) (1),(2),(3),(4) :68 . 3 07 . 1 36 . 0 86 . 01 2 N T T P, 2T :26 . 0 86 . 0 3 . 0 3 . 0max2 P fP T KN T 04 . 11 . 2T . :P P f T 3 . 02 (5) (1),(2),(3),(5) :7 . 3 02 . 1 29 . 0 97 . 01 2 N T T P (6) , :11 . 1 7 . 3 3 . 0 02 . 11 < N f T, 2T :02 T (7) (1),(2),(3),(7) :17 . 4 78 . 0 0 41 . 11 2 N T T P (8) , 25 . 1 17 . 4 3 . 0 78 . 01 < fN T31 , 2T , , (6) (8), :17 . 4 7 . 3 02 . 1 78 . 0 29 . 0 0 41 . 1 97 . 01 2 N T T P , ( ). , , .2.6. 2.6.1. dF Oxy , dS .dFxy :dF x dSdF y dSyx S F , F. , Oxy, : F Fy yF Fx xdF x dS SdF y dS S32dFxyF Oxy Oxy, b y ya x x+ + ''dFxyFyxy'x'OO'ba F :aF S dF a xdF dF a x dF x SbF S dF b ydF dF b y dF y SyF F F FyxF F F Fx+ + + + + + ) ( ') ( ''' : .2.6.2. F , F, 33 F, . ( ). . . F, Oxy : ' ' y Kx, . F , :0' ' y xS S(1) F ( ) :F x S SF y S Sk y yk x x+ + ''(2) (1) (2) k k y x , :FSyFSxxkyk 2.6.3. 1: " ". . -, b h. (xk,yk), .34 Oxy, () . , dF , ( ) (k). , h, d dF=hdx. = 0 , = b ., (7.3 ), , dF'= bdy y, y = 0 y = h , .. , yk=hl2. , (xk,yk)=(bl2,hl2). 2:" ". , .. b h. y, () . (xk,yx).35 dF y, z, dy dF= zdy. yk. , y . ', , z, : k , k=2b/3. ,(xk,yk) = (2b/3,h/3).3: . .36yx OdrcR rddFy R. Oxy . , (r,) Ox .dF, r Ox . dF dr r d . dF :dr c dF (1) c :)2tan( 2 dr c (2) d , 2)2tan( d d , (2) d r cdr c 22 (3) (1) (3) :dr d r dF (4) :) () (rSin yrCos x(5)37, Ox Oy :( ) [ ]( ) [ ] 0 0 ) 0 ( ) 2 () ( ) (0 0 ) 0 ( ) 2 () ( ) (0 0202020 020202

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423. , . , . , . , , , . ,, . , (, ...), , ' , , , . , , ., , :i. , .. , , ( ) , :') , .') , , , ...' ) .iii. , (), ., . , , , .. :" , , ( 43 ) ". (.. , ,:..), , , , ...3.1. . , , , , , .3.1.1. , , . : . . . ( ) . s s, :ss , .3.1.2. . . . . ( ) , : , . .44 , . .-PP -PP-M M-PP . . . . , , . ( ) .. , , . . , . , , , . . , , , . , , , ..., . , , , , , ...45, , (t > 0) , , , .3.1.3. . ( ), , , ) ) ) : : . .. , .. ( ) . .. . ( ) , . .. , .46 : () , . , , . : . , , ' . , (). , . ( ). , ,, ( ),,. , , . , . , , . , 1/3(2/3) . , ..., () . . , , m, tm. .. m, m ...47 , , , ., , . , - , . , . . , , ., , .3.1.4. . . . : , , . . , . . , . , . , . . , , , . . .483.1.5. , (, ...). , . , . . , . , . ., , . , , . , , . , , , . , , . , . , , , . , , , . ( ). , , , ' . , , , ( )., Saint Venant, :49" , - ". q (.1.2), , .. - " " , . , - . " " . , , . , -, , . , .3.1.6. . , . , : - . , (...) - (). () , ( ) ,,2,...,, . , () . . , , 50 (, , ...) . , . , , :" , ". , , . , () ., (), 1 , 2 ,..., . - (), () , () (). , . , , ( ) , . . , Newton (action= reaction, = ), .51 , , , ( ) , Q , . , , (...). , 52 . .3.1.7. ., . , , . , . . () (P) (F) . :FP . Pa() 1Pa=1N/m2. . . : . .3.1.8. , . , , . , , , . , . , . 53 , ., , ..., . , , . , ., , , . . , . , , . ( .. 1 ) , . , . , . , . , . , , . , .54 , , . , , , ., ( ) .- .,, , , . , , . , ( ) , , . , , ( ), () (). . , . , , ,, , , , , , ... . , , , , .3.1.9. , . , . .. , (.2.4.). ( ). " ", "", , - .55 -, S, . " "( ), , . , - , ., , , ., F (), : S = F= :/F /m2, kp/cm2, t/m2, .. , , ... F , ( ). , , (+). , , (-). ( ), , 56 , . , (.2.5) dF y. , dF, dF . S , , y - S xk,yk , , " S dF, " F y, Fxk., , S , , .ii. , F . , F Q, F. , , , : = P/F , F = N/F , F = Q/F , F57 , - , Q , ., . , - , F .. , , , . , . . dF, . , . . : ' ) 58' ) ' ) ( ), , .. . , , ( ), .. , . , , , , .. .3.1.10. , , ( ) , . , . , . .i. ~ , , '. l=(') . l' , l'_ l+ l. , l.59, , '.l=( . . , : >0, , , , d, ( ). , , ., dldx , . , : " (), " , , . , . , . , , , Q, , - , : , Q, , < < .'-; ) ( ) (2 1122 ) (x f [,] , x x= x=. ) (ix f x, [,]. x , .4.3.3. 1: 1 2 3 ) (2 x x x f , :( ) ( ) ( )x x x xx xdx xdx dx xdx dx x dx x dx x x dx x f 2 32 322 22233 2 31 2 3 1 2 3 ) ( 2: 2 21) (x ax f , :22 2 211 1) (axax ax f tax , :211 1) (tat f adt dx , :axt dttadttadx x f 2 21111 1) ( 3:123 x x x f ) ( xdx x d . , :x x x xdx x x x xd xdx x dx x f + ) ( 4: 1 x. 1. x x x dx x f x I 2 3) ( ) (. , 0 ) ( x f. 311 x ,12 x . :2732)31( )31( )31( ) 1 1 1 ( ) 3 / 1 ( ) 1 ( ) (2 3 2 313 / 1

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