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Transcription

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2 ,,, ;,, (CIP) /. 3. :, () ISBN TB301 CIP (000) : : 17, :71007 : : : : 787 mm1 09 mm 1/ 16 : 1.5 : 509 : : : 7.00

3 : (,,, ) : (,, ) (,, ) : ( ) (,, ) (,, ) (,, ) (, ) ( ) : :

4 ( )

5 * 1,,,,,, 1978, 0,,,,,,,,,,, ;, 1996, *,,,, 1

6 8,,,, 003,,3 ( ),,, 003 7

7 * 1,, ( ),,,,,,,,,,,,,,,,, *,,, 3

8 ,, 9,,,,,

9 ,,,,,, ( ),, 1 ( ) 4 1.,,,.,,,,, 3.,, 5

10 4.,,,,,,, 8,,,,,,,,,,,,,,,, ;,, ;,,,, ;,,,;,,,,,,,, 3,,,,

11 3,,,,,,, ;,,! 3,,,

12 1, 3,,,,,,,,,, 1,,,,,, 7, 8, 9, 10, 1,, 3, 4, 5, 6, 11,1, 13,,,

13 , (,,,,, ),, ;,,,,,,,,,,,,,,,,,

14

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18 (1 ), ( ) (3 ) (4 ) (5 ) : (1 ) ; ( ) ; (3 )

19 . (1 ) ( ) (3 ) (4 ) ,,,,,,.,,, ( ),, 1. 1 (a), mm C p F A F p = lim A0 A = d F d A, ;, (1. 1( b ) ) Pa( [ ], 1 Pa = 1 N/ m ),1 M Pa = 10 6 Pa, 1 GPa = 10 9 Pa,

20 3, , :, :,, :,,,,, FN x, FS y, FS z, Mx, My Mz ( 1. ) :,,, 4. 1.,,,, ;, : (1 ),, ( ) 1. 3, A, AB, AC,, A ( 1. 4( a) ), A ( ), ( 1. 4( b) ) Fx = 0, FN - FN cos= 0 Fy = 0, FN sin- F = 0 FN FN,

21 ( ), 1. 5( a), A, AB, AC A B A C,, A, BA D BA D = AB L1, A A B, B, BA ;, ( 1. 5 ( b) ) AA B, A B L1 AA= = L1 cos (3 ),,, ;,,,, , A ( ), AB, x, x( 1. 6( a) ), x + u,u AB, ( 1. 6( b ) )

22 5 AB, A x u x u x = lim x0 x = d u d x AB, AC, ( 1. 7),,,,,,, 6.,, 1. 7,,,,,,,, 1. 8,, B C,,, C F( 1. 8( a) ), ; B F ( 1. 8( b ) ), AB, ;,,, ,, 1. 9 (a) ( b),, 1. 9( a), 1. 9( b), F m = FL, F,,, 1. 10( a)

23 6 BC, F A B, B F M = Fa( 1. 10( b) ) ; BC, A F , m - m (1 ) F, Fsin, Fcos ( ) A : Fx = 0, FAx = Fcos M B = 0, FAy L = Fsin L 3 FAy = F 3 sin (3 ) m - m, FN, FS M (1. 1) , Fx = 0, FN = - FAx = - Fcos() Fy = 0, FS = FAy = F 3 sin m - m C MC = 0, M = FA y L = FL 6 sin, :,, (a) D (1 ), F A B, B F Fa( 1. 13( b ) ) F Fa B C, CF Fa( 1. 13(c) ) ( ) D D x y z,, FN,

24 7 My Mz,, Fx = 0, FN = F Mx = 0, Mx = Fa My = 0, My = Fa 1. 13,,, F A C, D , BC ( A), (B), ( C), (D), B, BC A B (),, , F, ( A) a (B) b ( C) c (D) D, a(b, c), (),,,

25 R, R R, R = 80 mm,r = mm, 1.,,? 1. F C E,?? P P ACB (1. 3 ), P A C B, P x, y, PA x, PB y, P x P y ( a), ( b) A, B 1. 5 A A B, AC 60 ( 1. 5),, 59.5, = , AB C, F A B C, (1 ) AB, BC? ( ) AB, BC?

26 9. 7 (1 ) ; ( ) ; ( 3) , l1, l, l1 l, AB 1. 8

27 (1 ), ( ), (3 ), s ( p, 0. ), b, (4 ) [ ], (5 ) (6 ) E, (7 ) (8 ), (9 ), ( ) (10). 1. : (1 ), ( ) (3 ) (4 ) (5 ) : (1 ) ( ) (3 ),

28 11. (1 ),, ( ) (3 ). 3 1., FN FN,,,,,, ;,,.,,,,,,,,,,, = FN A : (1 ) ( ), ( ) (3 ) 0, (4 ),,,

29 1. max = FN, max A [ ] = u n [ ] u,, n, 1, s, [ ],,, b,,,,,, : (1 ) : F, A, [ ], ( ) : F, [ ], A FN [ ] (3 ) : A [ ],, 4. F N, max A[ ] l = FN l E A, ; l, FN, E, A FN ( x) A( x), d x, d(l) = FN ( x) d x E A ( x) l = l FN ( x) d x 0 EA ( x),,, n l = i = 1 = l l FN, i l i E Ai = E = - =,,

30 13.,,, = FN/ A, = l/ l, (. 1 ) : (1 ) : ob, ( ) cd, de, ef ( ) : p, ( a ) e, ( b ) s, c b,. 1 (3 ) :. 1, E = = tan a (4 ) : l, l1, d d1 ( d1 ), = A - A1 A = l1 - l 100 % l 100% ( A = d 4 d 1, A1 = 4 ) (. 1 k),,,,, 6.,,, ;,,,, : (1 ),, ( ) (3 ),,, (4 ),,,

31 ( a), AB AB = E1 ( AB ) 1/, AC AC = E AC, A, A A.. ( b) A Fx = 0, FN, AC - FN, AB cos45= 0 Fy = 0, FN, AB sin45- F = 0 FN, AB = F ( ), FN, AC = F ( ) AB AC, AB = AB lab E1 AC = AB l A B = = FN, AB E1 A = = AC E = FN, AC E A = F EA lac F A A lab. ( c), E1 = AC l AC = Fl E A F A E1 l = lf E 1 A A = AA 4 = AD + DA4 = lab cos45 + lac = lab + lac = 4 lf E 1 A + Fl E A, l AC, (4 EF + E 1 A) Fl = E 1 EA

32 15,,, AC, AB,,,.. 3 (a) l, F fs, fs,. 3 ( b), F, l, E, A ( : k). 3 (1 ) k d y (. 3( a) ) FS d FS = fs d y = ky d y = d FS = l F = FS k = 3 F l 3 0 ky d y = kl3 3 = kl3 3 ( ). 3( b ), d y FN ( y) = y ky d y = k 0 3 y3 = d(l) = l = l d (l) 0 = l FN ( y) d y 0 E A FN ( y) d y E A = l F 0 y l 3 F E A l 3 y 3 d y = Fl 4 EA, l FN A,,,,

33 16,. 3. 4( a), ; A = 00 mm, E = 00 G Pa, s = 80 M Pa, b = 460 M Pa, : F = 50 kn, =, =, =, B B x =, By =, B =, () n =. 4 (1 ) M A = 0, FN1 = F = 5 kn Fx = 0, FN = 0 M B = 0, FN3 = F = 5 kn = FN1 EA = = = = , ( ) B (. 4( b ) ) A = 0 By = l1 = m A y = l3, A A B = B y = m A x = Bx = 1 3 Ay = m = 3 Ay = m (3 ) : n = s FN1/ A = = ,,,,,,

34 , AC, BD, F,?BD F A x, BD FN B, FN B = x = l, FN B M A = 0 Fx - FN B sinhcot= 0 Fx hcos, FN B, max = Fl hcos, BD A BD V Al BD = A FN B = [ ], =, V, 4 Fl h [ ]cos Fl h h[ ]cossin = Fl [ ] sin. 5,,, ;,,,, (a) AB ( ),, A0, ( ),,, 1, B (. 6( b) ), : (1 ) =? ( ) F =?E, A0, l 1, ( 1), FN1, FN3, FN,. 6 (c). 6( c) (3 ) MC = 0, FN1 = FN3 ( 1) M A = 0, FN = FN3 ( ) (- l3 ) + l1 = (l1 + l ) l1 + l + l3 = ( 3) FN1 E A0 l + FN l E A0 + FN3 l EA 0 =

35 18 (1 )( )(4 ), FN + FN + FN3 = E A 0/ l ( 4) FN3 1 = FN3 EA 0 = E A0/ 6 l = / 6 l = 6 l 1. 6 ( ), F B, F,, FN1, FN, FN3,. 6 ( d),. 6( d ) MC = 0, FN1+ F - FN3= 0 ( 5) M A = 0, FN+ FN3- F = 0 ( 6) l= l1+ l3 ( 7)

36 19 7 ) FN= FN1+ FN3 ( 8) (5 )(6 )(8 ) FN3= 3 4 F ( 9) (9 ) 3 = FN3 = E = E( - 1 ) A0 F = 4 3 EA 0 ( - 1 ),,,,,, 1 ;,,. 6 AB C, A B A E BD (. 7( a) )AE = 0.1 mm; t = 10, E = 00 GPa, = ,. 7 AB,, A CB (. 7 ( b) ), A E B D A E FN1, B D F N (. 7 (c) ) (1 ) MC = 0, FN1 sin30 3 = FN sin60 1

37 0 ( ) : FN = 3 FN1 ( 1) l1 = m, l = 3 m, - l1 AA = sin30 AA= (- l1 ), l BB = cos30 BB= l, AA= 3 BB 3 (3 ) : l1 = FN1 l1 EA - tl1, l = FN l EA - tl AA= (- FN1 l1 EA + tl1 ) = FN1 EA = BB= FN1 EA FN l EA - tl = 4 3 FN EA = FN1 EA = 3 4 FN 3 EA (1 ) ( ) 4 FN1 EA + 4 FN EA = FN1 + FN = EA ( ) 3 FN1 + FN1 = EA 1 = FN1 A = E = MPa = FN A = 3 FN1 A = 38.1 MPa,,,,,,,,,. 7. 8( a) A, B d = 1 mm, C F, = , C F. 8( b ), E = AC l = l0 (1 + ) l = = ( ) M Pa,

38 = 10 6 ( ) C, = mm = E E( ) = F = FN = MPa l + l = A l( 1 + ) = N ( ) =. 8,,,. 8. 9( a), B F,. 9

39 (1 ) A (.9 ( b) ) AC (.9(c) ) Fx = 0, FN1 = FN ( 1) Fy = 0, FN3 = FN1 cos45 ( ) FN3 + FN4 = F ( 3) ( ),.9 ( d), A A, AA A1 A1 A= l (3 ) AA= l AC = la B + lbc A A 1 = cos45 ( 4) AA l1 = l = lbc = FN4 l E A FN1 l1 EA = FN1 l EA = ( F - FN3 ) l E A lab = FN3 l EA (4 ) ( 5)( 6)( 7) ( 4), FN1 l E A = (5 ) ( 1), ( ), ( 3) ( 5) ( ) ( 6) ( ) ( 7) ( F - FN3 ) l E A - FN3 l E A FN1 = F - FN3 ( 8) FN1 = FN = - 1 FN3 = - F F FN4 = F ( ) ( ) ( ),,,, A,,, 4, AC, 3, AC AB BC, AB, BC, AC (a), ( l) l ( 1), 5, AB 4, 1.10 ( b) A B A: Fx = 0, FN1 = FN ( 1) Fy = 0, FN3 = FN1 cos60 ( )

40 3 B Fx = 0, FN4 = FN5 ( 3) Fy = 0, F = FN4 cos30+ FN3 ( 4). 10 ( ).10 (c), A A, B B AA A 1, A AA= BB B 1, B AB l3 (3 ) : BB= = BB- AA= l1 = l = A1 A cos60 = B1 B cos30 = l4 cos30 - FN1 l 3 EA l4 = l5 = FN4 l E A l3 = FN3 EA (4 ) ( 6), ( 7), ( 8) ( 5) l1 cos60 l4 cos30 l1 cos60 = l4 3 = F N1 l 3 EA (5 ) ( 1), ( ), ( 3), ( 4) ( 9), l 3 - l1 ( 5) ( 6) ( 7) ( 8) FN3 = FN4 - FN1 ( 9)

41 4 FN = FN = FN3 = F ( ) 3 FN4 = FN5 = F ( ) A B, 4, 5, 1, A B ( AB, ), AB ,,,,, 1, 1.3,, : T 0, T? (1 ). 11,,, T,, c =, c, Ec, A ; s, Es, s, s c A = s A = s A ( 1) ( ) l, l,,, l1 = l = l ( ) ( 3) (3 ) ( 4) s = c = l- l = l ct - ( c A) l Ec A l- l = l st + ( s A) l1 Es A + ( s A) l Es A l- l = l st + s l + s l Es Es ( c - s )T = c + s + s ( c - s )T = 4 Es ( c - s )T 11 s 0.5 Es = Ec Es Es + s + s = 11 s Es 4 Es 4 Es 0.3T 11 s= s = EsT 4 Es = EsT ( ) ( 3) ( 4)

42 5 4 ) 0, s 0 s0 0 A = s0 A = s 0 A T, 0 = s0 = s0 ( 1) EsT s EsT = EsT s EsT = EsT 0,, ( ) ;,,,, ;,,,,. 5. 1, E, [ ], ;.. AB A = cm, B, C F1 = 60 kn, F = 100 kn, p = 10 MPa, s = 60 M Pa, E = 00 G Pa, AB 0.9 mm, AC, BC A, F, A , F1 = 0 kn, F = 55 kn, q = 10 kn/ m, a = 1 m,. 5. 5, E = 00 GPa, B, , 140 MPa, =?. 6,. 6, : (1 ) E ; ( ) ; (3 )

43 , A F, : (1 )? ( ) A?? ,. 8, E = 00 GPa, l = 6 mm,?. 9,,, F 3 kn, 1 = , = , E, G,

44 7. 11 F1, F (. 11) A, E, F1, F, V 1 V, V= V 1 + V = F 1 l1 EA + F l EA , 5 (l0 = 5 d(. 1) ) 10, , C, EA ( a) ( b ), A1 = A, L1 = L,

45 8 F = F, C1 C 1, ( A) 1 = ; ( B) 1 < ; ( C) 1 > ; (D) , H K, AB CD, A, A = 4 cm, [ ] = 160 M Pa, AB, CD, F , A, B,, , AD, BD CD E A,, F, = = 45, D, ABC,, 15, C F, ABC, F? AD, BE, : : Es = M Pa, s = , As = 6 cm, : Ec = M Pa, c = , Ac = 4 cm , 50 mm, 15 mm, 50 mm, 45 mm,, EB = 70 GPa,, EA = 100 GPa

46 9 0, 50, 15 kn, ( B = , A = )?. 0 a. 0, ( ), A B,, [ ] = 10 MPa, E = 10 5 M Pa, F = 60 kn, a = 0 cm , DB, DC, E = 10 GPa, DC = l AC, DB DC ( ).., a = 1 m, F = 150 kn, [ ], [ ] = 160 M PaA1 A A3 A4 A5 = 11 11,. 1.

47 (1 ), ( ), (3 ) (4 ) (5 ) (6 ), (7 ) (8 ) (9 ) (10) : (1 ), ( ), ; (3 ), (4 ), (5 ) (6 ) (7 ) (8 ) : (1 ) ( )

48 31 3 ) 3. (1 ) ( ) (3 ),, (4 ) :,, :,, ( 3. 1 ), 3. 1 :, 3. 1( b), F,,,, ;,

49 3. :,, :,, = FS A [ ] [ ],, FS, u, u = FS, u A u [ ], [ ] ( b ),,,,,,, b s,,,,, FbS ; Ab S ; b s = Fb S AbS [ b s ] [ b s ],, (1 ) ( ),, h ; l Ab S = hl ( ) ( ),, d ; t 4. AbS = dt ( 3. ) :,,,, : F l, T (

50 33. 3), p,, G, Pa = G :, 5. (1 ) T ; v= Ip, : L 4 ; 1 = G = max = T R I p Wp, : L 3 T : Ip = D4 3, W p = D3 16 : Ip = D4 3 (1 - a4 ) : Wp ; ; Ip = T Wp = D3 16 ( 1 - a4 ), a = d/ D,, < 0, < 3 % ( ) : : max = Tmax Wp [ ] : W p Tmax [ ] : Tmax Wp [ ]

51 34., (1 ) : n P, Me = 159. P n ( Nm) ( P k W, n r/ s ) Me = P n ( Nm) ( P kw, n r/ min) Me = 7 04 P n ( Nm) ( P, 1 = W, n r/ min ) ( ) :,, T,,, ;,,, 7. (1 ) : d d x = T ( x) GI p ( x) L, T ( x) = L d= L GI p ( x) d x, L T, ( 3. 4 ) = TL GI p,, n T i L i = i = 1 GI p ( ) :, max= Tmax GI p [ ] 3. 4 [ ],, [ ] ( )/ m,, GI p max= Tmax GI p 180 [ ] ( ( )/ m ),,,,

52 ( a), F = 40 kn, 5, d = 0 mm, 3. 5 (1 ) F, 3. 5 ( b) M = Fa = = 0 knm ( ) F 5, FS1 ( 3. 5 (c) ) FS1 = F 5 = 8 kn (3 ) M 4 FS, M = 4 FS r FS = M 4 r = = 50 kn (4 ) 3. 5 (c), m in m in = FS1 d / 4 = = 5.5 MPa (0) 10-6, FS FS y = FS1 + FS 3 5 = = 38 kn FS FS x = FS 4 5 = 40 kn FS = F S x + F S y = = 55. kn max = FS A = ( 0 ) 10-6 = MPa, F ;,,

53 ( a) AB A, B, C,, BC A B 30 F = 50 kn, L = 4 m, [ ] = 150 M Pa, [ ] = 80 M Pa, [ b s ] = 00 M Pa 3. 6 (1 ) 3. 6( b), FA = 50 kn FB = 50 kn ( ),,,, max = FN A + Mmax W = cos MPa = [ ] (3 ) = FS A b s = FbS AbS = = 79.6 MPa < [ ] = = 31.3 M Pa < [ b s ] =,,,, ( a) d0 = 5 mm D = 50 mm, d = 5 mm, 0 mm, 50, Es = M Pa, s = ; Ec = MPa, c =

54 (1 ), 3. 7 ( b ) FN s - FN c = 0 ( ) 50,,,, (3 ) : (4 ) FN s = ( c - s ) te s As Ec Ac Ec Ac + Es As s = c s = FN s L c = - = Es As FN c L E c Ac + s tl + c t L ( 17-11) (50-5 ) kn (5 ), 4 ( 50-5 ) = Fs = FN s = 9.8 kn Fs A = = 9.5 M Pa,, , L = 510 mm, D = 50 mm d1 = 5 mm, d = 38 mm, 70 M Pa, : (1 ) T 3. 8 =

55 38 ( ), L? (1 ) T Wp1 [ ] = T Wp [ ] = Nm ( ), 1 =, L1 L = Ip1 Ip = T L1 GI p = T L GI p 3 ( ) 3 ( ) L1 + L = 510 mm = L1 = 98 mm, L = 1 mm = Nm = Nm,,, L,,,,, 3. 5, 3. 9, Me, : l, R, t1, t, G (1 ) ( ) 3. 9 q (1 ) : q1 1 ;

56 39, q1 T = Me = q = q1 RR q1 = q =, Me R 1 = q 1 t1 = Me R t1 = q t ( ),, = Rl Me G 1 Me= 1 Me R t1 = Me R t 1 G (Rt1 ) l + 1 t1 + Me R t t = G (Rt ) l Me l 4R 3 G,,,,, , 5 mm, A B, 600 mm, 50 mm mm,, 00 Nm,, G = 80 G Pa, 1 t1 + 1 t ( 1) T = 00 Nm, T, M = M = M ( ) T, = Tl GIp

57 40 T,, + = (3 ), Ip Ip M = = Ip = d4 3 = 54 3 T 1. = M r t Ml + Ml GI p GI p Tl GI p = Ml GIp, Ip = D = = Nm Ip Ip Tl GI p + 1 (1-4 ), = = 0. = =.65 N/ mm =.65 MPa,, ;,, 3. 7 = B( (a) ), B, : (1 ) v( ) ; ( ), V ( max ), R, l( ( b) ) (1 ) v, v= 0 d= ( B) 1 d= 0 3 B 1 3 B = 3 B 1 ( ) V, = d d x 3 = 3 3 B

58 ( c) ) T = A d A = A 1 B d d x 4 7 A B d d x ( B d d x ) 1 d A = 3/ d A = B d d x 1 R 7 = R, max = 7 T 4R 3 V= = 3 vd v v = l A 3 B 7 T 4R 7/ 4 7 T 3 B 4R 7/ 3 = B = B d d x 1 B d d x R 0 1 3/ d= B d d x = B d 1/ d x 7 T 4R 7/ = 3 B d A d x = 3 B 0 l R T 1 4R 7/ l A 3/ dd x = 4 7 T 3 B 4R 7/ 7 R7/ l = 8 7 T 1 B 4R R 5/ d= 0 7 T 1 3 4R 7/ d A d x = 3 0 l R 0 R l = 8R l 1 B 3 max 5/ dd x =,,, (a), l, R0, Me, m = Me l,,, Me, l, R0 [ ] (1 ) l, ; l1, 1 ( 3.1 ( b) ) ; l1 + l = l ( ) 3.1( c), ( B ) ( A ) Tmax = Me + l1 l Me Tmax (3 ) 1, = Me max = Tmax [ ] R 0 1

59 4 Tmax = R 0 [ ] (4 ), 1 + l1 Me l R 0 [ ] max = Tmax = R 0 Me [ ] R 0 (5 ), M e R 0 [ ] V1 V = R0 1 l1 = 1 + l1 l = R0 l = ( l - l1 ) l1 Me R0 [ ] Me R0 [ ], V = V1 + V = dv d l1 Me l 1 R0 [ ] l = 0 + l - l1 l1 l 1 = - 1 = 0, l1 = l = l 3 Me 4R 0 [ ], = Me R 0 [ ] 3. 1

60 43,,, ( a) = 8 mm, D = 00 mm,, d = 0 mm, [ ] = 60 M Pa, [ b s ] = 160 M Pa, Me, s = 30 knm (1 ), = T R 0 = Me D = ( ) = 59.7 M Pa ( ), ( b),, (3 ), FS FS = = 59.7 M Pa l = l s FS = s = 59.7 ( ) s, l (4 ), (5 ), A = s [ ] d 4 FS s d 4 [ ] 1 = m = 39.5 mm b s = FbS AbS 39.5 mm = FS d = s d [ b s ] s d[ b s ] = m = 53.6 mm,,,

61 ( a), R, ABE, CDF ABCD,, ( b),? (1 ) Ox y z, 3. 14( c), max = Me Wp = Me R 3 ( ) ABCD, x d A d A d F z d A = ad y d F = d A = T y I p ad y d Mz = yd F = Ty Ip ad y z Mz T y = R 0 Ip ad y = 4 3 Me a R (3 ) CDF, d A = d d, d F y z, d F = d A = T d d d Fy = d Fsin= T sin d d I p I p

62 45, Mz d Fz d Fcos = T cos d d y z Mz= ad Fy = R T a sin d= 4 Me a 0 I p 3R = Mz 0 I p,,,,,, z (), 3. 1,, 3.,,,, , Me = 0 knm, me = 5 knm/ m, l = 1.5 m,

63 , [ ], [ b s ],, L/ d? ( a) ( b ) , d = 75 mm 1 Me, D G = 80 M Pa, G = 10 GPa, Me = 16 knm, , B A A B ( A), Me, a, G, d, m

64 , Me1 = Me, a = c = L/ 4, b = L/, d, L, R, t, (a),, R( R t), 3. 10( b) 3. 9 (1 ) T, ; ( ), (c), T, :?? , [ ] = 0.6 MPa, a = 4 cm, b = 6 cm, F = 10-3 MN, x? d, 15, E, (), ( ) d1 = 44 mm d D = 1, Me, = [ ] = 50 M Pa,

65 48 E 10 5 M Pa, = 0.3 : (1 ) ; ( ) ; (3 ) d, D D = 100 mm, d = 80 mm d= 80 mm A P 1 = 300, B, C P = 150, P3 = 150 n = 300 r/ min; G = 80 GPa, [ ] = 40 MPa, [ ] = 1 / m, [ ] = 100 MPa, [ b s ] = 80 MPa, 10 mm 10 mm 30 mm (1 ) ( ) ( ) (3 ), ,, 3. 15,, D, l; [ ], A, Me, ABC, d1 = 100 mm, A, B Me = 7 knm, C d = 0 mm EF G H, G = 0.4 E, G = 80 GPa ABC

66

67 (1 ), ( ) (3 ), (4 ) (5 ) (1 ) ( ) (3 ) 4. FS FS ( x) (1 ) M M( x) FN FN ( x) FN ( ) ( ) FS FS ( x) FS ( ) (3 ) (4 ) M M( x) M( ) FN ( x) : FN ( x) FS ( x) :, M( x) :,

68 ,,,, (1 ) ( ), 4. 1( a), ( ), 4. 1 ( b) (3 ) 4. 1( c), 4. 1 :. 90, ; 4. (a) : (1 ) 4. ( b ) ( ),, 4. ( c) (3 ), 4. :,,

69 5, 3., : ( ) :, 4. (1 ) d M( x) d x = d FS ( x) d x = q( x) : ; x, y q( x) = 0, FS ( x), M( x) q( x) = 0, FS ( x) > 0, M( x) ; q( x) = 0, FS ( x) = 0, M( x) (M( x) ) ; q( x) = 0, FS ( x) < 0, M( x) q( x) = q( x) < 0( ), FS ( x), M( x) q( x) = q( x) > 0( ), FS ( x), M( x) ( ) FS M :, FS, FS, ; M,, FS, ; 5. FS M, M, M FS, M,, 6. :, , F1 = 10 kn, F = 60 kn, q1 = 30 kn/ m, q = 0 kn/ m, M = 80 knm 4. 3, DE EB,, DE, EB ; F G, M, MF = = knm

70 53 MG = knm 4. 3 ) ( a) AD ( AD, AD ( 4. 4 ( b) ), 30 kn A, A FA y = 30 cos60= 15 kn () FAx = 30 sin60 6 kn() MA = FAx 5 knm( ), AD 4. 4( c), 4. 4 ( d) BC C m, FS,, ME = = 15. knm AD, A, A, MA AD, AD, ( a),,,,,,,

71 , FS = 0 x( 4. 5 ( b) ) FS = 4 18 q0 L M 4 18 q0 L - 1 M = 4 18 q0 L 3 L - 1 q0 L x = 0, x = 4 9 L, x = 3 L q0 L 3 L 3 L1 3 3 L q0 L = 7 q0 L 16

72 55. 5( c), ( d) 4. 5,, ( FS),,,, 1/ ( a) 4. 6 ( b), ( c), C,, AB A 1. 8 m,, M = = 3.1 knm, ( AC CE ) C F1, C, AC CE, ( c),, :,, ;,,,,, d M FS =d x, d FS = q( x) d x,, FS M, FS, M, M, FS 4. 7( b), 4. 7 (a),,,

73 56,,, ( a) ( ), 4. 8, FA = FC = F

74 57 BD ED FD, AB B, D F a - FN, DE sin45 a = 0 FN, DE = F ( ) Fx = 0, FN, DF = FN, DE = F ( ) Fy = 0, FN, DB = F - FN, D E cos45= - F ( ) 4. 8( b ), 4. 8(c),,, EB BF, d M d x (a), = d FS d x = q( x)?? 4. 9 FS ( x) = ( b) d M = d x d FS ( x) d x M( x) = qx h Mmax = ql h = q( x)

75 58, q( x),,,, qh, (a), F = F1,, ( FS ) ( b ) (f), C D,,, AB, F1, F B, BC ; B C, CD,, (a) ABC,

76 59 FN FS AB : M = FR, FS = 0, FN = - F BC : M, FS, FN M ( 4. 11( b ) ),, M = FR ( 1 - cos ), FS = Fsin, FN = Fcos 4. 11( c), ( d), ( e) ( a) AB BC,, AB, F C B AB,, 4. 1( a),, p, Fy = 0, 4 ap = 1 4 a q p = q FS ( x) = qx - qx a M( x) = qx - qx3 6 a q( x), FS ( x), M( x), 4. 1( b)

77 60, x, x,,,,, M, FN 4. 4.,, FS, max Mmax ( FN, FS M), q, D , FS M , Me, q0 BC CABD ( ), A, B FA y = 40 kn( ), FBy = 8.5 kn() , FS, max M max

78

79 , FS, max M max ( a), ( b), , ( a) ( b )

80 R 4. 1, q0 M AB 4. 13, B 1 m, , ABC, R, B Me

81 (1 ), ( ) (3 ), (4 ) (5 ), (6 ) : (1 ) ( ) (3 ), (4 ), : (1 ) ( ) (3 ) 5. (1 ) ( )

82 ,,,,,,. (1 ) :,, ( ) :,, (3 ) :, 3. (1 ) : = My I z,, ) ; max = M W z : ; l/ h 5, h, l ( x ( ), y z, xo y xoz, 4. (1 ) = FS S * z bi z, max = 3 FS bh max = FS S zmax * bi z :, ( )

83 66 max = FS A : max = 4 3 FS A : 5. ma x = FS A max = Mmax W z [ ] : max = FS, max S* zmax bi z [ ] (1 ),,,, ( ),,,, M max, y max (3 ),,, :, ymax ymin, (4 ),,, FS max, max [ ] 6., y z ( ),,,,,,,

84 AB 5. 1 (a), q = 0 kn/ m, c y c = 8 mm (1 ) FS, M ; ( ), 5. 1, FS, M 5. 1( b ) I z = cm ( 10-8.) ( ) = C, t ; D, c, t = - c = Mmax ymax Iz A, B, F max, max = FS, max S* z max Iz b = = = * FS, max S z I z b * FS, max S z I z b = (0-8.) = M Pa ( 0-8. ) = 7.01 MPa = = 1.45 M Pa = = 5.08 M Pa

85 68,,, z, ( ),, ( b),, 40 mm, 140 mm 5., 5., Iz 170 MPa, 6 m, B, : (1 ) B ; ( ) q, ( : AB M max ) = cm 4, [ ] = 5. (1 ) B, MB = - qx, M = - qx 4 + q 8 (6 - x), - qx = - qx 4 + q 8 ( 6 - x) x = 1.74 m Mmax M = qx = q = Mmax ymax I z [ ] q q 19 kn/ m ( ) MA = 0, q6 3 - FB ( ) = 0, B, FB = 80.8 kn FS, max = - FB + q1.74 = kn

86 69 max = FS, max S* z max Iz b MPa = [ ] =,,,,, 5. 3 W z = 300 cm 3 AB,, 4 m, 1 m, b = 4 cm, h = 1 cm, [ ] = 100 M Pa( 5. 3( a) ), F,? 5. 3, W z1 (1 ) [ F] : Mmax [ ] W z1, l, Mmax = Fl 4 = F 4 ( Nm ) W z1 = bh 6 = = m 3 [ F] = 4 [ ] W z1 = = 38.4 kn ( ) :, 1 [ F], A, A x, 5. 3( b ) x MB = 0, C FA = x [ F] 4 Mx = FA x = [ F] 4 ( 3.5 x - x )

87 70 Mx (3 ) : d Mx d x = [ F] 4 ( x) = 0 x = 1.75 m Mma x = [ F] 4 ( ) = Nm max = Mmax W z = = 98 MPa < [ ] ,,,,,, D 5. 4,, 5. 4,, E = 00 GPa, E = 10 G Pa 5. 4 q = 10 kn/ m, Mmax = 1 8 ql = = 0 knm Mmax = M+ M,, M E I = M E I I = = cm 4 I = ( ) = 700 cm 4 M = 40 3 M = M knm, M = 0 3 knm

88 71 max = M, max W = M W = = = M Pa = 3.70 MPa,,, Mmax = M+ M,, MM 5. 5 ( 5. 5 ), l = 10.5 m, 36 a, I z = cm 4, W z = 875 cm 3, [ ] = 140 MPa, 1 kn, 50 kn,,, 5. 5 ( b), L 5. 5 (1 ), Mmax = 1 4 Fl = (50 + 1) = knm : Iz = = cm 4 max = M max ymax I z = = MPa < [ ] ( ), Mmax [ ] W z = = 1.5 knm x, x, Mx = l - x ( ) 10 3 x = l 6 x x = 0 x = = 7.86 m.64 m

89 7 L = 5. m,,, ; x,, x , T, : (1 ) ; ( ) ; (3 ) 5. 6 (1 ) I z : Iz = = cm 4 ( ) : A,,, t = = Pa c = = Pa B,,,, (3 ) max : t = = Pa c = = Pa tmax = 57.6 M Pa ( A ) cmax = 69.1 M Pa ( B )

90 73 max = Pa = = Pa ,, S * z *, ( a) q = 1. kn/ cm: (1 ) m - m, 5. 7 ( b) ; ( ) A, B, C, 5. 7 (c) ( A, B, C 4 cm) ; (3 ) 5. 7, ( 5. 7 (e) ) d x, FN = qx M = qh x F * N1 = MS * z I z F * N = ( M + dm) S * z I z + FN bh ( h + ( FN + d FN ) bh Fx = 0 - y) b ( h - y) b

91 74 FN - F * N1 - qd x + bd x = 0 d M S z * I z + d FN h ( h - y) = ( q - b) d x = q b - d M d x S * z bi z d M d x = qh, d FN d x S * z = 1 - d FN d x ( h - y) bh = q, Iz = bh3 1 h 4 - y b y h =, (1 ) y = 0, = 0, = - = q b q 4b = q b ( ) y = 4 cm, = 1 6, = 0; y = - 4 cm, = ( c) ; (3 ) y = h, = 1, = q b ; y = - h, = = M Pa, 5. 7( b ) ;, = q/ b = M Pa,, = ( d ),,,,, ,, M, 5. 8, : Ew, Es (1 ) ; ( ) :,, 5. 8 (1 ) = y ( a)

92 75 Fx = 0, h 0 - ( h - h ) 0 w = Ew y, A1 Ew w d A + s = Es y s d A = 0 A y bd y + h 0 + h/ 6 h 0 Es y bd y = 0 ( b) (c) ( b ) h0 = M = A y d A w = Ew A1 A 1 y d A + Es 3 h( Ew - 6 Ew + Es Es 36 ) yd A + A s yd A = w = s = A y d A = 1 [ Ew I1 + Es I ] (c) ME w y Ew I1 + Es I MEs y E w I1 + Es I, E1, E, A1, A,, = y,,, FN E1 = A1,, E1 E M = A1 y d A + A y d A + E A yd A = 0 y d A =, E1 I1 + E I ( a), l = 300 mm, F = 500 N,, Ew Est = 10 GPa, = 10 GPa, (1 ),, z,= Est b1 Ew = ( ) ( 5. 9( b ) ), = 1, = 1 0 = 40 mm

93 76 y = y = ( ) - 14 = 38.5 mm = 14 mm I z = (3 ) : w, max st, max = = mm 4 Mmax y Iz M max y1 Iz = = = Pa = 10.3 M Pa = = Pa = 78.7 M Pa ,,, z,= Est,,,,, st, max = Ew Mmax y1 I z T, A ( ), B, F = 5 kn, I z = cm 4 (1 ) F, t, max, ; ( ) F, c, max, ; (3 ) max ; (4 ) B [ ] = kpa, d = 0 mm, (1 ) F A B,,,,

94 77 t max = = Pa = MPa ( ) F A B, F, F AB, F, c, max c, max = t, ma x = M M t, max = t, max, F, 14.4 MPa = M Pa = 14.4 M Pa (3 ) F A,, FS = F,,, max = FS S* z I z b = = M Pa (4 ) F B, FS F,, = P A = = 39.8 MPa < [ ] ,,,, A - A, 5. 5., 5. 3 Z, 5. 3( a), ( b ),

95 ( a), T ( ) , O, A,, 5. 6, a = l/ 4 (5. 6 ) d, D, [ ], E, D 5. 8 h, b, Me 5. 8( a),?, h/, b (

96 79. 8( b) ) 5. 8( a)?? , q(n/ cm),,, x, ( a),, (1 ) x ( 5. 10( b ) ) ;

97 80 ) AD, (1 ) ; ( ) q = 60 kn/ m, a = 1 m,? , m, q = 6 kn/ m, 1 m,,, 5. 1 (1 ) ; ( ), 5. 1

98 ABC 5. 13,, [ t ] = 3 MPa, [ c ] = 80 M Pa, [ ] = 5 M Pa, z, I z = mm 4 (1 ) ; ( ) Iz ( ) ; (3 ) ; (4 ) ; (5 ), T?? cm, 0 cm, 1 cm, 5. 14,,, E = 0 E 5. 15,, E1 [ ] = 1 M Pa = 11 GPa, [ 1 ] = 14 M Pa; E = 8 GPa, , l, b, h, h 6, h 3, h,, F E, [ ],

99 8 E, E, ( ) E1 > E,?

100 (1 ), ( ) (3 ) (4 ) : (1 ) ( ) (3 ) : (1 ), ( ) (3 ) 6. (1 ) ( ) wmax [ w] (3 ) max [ ] (4 )

101 (1 ) :, w = w( x) ( ) :, 1 ( x) = M( x) EI, ; l/ h 5 ; (3 ) :, : tan= d w d x, w, ;,., d w d x 1, d w = d x M( x) EI, w, x, 3.,,, : (1 ) ; d w = d x M( x) EI = d w d x = M( x) d x + C EI M( x) w = d x d x + Cx + D EI ( ) ; (3 ), 4.,

102 85 (1 ), ( ), 1 = M EI, w max [ w] max [ ],,,,,, ,, h1 h (), q, 6. 1 wc (1 ),,, 1 ( x) = M1 ( x) E1 I1 = M ( x) E I ( 1) 6. 1, M1 ( x), M ( x) 1, I1 I (1 ) ( ) M1 ( x) + M ( x) = M( x) = 1 ql x - 1 qx ( ), M1 ( x) = M ( x) = E1 I1 E1 I1 + E I E I E1 I1 + E I M( x) M( x) Ei Ii w i= Mi = Ei I i E1 I1 + E I M( x) ( i = 1, )

103 86, w = w= M( x) E1 I1 + E I M( x) E1 I1 + E I ( ) wc = - 5 ql EI = - 5 ql E( I1 + I ) = - 5 ql 4 3 Eb( h h 3 ) :, EI = E1 I1 + E I, E 6., 6. (a),, 6. ( b), MC C, BC, A C, B C/ B EI ( x) = x 0 M( x) d x + C C, x = 0, C = EI (0 ) = EI A EI C = EI EI B = EI ( l1 ) = l 1 0 ( l1 + l ) = l 1 + l 0 M( x) d x + C M( x) d x + C = l 1 o M ( x) d x + l 1 + l l 1 6. M( x) d x + C EI ( B - C ) = EI C/ B = l 1 + l l 1 M( x) d x = 1 MC l C/ B = MC l EI = A E I,, A/ EI, = AMC E I A M ( x), MC, M( x) M( x), 1, = A E I 6. 3, 6. 3 (1 ) ; ( ),

104 87 FA = 1 l ( 1 ql 1 3 M( x) = ql 6 x EI w= - M( x) = - EI w= - EI w = - l) = ql 6 () q l x3 ql 6 x ql 1 x + q 4 l x 4 + C ql 36 x3 + q l x3 q 10 l x5 + Cx + D x = 0, w = 0 x = l, w = D = 0, C = 7 ql3 360 wmax, EI w = - ql 36 x3 + q 10 l x5 + 7ql3 360 x = qx 360 l ( - 10 l x + 3 x l 4 ) EI= - ql 1 x + q 4 l x4 + 7 ql3 360 = 0 - l x + x l4 = 0 x = l wmax = ql4 EI, ;,, w, ( a), : (1 ) ( x = 0 x = l) ; ( ) ; (3 ), w = q0 x 48 EI ( l3-3 lx + x 3 ) w = q0 x 48 EI ( l3-3 lx + x 3 ) ( 1)

105 88 w w= w= q0 48 EI ( l3-9 lx + 8 x 3 ) q0 4 EI ( - 9 lx + 1 x ) q0 ( - 9 l + 4 x) 4 EI w= q0 EI, (1 ) ( ) (3 ) M( x) = EI w= q0 4 ( - 9 lx + 1 x ) ( ) FS ( x) = EI w= x = 0, w( 0) = 0, M(0 ) = 0, FS ( 0) = - 3 q0 l 8 x = l, w( l) = 0, M( l) = q0 8 : (1 ), FA = 3 8 q0 ( - 9 l + 4 x) ( 3) 4 q( x) = EI w= q0 ( 4) l, FS ( l) = 5 q0 l 8 q0 l (), FB = 5 q0 l 8 ( ), FS ( x) = 0, () M( 3 8 q0 ( - 9 l + 4 x0 ) = 0 4 x0 q0 l) = 4-9 l 3 l 8 = 3 l ( 3 l 8 ) = - 9 q0 l 18 M 3 8 Mmax = l < q0 l 8 q0 l 8 FS, max = FB = 5 8 q0 l (3 ) q0 B q 0 l 8 ( )

106 89. 4( b ) 6. 4 d M( x), d x EI w= M( x),, = FS ( x),, d FS ( x) d x = q( x), EI w= FS ( x), FI w= q( x) AB,, b, h,, F, C - C : E l,, b, h, F, 6. 5 ( 1) F AB, q = F, 6. 5( b), l ( 6 = 5 ql4 384 EI = 5 5 (c) ),, 384 F l 1 l4 = 5 F Ebh 3 16 Eb l h 3

107 90 F 16 Ebh 5 l ( ) AB max Mmax = Mmax W = Fl/ 4 bh / 6 = = ql 8 = F l 3 l 8 = Fl 4 3 Fl = 3 l 16 Ebh bh bh 5 l 3 = 4 Eh 5 l Fq,, 6. 5( b ), q = F/ l F, 6. 5( c) F, r, A, EI, l, F E I rl B, AB, 6. 6 AB,, A F0, A F0 l, 1 = 1 A r, 1 r = F0 l EI F0 = EI rl F > EI (F > F0 ), AC, AC x, rl C 1 C = 1 r x = l - = F( l - x) EI EI Fr = Frl - EI Fr

108 91 C B w B ( 6. 6( b ) ),, wb1 wb wb3 w B = wb1 + wb + wb3 C B, wb1 = wc = - ( r - rcos C ) = - r( 1 - cos C ) = - - r sin C r C = - x r = - ( Frl - EI ) F r 3 C C B, wb = - C ( l - x) = - - Frl - EI Fr l - r x r ( l - x) = Frl - EI Fr x r = - BC, F B w B3 = -, B F( l - x) 3 3 EI = - wb = wb1 + wb + wb3 = - - ( Frl - EI ) F r r l - E I 3 F r F EI Fr 3 EI 3 = - = ( Frl - EI ) EI F r 3 FE I 3 F 3 r 3 ( Frl - EI ) EI F r 3 + E I 3 F r 3 =, ( ), 1 = M,,, EI, 6. 7,,,, 6. 7( c),,, E1, E, y I y1, y I y : (1 ) 1, 6. 7 (a) ; ( ) F w B, 6. 7( b) (1 ),,, 1 = E1 = z, z = z E

109 9 M 1 zd A1 + A 1 zd A = 1 ( E1 Iy 1 + E I y ) A ( ), 1 w w= 1 = M( x) E1 I y 1 + E Iy = M E 1 I y 1 + E Iy F( l - x) E1 I y 1 + E Iy w= F E1 I y 1 + E Iy ( lx - 1 x ) + C w = F E1 I y 1 + E Iy ( 1 lx x3 ) + Cx + D x = 0, w= 0, C = 0 x = 0, w = 0, D = 0 x = l, wb = w = F E1 I y 1 + E Iy ( 1 lx x3 ) Fl 3 3( E1 Iy + E I y 1, F = ) 3( E1 Iy 1 + E I y ) l 3 wb 6. 7,,,,,,,, 6. 8 AB, L, F,, 6. 8( a), A F/ 4, : (1 ) ; ( ) A (1 ) A F/ 4, a( 6. 8 ( b) ),,,, x = a

110 93 FS 6. 8 q = F L, Fy = 0, MC = 0, F 4 + FS - qa = Fa - q a = 0 q = F L, a C FS a = L, FS = F 4, 6. 8 (c), Mmax = qa 8 = Fa 8 L ( ) A EI w= M( x) = q ( L x - x ) EI w= q EI w = q L L 1 x3 - x = a, w= w = 0, ( 1), ( ), q q L 1 a3 - L 4 a - x x3 + C1 ( 1) 1 1 x4 + C1 x + C ( ) 1 3 a3 + C1 = a4 + C1 a + C = 0 C1 = q a a 3 - L 4 = - FL 96 C = FL3 384

111 94 EI w x = 0, A w A = qx 3 4 FL EI ( L - x) - ql3 96 x + ql4 384 wa = Fa3 48 EI,,,, C,, , A, C ;, B F, = , B w B =? 6. 9, W = = M W I h = I h M = W = E I h,, C MC = = E I h MC = 3 Fl = E I h F = 3 MC l = 3 l E I h wb = Fl3 3 EI

112 95 wb l 3 3 EI 3 l E I h = l h = ( ) = ,,, ( a), AB CD BD, AB CD EI, l, F m (1 ) AB CD, 6. 10( b ), ( b), B = B = D = 0 FS l EI ( ) AB CD, m = FS l, wb = - m = FS l ml EI = 0 wb = wd = FS l3 3 EI - m = 6 EI l FS = ml EI = 1 EI l 3 (3 ) AB CD ( ( b) ),, F - FS = FS F = FS F = 4 EI l 3 AB CD, B D,,

113 (a) w1 = 5ql4, 6. 1 ( b ) 384 EI w = ,,,,,, ( a), ( b ), (c), ( d ), ( ) 6. 3

114 , EI,, y = - ax 3,,? , AB b = 40 mm, h = 60 mm, E = 10 G Pa, : (1 ) S 1 ( 1/ 100 mm), F? ( ) AB = , F? ABC 6. 6, AB BC E I, AB q, A w A () ( ), EI = ( EI = ), B, k , AB, EI, l,, w, l, t, : w ( ) :

115 98 w t l AB CD, C, (1 ) ; ( ) EI, A A w C 6. 1 ABCD 6. 1, AC I, CD I, E, D , E1, h1, 1, b = 1, E, h,, b = 1, 1 >, t,, B wb t , (l), h, T1, T ( T > T1 ), (, E, ),, AB, EI, B BC, C, k, FC

116 , EI, EA,,,

117 (1 ), ( ), (3 ), (4 ), (5 ) (6 ), (7 ) : (1 ) ( ),, : (1 ) ( ) (3 ), 7. (1 ),

118 101 ) (3 ) (4 ) (1 ) : ( ),,, ( ) :,,, 1 3 (3 ) :,, ;, ;,. (1 ) : ( 7. 1 ) = 1 ( x + y ) + 1 ( x - y ) cos- x y sin = 1 ( x - y ) sin+ x y cos 1= 1 ( x + y ) + ( x - y ) 4 + x y = 1 ( x + y ) - ( x - y ) 4 + x y t an 0 = - x y x - y :

119 10 ; ;,, 1, 1,,, 1, 3 ; 0, 180, ( ) : C ( x + y,0 ), R = : ; ( x - y ) 4 + x y, ;, 3. max = 1 ( 1-3 ),, 4. x = 1 E [ x - ( y + z ) ] y = 1 E [ y - ( z + x ) ] z = 1 E [ z - ( x + y ) ] x y y z zx = x y G = yz G = zx G

120 103,,, =, E 5. v= v= 1 E [ ( ) ] vd 6. = vv = 1-6 E ( ) = E [ ( 1 - ) + ( - 3 ) + ( 3-1 ) ] 1 ( x + y ) + 1 ( x - y )cos- 1 x y sin 1 = 1 ( x - y ) sin+ 1 x y cos 1 = 1 ( x + y ) + 1 ( x - y ) + x y : = 1 ( x + y ) - 1 tan 0 = - ; ( x - y ) x y x - y + x y, 1 1, x, y, x y x, y 1 x y 7. max [ ] max [ ], : [ ] [ ],

121 104 8., (1 ) ( ) : r1 = 1 [ ] ( ) ( ) : : r = 1 - ( + 3 ) [ ], 5 % ;,,, 9. (1 ) ( ) : r3 = 1-3 [ ] ( ) ( ) : () : r4 = ; 1 [ ( 1 - ) + ( - 3 ) + ( 3-1 ) ] [ ] ( a), (1 ) A, B, C, ( ) A, B, C (3 ), (4 ), ( ) B, C ( 1), C, 7. ( b ) ( ) B, C, 7. (c) (3 ) 7. ( d) (4 ),, 1, 7. ( e),,

122 = , = , E = 00 GPa,= 0.3, d = 10 cm, Me 7. 3, = = 1 [- E ( - ) ] = E ( 1 + ) E = =, E = MPa 1 + = 50 M Pa = - sin ( 1)

123 106 (1 ) ( ) sin (45+ ) = cos ( ) ( ) + ( ) = = ( ) + ( ) = 100 MPa Me = Wp = = 19.6 knm,,,, 1 +,, E 7. 3 R = 0 mm, t = 10 mm, 7. 4( a), E = 00 G Pa, G = 77 GPa, = 0.3, max = 100 MPa, : (1 ) A x =? y =? ( ) 7. 4 (1 ) 7. 4( b) max = 100 M Pa, - max = MPa 7. 4( c), 7. 4( d),, 1 = max = 100 M Pa = y 3 = - max = MPa = x x = 1 E [ x - y ] = 1 E [ - max - max ] =

124 ( ) = y = - x = ( ) ( ) z, ( ), z = 1 E [ - ( - max + max ) ] = 0 z= 1 E [ - ( - + ) ] = 0,, 10 mm, ,,,, ( a) D, Me F, Me F,?FMe E, G, 7. 5, 7. 5( b ) (1 ) F = F A = F D 4 F = D 4 E 0 = E 0 ( ) Me,, 7. 5( c), 45= 45 E 45 - E 45= + = + = M e Wp + F A

125 108 5 = - + = - Me Wp Me = + F A E 1 + ( ) Wp Wp = D3 16, 45 (),, + ; , ( a), 7. 6( b ), ( b) x - y, ( 7. 6 (c) ), x, y x y x x+ y = y = x- y cos( - 90 ) - x ysin( - 90 ) = 0 - ( - 10 ) ( - 1 ) = ( - 10 ) 1 = 0 M Pa x y = 0-0 ( - 1 ) + ( - 10) 0 = 10 M Pa ( 7. 6 (a) ( b ) ) x = x1 + x = = - 30 M Pa y = y1 + y = = 30 MPa x y = x y1 + x y = = 30 MPa

126 109 1 = x + y ( x - y ) x y = + 30 = 30 = 4.43 M Pa = 1 - x y arctan ( x - y = 1 arct an = 8 ) - 3 8, (, 7. 6 ( b) x, y, x y), ( x, y, x y ),, 7. 6 AB 7. 7 (a), Q35, [ ] = 160 M Pa, 0 b, : I x = 500 cm 4, W x = 50 cm 3, I x S x = 16.9 cm () (c), max = = 144 MPa < [ ] F( m - m ), F = = 17.6 MPa F = ( ) ( ) 10-9 = 9. MPa r 4 = = M Pa < [ ]

127 110 max = = 39.4 MPa r4 = = 68. MPa < [ ],,,,, ; m - m, ; ( ),,, 7. 7, q ( 7. 8 (a) ) 7. 8

128 111 1 ) ; ( ) l ), ( : (1 ) : q ( 7. 8( b) ) ( 7. 8 (c) ) FS, max = q l + b Mma x = ql Tmax = qb 8 l + b l + b ( ) ( ), 7. 8 ( d) l : 1), 7. 8 (e) ; ),, 7. 8( f),,,,, , b, h, 7. 9 ABC, F, E, ABC BC lbc 7. 9 x = F bh x = x E = F bhe y = - x = - x y = 0 F bhe BC = x cos + y sin - ( x y ) sin= F bhe ( )

129 11, lbc l BC ABC AB C = 3 BC l BC = F (3 - ) be = x - y sin+ x y cos (1 + ) F bhe ( ) x, y, AB C,,, : = x cos = = x sin = 3 4 x (= 30 ) 1 4 x = 1 E [ - ] = = x sin= 3 4 x 1 E [ 3 4 x - x 4 ] = x 4 E ( 3 - ) = F lbc = G = = l BC = 3 4 x = 3 E ( 1 + ) F be ( 3 - ) F (1 + hbe ) 4 bhe (3 - ) , E,, A, 90, F E= E= - - E(+ ) = ( 1 - ) ( + ) + = = F A F = A(+ ) = EA 1 - ( + ),

130 A60, A 7. 11( a), F A ( b ), - ( = F = cos ) = F = = 1-3 F = 1 - sin cos [ - (10 - ) ] 1 = 5 F, = F, = ( c), - 1 0= F = F + y + F - y cos( - 40 ) - 3 Fsin ( - 40 ) 1 = F + 4 F y = 4 F F - 4 F + ( 3 F) = = 1 arctan [ - ( + 3 F) F - 4 F ] = 1 arctan( + 3 ) = a( F, 3 F) b( F, - 3 F), 60, ab bac = - 60, C, C, Ca, ( d): 5 F F 1 = 5 F, = F, 1 = - 60, = 30,,,,,

131 , 1,, 3, max 7. 7.,,, p,?? p = Pa , 7. 4, a A, ( : M Pa)

132 M FS (7. 6),,, D = 1 cm, t = 4 mm, p = 6 MPa, Me = 4 knm, : (1 ) ; ( ),?? (3 ),? ( )?0 mm, ,, F FN, E = 10 5 M Pa, = 0.3, A, D 3 0= , 6 0= (1 ) D ; ( ) D , D = 5 cm, t = 5 mm, p = 8 M Pa, T = 15 knm d = 5 cm, 7. 9, E = 00 GPa, = 0.3, AB, AC , l, 45, = , D = 80 mm, d = 60 mm, l = 80 mm, E =.0 10 GPa,= 0.3, : (1 ) T =? ( )

133 ,, A ( ), E G = E, F,?(E,, b, h, l ) ( 1 + ) A x, ,, x, y, x y x 60, 1 0 (7. 13 ) O,, , :

134 117 1 = 3 E (1 - ) ( a + c ) E ( 1 + ) tan 0 = a + c - b a - c ( a - b ) + ( b - c ), a, b, c ; E ; ; 0 1 x 7. 15,, 7. 15, 3 0= 5 MPa, 10= 18 MPa, 30= 34 M Pa, : (1 ) x, y, x y, y x ; ( ) [ ] = 160 M Pa, Me, Me, Me (a), D = 8 cm, d = 4 cm, H - H A, B, ( b) Q35, E = 00 GPa,= 0.3, : (1 ), ; ( ) A, B ; (3 ) B, 7. 17( c),,,? ( M Pa) , x y = u - ( x + y ) (7. 18) cm, 5 cm,, 7. 19,, F ( F = 80 kn), FN ( FN = 30 kn), = 0.3, : (1 ) ; ( ) AA (= 30 ),

135

136 (1 ), ( ) ( ) (3 ) : (1 ), ( ) ; (3 ), : (1 ) ( ) ( ) ( ) 8. (1 ) : xoy Mz ( xoz My, ) ( ) ( ) (, )

137 10 (3 ) (, ) r (1 ), :, ( ),,, :., (1 ) :,, ma x = My W y + Mz W z [ ],, ( ) :,, max = M y + M z W [ ] (3 ) :,, My Mz My Mz, My M z, M = M y + M z, 3. ( ),,,, 4. max = FN A max = FN A + My W y + M y + Mz Wz + M z W [ ] [ ],,,

138 11 r = 1 W M + T [ ] : r4 = 1 W M T [ ] (1 ), ( ) ( ) (3 ), M ( a), A = m, W = m 3, Wp = m 3, [ ] = 134 M Pa, 8. 1 ( b), D My Mz = 10 knm = 8 knm T = 4 knm, FN K, 8. 1 (c) = 0 kn MW = M y + M z = = 1.8 knm W = MW W = = 18.1 M Pa N = FN A = =.5 M Pa = W + N = M Pa = T Wp 1 = ( 3 ) + = 1.93%, = = 0 MPa ( ) + (0) = r3 = 1-3 = M Pa > [ ] = 134 MPa AB,,, r3 = + 4 = W + N = M Pa

139 ( ), 8. (a), 4 m, 1 m, 6 mm, 0.36 M Pa, N/ m, A, B, F = = N q = N/ m F1 = FN = F sin = 5 F F t an = F t an= 1, sin= 5 5 AB

140 13 M F B = pd 4 t - FN A B = = pd t A, = pd 4t A - q 4 + FN 0.5 = 3 4 F = Nm = M Pa () = = 30 M Pa () FN A - M W = = MPa W = 3 D3 ( 1-4 ) 1 = pd t = 30 M Pa A, B 8. ( b) 8. (c) 8.,, B, 1 = MPa, = 30 MPa, 3 = 0 AB C , F T, F

141 14 e AB a b, a = , b = d = 100 mm, T = 3.93 knm, E = 00 GPa, F e,, (1 ) + ( ) a = E a = b = E b = F d 4 F d 4 + Fe d 3-3 Fe d 3 3 ( 1) ( ) F = E( a + b ) d 8 = ( ) ( kn (1 ) - ( ) 64 Fe d 3 = E( a - b ) 8 ) = e = E( a - b ) d3 64 F = ( ) ( ) = 1.3 cm, 8. 3,,,,, 8. 4 AB C, AB BC, 8. 4( a), A, C, s =.1 m, A = 0.1 cm, D, F = 100 N a = 40 cm, l = 1 m, d = 4 cm, b = 1.5 cm, h = cm, E = 10 G Pa, G = 8 GPa, [ ] = 160 MPa,, : (1 ) AB,, ; ( ) AB ; (3 ) C F, 8. 4( b ) W = d3 3 = cm3 Iz = d4 64 = 4cm4

142 15 Ip d 4 3 = 8cm4 I = bh3 1 = 1 cm4 Wp = d3 16 = 4cm (1 ) A, ( 8. 4 (c) ), 8. 4( d ), (e) = M W = = T Wp ( ), Fl W = Fa Wp = 15.9 MPa = 3. M Pa r 4 = + 3 = 16.8 M Pa < [ ]

143 16 3 ) C w C : wc1 = wc = Fal GI p Fl 3 3 EI z = 0.16 cm a = cm wc3 = Fa3 3 EI = 0.10 cm wc = wc1 + wc + wc3 = c m, r4 = 1 W M T ; C, (a), 100 kw, 00 r/ min,, 0 () F1 ;,, [ ] = 80 M Pa( sin0= 0.34, cos0= 0.94 ), T = P n = F1 ( 8. 5 ( b) ), = Nm F1 F1 F1 = F1 cos0 D1 = T T 4.77 = D1 cos = 16.9 kn F1 y = F1 sin0= = 5.79 kn F1 z F, = F1 cos0= = 15.9 kn ( F - F ) D F 8. 5( c) = T D = = T F = = 8.6 kn = 9.54 kn

144

145 18 My, Mz Fz 8. 5 ( d), MA = 0, = ( f), M B Fy FAy = = 0, FBz = F1 z 0.5 = = 3.98 kn FAz = F1 z + FBz = = 19.9 kn = 0, FAy -.5 F1 y - 3 F 1 = 0 3 F +.5 F1 y = FBy - 3 F + FA y - F1 y = 0 = 1.54 kn FBy = 3 F - FA y + F1 y = = 1.85 kn M8. 5 (e), ( g), ( h ),, M = M y + M z = = knm T = 4.77 knm 1 W M + T [ ] W = d3 3 M + T = = 14.7 knm d d 1 mm = mm 3,,,,, ( z ) ( y ),,, ABC,, D = 80 mm, d = 70 mm, [ ] = 100 MPa, F1 = 4 kn, F = 1 kn, (1 ) Ax y z, A F1 F1 z Mz = F1 ( ) 10-3 = = Nm, x ( ) F x, FN = = N

146 19 T F = 17. Nm My = F = 551 Nm (3 ) (4 ) M = M y + M z = 1 69 Nm r3 = + 4 = M W + FN A = ( ) = ( ) 1 - T Wp = ( ) = Pa = Pa r3 = = 84.4 MPa < [ ] 8. 6,,,, ( ), r3 = 1 W M + T,,,, ( a) AB,

147 130 Fx Fsin = 5 sin30= 1.5 kn ( 8. 7 ( b) ) Fy = Fcos= 1.6 kn N = Fx A = = 0.6 MPa () Mma x = 1 4 Fy l = W = Mmax bh C, 6 3 = 18.7 knm = = 7.8 M Pa c, max = - ( ) = M Pa C, t, max = = 7.8 M Pa 8. 7 F C, 1 4 Fy l F x,, ; C,, 8. 8 D = 40 mm, FN T, 8. 8( a), 10 4, , FN, E = 00 GPa, = 0.3 T, 8. 8 ( b) FN, 8. 8 (c), R1 T 1 3, 1 ; R 3 1,

148 131, R1 1, R1, R, t = t (1 - E ), t = FN D t, R t : : : = 1 + t - ( t - 1 ) = 1 = 1 + t + ( t - 1 ) = t = , = , 1 = 1 (1 + ), E T = E 1 D = t = = = T W p = Nm

149 13 FN E t D 1-4 = 35.9 kn,,, ;,,, (a) M T, A 0= , B = W = 600 mm 3, E = 00 GPa, = 0.5, [ ] = 160 MPa, M T, 8. 9 (1 ) A 8. 9( b ) A = M W = E 0 M = W E 0= = 60 Nm ( ) B 8. 9 (c) T = 45= 1 E ( ) = T = E E EWp = EW = (3 ) Wp r4 = 1 W M T = M Pa < [ ] = 86.4 Nm,,, 45, (),,, ABC, (a), d, AB = BC = l, A, C F F,, (1 ) BC B ; ( ) AB B ; (3 ) AB A () (1 ) Ax y z, 8. 10( b ) AB, xay x A z,

150 133 A My = FL, Mz = FL, T = FL ( = Mx ) BAB : My = FL, T = FL ( = Mx ) ( ) BC y A z x A z, BBC : (3 ) : BC B B BC, AB B B AB, AB A : Mx = FL, My = FL M = M x + M y = FL, T = 0 r 3 = 1 W M + T = 3 FL d 3 r 3 = 1 W M y + T = 3 ( FL ) + ( FL ) = 3 FL d 3 d 3 M = M y + M z = FL T = FL r 3 = 1 W M + T = 3 3 FL d 3,,, AB B B C B ; A AB, A r3 = + 4 = FN A + M W + 4 =

151 134 F d + FL 3 d FL 16 d 3 1 d 3 (3 FL + 4 Fd ) + ( 3 FL ) BC, B, BC ; AB, C B, AB 8. 5 = ( a), ( b) : (1 ) ; ( ), ( ) ; (3 ) ( a), ( b),,, F = 1 kn ,, () 8. 4 d, F1, F T, 8. 4,

152 d 8. 5, 8. 6, F = 90 kn, 10 mm, : (1 )? ( ) ( 8. 6 ),???( ) AB ( 8. 7( a) ) CD (8. 7( b) ),? 8.8, ( ), F, 8. 8 (a) E1 = M Pa, E = M Pa, b = 10 mm, h = 40 mm: (1 ) m - m, = (8. 8 ( b) ),, F e ( ) m - m ( 8. 8 (c) ),, F e , d A B, B m = Fd ( ) F() E, ( ) = 1 3 O a 45O b a b , Z, Fy = 4 kn,

153 Iy = m 4 ; I z = m 4 l = 3 m

154 ,, B, l = 500 mm, E = 00 G Pa, BC 50 mm100 mm, AB D = 10 mm, d = 80 mm, C F, AB 45 = 10-4, F? F, C w C? ,, F, d = 4 mm, E = 00 GPa, a = , b = F e , AB, d = cm, l = 0.3 m, a = 0. m, [ ] = 140 M Pa AB ,, A = 45, E, b, h F , d = 8 cm,

155 [ ] = 160 MPa

156 , Me = 3 Me1 = 900 kn mm F = 0.5 kn, Me1, Me C, B F d = 50 mm, l = 1 m, E = M Pa, = 0.8 a 45a B (a), 1 Me = 480 Nm,, 8. 18( b ) D1 = 80 mm, D = 100 mm, : F1 = 1 kn, Fr 1 = 4.4 kn ; F = 9.6 kn, Fr = 3 kn; Fa = 1.75 kn [ ] = 80 M Pa (1 ) ; ( ) ( ) 8. 18

157 (1 ), ( ) (3 ) (4 ) : (1 ) ( ) (3 ) (4 ) : () 9. (1 ) ( ) ( ) ( ) (3 )

158 (1 ) : ( ) : (3 ) : (4 ) :, k, k = k = A F V= l N ( x) EA d x T V= ( x) l d x GI p M V= ( x) l d x EI F V= k l I, : F V= N l EA d x + T l GI p k l F S y GA d x + k FS z l GA d x S ( x) GA d x ( S * z ) d Ak = 6 A b 5, k = 10 9, M d x + y l d x EI + y l M z d x + EI z (1 ),, ( ), ( ), (3 ),. V ; Fi FN V=d(l) l + T FS l d+ l Md+d l i = V Fi ; i : (1 ) ( ),,

159 14 i FN l FN EA Fi i = V Fi 3. M y T T d x + l d x GI p F + i l E I y My Fi M z d x + l i, FN, T, My, Mz : FN = l EA F N d x + T l GIp M y Td x + l Mz M y d x E I y + l E I z E I z Mz F i M z d x (1 ) ( ),, FN, T, My, Mz i = FN d(l) l + T l d+ M y d y l + Mz d z l, d(l), d, d y, d z (3 ) FN, T, My, Mz ; FN, T, My, Mz 4. i = 1 EA F N FN C d x + 1 T T C + 1 M GI p EI y M yc + 1 M MzC z y EIz, F N, T, M y, M z ; FN C, TC, MyC, MzC : (1 ), ( ),, i M Ci (3 ), MC (4 ),,, (5 ) MC 5. (1 ) F1 w1 = F w1 F1 F w1, F F1 w1 ( ), F1 = F, w1 = w 1 1 w1, 1 w1

160 ( a) U, l,, F1 F A D ( FN FS ) 9. 1 ( 9. 1( b ) ), AB, BE, F A, D A D = l F 0 EI y d y l FB = FC = F1 M( y) = F y M ( y) F = y M( x) = F l - EI ( F M ( x) F l - F1 = l A D = 0 5 F l 3 3 EI = F1 x x) ld x = F l3 3 EI F1 l3 8 EI F1 = 40 3 F + F l3 EI - F1 l3 16 EI,,, F, F, F (a), AB C F, AB BC, EI, C F, 0 <

161 144, 9. F, FF = 1, F M M, 9. ( b) ( c) C = 1 EI FL sin ( 3 Lcos ) - FL sin ( Lcos+ 1 Lsin ) + 1 FL cos ( Lcos+ 3 Lsin ) = sin cos- sin cos- 1 sin + 1 cos sin cos= 0 cos - sin - sin cos= 0 cos- sin= 0 tan= 1, = 4 = 8 ( ), F,, F, F (a) AB, R, d, A, E, B F x F z B w B y (: ), B y F = 1 ( 9. 3 (c) ), w By M, T ; M T = MM E I d x + T T d x GIp

162 145 Fx 9. 3 ( b) ), ( 9. 3 (c) ), Mz Fz ( 9. 3( d) ), I = d4 64, Mz = - Fx R sin = FR (1 - cos ) = R(1 - cos ) My = Fz R( 1 - cos) Mx = Fz R sin Mz = 0 wby = EI 1 0 Mz Mz Rd= EI 1 0 EI 0 Fx R 3 - Fx R 3 sin (1 - cos ) d= ( sincos- sin) d= - Fx R 3 wby = - 18 Fx R3 Ed 4 Fx ( ) Fz (), Mx, My M z,,, Ox y z EI, Mx, My M z,, B F z ( a) A, EI( )

163 (a), A, D F,, A F1, D F, 9. 4( b ), F1 ED M = 0, DC M = F x, BC M = ( ql M F1 M F1 = 0 + F1 - F = 0 ) x - F l - 1 qx, BA M = ( F1 - F ) ( x + l ) - F1 x, M F1 AG M = ( F1 - F ) x, A wa M F1 M ( x) M ( x) = d x = l EI F1 l 1 0 = x = l M F1 EI ( ql x - Fl - qx ) x d x EI ( - Fx ) ql 4 EI ( ) = - ql 4 6 EI = - Fl 3 6 EI l = x l d x =, ( A, D F),, A F F1, U F1 A ; D F F, U, F1, F F, U F F D, A, D, A D (a) D,

164 147 EA a 9. 5 D, D, 9. 5(b),, FN,,, 1 a a, 9. 5 (c),, FN 9. 5( a), FN F N l F N F N F N l F N F N F N l F a - 3 F a - 0 a 0 a F a 1 3 F a 1 3 F a Fa - 3 Fa a 1 a 3 F 3 F Fa Fa Fa a 1 a 1 a 3 F 3 F 3 F

165 148 D wd = 1, 7 EA i = 1, = 1 ( FN FN l)i 7 EA i = 1,, = Fa E A () ( FN FN l) i = 10 F 3 EA,, = FN i F N i L i E A, FN i, FN i, Li, EA,,,,, FN 9. 6, D, E,, F 9. 6( a), 9. 6, 9. 6 (c), q,, (V) F F( AB ) q = q(v) F F ; ( AB ) q q AB q, = 1 - ( x + y + z ) = x + y + z E x = y = z = - q, x = y = z = 1 - ( - 3 q) = x + y + z E x = y = z = - ( 1 - ) q E

166 149 q AB ( AB ) q = ( 1 - ) qd E F 1 - qd = q(v) F E (V ) F = FD( 1 - ) E F1, F, F1 F w1, F F1 w1,, F, q, A, B ; q, F,, A, B, A, B q F (a), Me EI, GI p, A, B, 9. 7 CD,, C, D 9. 7( b ) Me ( 9. 7 (c) ) 9. 7( d ) M = 1, A, B, M( ) = Me cos T( ) = M e sin M( ) = 1 cos T ( ) = 1 sin

167 150 AB Me 4 0 cos 1 cos EI Rd+ Me sin 1 sin Rd = 0 GI p Me R + 4 EI Me R 4 GI p ;, 1/ 4, , q,, E, A 9. 8 (1 ) A : A, 9. 8 ( b), x M( x) = - q h x, A, FN ( x) = qx M( x) = - x, FN ( x) = 0 wy = EI 1 l 1 M( x) M( x) d x + 0 EA l 0 1 EI l ( - q hx 0 FN ( x) FN ( x) d x = ) ( - x) d x = qhl3 6 EI = ql3 Ebh () ( ) A : A, 9. 8 (c), x M( x) = - q h M( x) = h x, FN ( x) = qx, FN ( x) = 1, A wx = EI 1 l 1 M( x) M( x) d x + 0 EA l 0 1 EI l ( - q h 0 x) h d x + 1 FN ( x) FN ( x) d x = EA l 0 qx 1 d x =

168 151 qh l 8 EI + ql EA = - 3 ql Ebh + ql Ebh = - ql Ebh ( ),, A, A,, ( a), ABC t1, t, C wh, wv ( h) t > t AB, BC,, t1, t,, t = t1 t = t - t1, + t, h, d x, 9. 9 ( b), t1 d x, t d x,, (t > t1 ) d * = td x = ( t1 + t ) d x d * = t d x - t1 d x h = td x h (1 ) wv wh C, 9. 9 (c),

169 15 BC M( x1 ) = - x1, FN ( x1 ) = 0 ( 0 x1 l) AB M( x ) = - l, FN ( x ) = - 1 ( 0 x < H), 1 wv FN =d+ * Md * = H 0 ( - 1 ) ( t1 + t ) - ( t1 + t ) H wv, wv d x - tl h = - ( t1 + t ) H + l t ( - x1 ) 0 h d x1 ( l + H) - ( t - t1 ) l ( l h + H t ( - l) 0 h d x = + H) ( ) C, 9. 9 ( d), BC M( x1 ) = 0, FN ( x1 ) = 1 (0 x1 l) AB M( x ) = - x, FN ( x ) = 0 (0 x < H) wh FN =d+ * Md * = l 1 ( t1 + t ) 0 ( t1 + t ) l d x1 - ( t - t1 ) H h + H ( - x ) t 0 h d x = ( t1 + t ) l - th h ( ) C C, 9. 9( e), BC M( x1 ) = 1, FN ( x1 ) = 0 (0 < x1 l) AB M( x ) = 1, FN ( x ) = 0 (0 x < H ) C C FN =d+ * Md = * Md * = l 1 t 0 h d x1 ( t - t1 ) ( l + H) h + H 1 t 0 h d x = t h ( l + H) =,,,,,,,,,,, =

170 (a), r1, r, b,,, A ( ) G r,, r, ( b), M0 = 0, rb rr = r br r= ( r r ) r () V= V vdv = r G r 1 r r 4 v= r G = G ( r r ) 4 rbd r = b r 4 ( A s) G r 1 r r 3 1 d r = b G r r1 ( r - r 1 ) W = 1 r b s = r b s W V, A b G r r1 s = V= W ( r - r 1 ) = r b s r ( r Gr - r 1 ) 1 1,,

171 , G = 3 4 E, a, F I, C w C = 4 Fa3 3 EI 9. 9.,, F1, V( F1 ) ; F, V( F )F1, F?? V( F1, F ) = V( F1 ) + V( F ) ,, M, V( M), T, V( T), V( M, T ), V( M, T) = V( M) + V( T )? ,? V F? 9. 6 wa EI, F, a (9. 6 ) ) 9. 7 abcd FS, 9. 7,, G, AFS (1 ) ; ( ), :

172 d 9. 8, R, O F, OA, O : (1 ) a ; ( ) EI, , Me, EI B F wb = F E I E ; ; I ; 1 3 ( a3 + b 3 ) + C( a + b ) + (1 + ) a b + C I A

173 156 A 9. 1, R0, ( ), e, 9. 1, E,, x , A, EI, C F C ( ) d = 1 cm, / 4, OA, r = 10 cm, O F = 100 N, G = 85 GPa,, O? , F = 500 N, L = 1 m, a = 4 cm, E = 00 GPa B,

174 , C F, 9. 16, b h, l = 10 h, ED AB E I, B, 9. 17, k, F C , BC AD, BC EI, AD EA, C F, C

175 (1 ), ( ) (3 ), (4 ), : (1 ) ( ) (3 ) : (1 ) ( ) (3 ) 10. (1 )

176 159 ) (3 ) (1 ) :,,,,, ( ) :,, ;,,. (1 ),, ( ),,, (3 ),,, 10. 1, ( ),,, 10. 1( b) (c), (a) ( b),, 10. 1( b) B, wb = 0, (c) A = (4 ),,

177 160., (1 ) :,,, ( ) :,,, 1 = 11 x1 + 1 x n x n + 1 F = 0 n = n1 x1 + n x + + nn x n + nf = 0, x1, x,, 11, 1, x1 *, ( 3) : Mn - 1 ln I n + Mn ( ln I n + ln + 1 In + 1 ) + Mn+ 1 ln+ 1 In+ 1 = - 6 ( n an l n I n + n+ 1 bn+ 1 ln+ 1 I n+ 1,, (4 ),, :,, FN, M, FS = 0,, FS, FN = 0, M = (a),, 10. ( b), ) (1 ),

178 161 ) (3 ) ABC, d = 0 mm, C CD, ( C, D ), d0 = 1 mm, 10. 3( a) t = 80, K, : E = 00 GPa, G = 84 GPa = , X1 X1 ( ( b) ) t, 1 1 X1 + 1 t = 0 = ( c), 11 = 1 EI ( b 3 b + a 3 a 3 + b 3 3 EI + ab GI p + a) + bab GI p l E A = 64( a3 + b 3 ) + 3 Ed 4 64 ( ) l1 EA = = 3 ab Gd l Ed m/ N =

179 16 t = - lt = = m X1 = - 1 t = = 43 N K ( d), = M W = = T Wp X1 a d 3 3 = X1 b d 3 16 = = = 3.87 MPa = 8. M Pa,,, X1, C, C w C,, wc = lt ( a) EI a E A, F, X1 l E A ( ) ( b ) F X, 10. 4( c), ( d )

180 163 F 1 F = 1 EI - ( aa ) 5 6 ( Fa) - ( aa ) Fa = EI Fa3 11 = 1 EI, ( aa ) 3 ( a) = a3 3 EI 1 F + X( 11 + a EA ) = 0 X = , 10. 4( e), I Aa (c), ( d) w = 1 EI Fa 3 EI ( Fa a) a - X( I A a F aa ) 1 6 ( a) =,,,,,, ABCDE, C, F, (a) (1 ) ; ( ) CD ; (3 ) ( 1), C X 1, X, ( b), C (), C, C l ( lx X x) xd x = l ( 0 X x) ( - x) d x + l 0 lx 1 ( l) + X ( l) 3 3 = - X [ ( F - X1 ) x - X l] ld x l ( F - X1 ) l l - X l l 4 X X = - X 3 9 X1 + 4 X = F - X1 + F - X ( 1)

181 164 C C l ( 0 X1 x) xd x + l ( 0 X1 l + X x) ld x = l 0 X1 ( l) l X1 l + l X 8 3 (1 ) ( ) (c) ( l) [ ( F - X1 ) x - X l] xd x = ( F - X1 ) X1 + 8 X1 + 4 X = F - X1 3 X1 = - - X l X l l 66 X1 + 7 X = F ( ) 11 F, X = F X1 X, B M B M B = 11 F l = Fl

182 165 A M A D M D E M E ( ) CD M A F F) l = Fl MD = Fl ME = ( F F - 48 F) l = Fl FN, CD = F ( ) (3 ) AB C D E ( d) C, X1 C, X, (a), E, I, A 10. 6, ( b), X1, 11 X1 + 1 F = (c) ( d), 11 1 F :

183 166 1 F = 1 EI - ( 1 1 = 1 EI a ( a a) a + ( 1 a ) 5 6 Fa - 1 X1 = - 1 F = 11 a a 3 a ) + a E A = a 3 4 Fa a - ( Fa Fa) 1 5 Fa 3 a 3 3 EI + a = E A 1 EI 5 Fa 3 1 a3 3 + Ia A a3 3 EI + a E A,, X F a a = EI Fa3, (a) ACB,, d = 11 cm,, C, L = m, F = 7.5 kne = 10 5 G = M Pa, [ ] = 170 MPa : (1 ) ; ( ) Pa, C ( 10. 7( b) ) w1 = w w1 = 1 3 ( F - FC ) L 3 EI w = 1 3 FC E I ( L ) 3 + ( L ) 3 + FC L L GI p L Ip = I, E G =.5

184 167 A M A = MA W z 3.5%, FC B, 16 F = 16 kn 7.5 = ( F - FC ) L = 11.5 = 3 knm = = 176 M Pa > [ ] MB = FC L = 16 knm T = FC L = 16 knm r 4 = M B T W z = (11) = 16 M Pa < [ ], A, 1,, B 3, ( c),,,,,,, F AC C, CB C, AC B C F,, ( a),, (: ),,, 10. 8( b ),,, F, 10. 8(c), ( d) 1 F, 1 1 X1 1 F = [ 1 EI ( 1 Fa 3 11 = [ 1 EI ( 1 a 3 ) ( aa) ( 3 a) ] = - 4 Fa3 81 EI a) ] = a3 3 EI X1 = - 1 F = Fa 3 81 EI a 3 3 EI = 4 7 F

185 (e) 10. 8,, X1,, 45, X1, X1,, ABCD, d, I I p, B, DMe1 = Me,,, (a) AB aa A D bb, EI, GI p 10. 9

186 169 ABCD ( 10. 9( a) ) Me1 = Me = Me AD bb, Mb ( 10. 9( b) ), Mb, Me1, Me Mb, AD, BC, AB, CD, V= M b H EI + M b S GI p + ( M e - Mb ) H EI bb, = 0, = V Mb Mb = Mb H E I H E I + S GI p + Mb S GIp - Me - ( Me - Mb ) H E I H E I + ( Mb - Me ) Mb = Me S GI p H E I ( M e - Mb ) S GI p ( Me - Mb ) S GIp = ( Mb - Me ) S GIp Mb - Me = 0 = 0 ( Mb ) = H E I + aa, 1/ 4, 10. 9(c),, aa Ma Ma = Mb = Me, 10. 9( c) ABCD Me1 Me, AD, BC, AB, CD, AD, BC, AB, CD, V AD, Mb, Mb, 1/ 4 Mb, AB (a) A, B, EI, ( 1), AB, AB, B,,, A, ( ) ( b) (3 ) B, (c) ( b) ( c), 1 F = - 1 EI Fa 5 a 3 + Fa a = - 17 Fa3 6 EI S GI p

187 170 1 = 1 EI aa 4 a 3 + a a = 11 X1 + 1 F = 0 X1 = 17 F 40 (4 ) A, B, B, ( d) AB = 1 EI 0 a3 3 EI 1 17 F a aa F a a - 1 Fa aa - Fa aa = 11 Fa3 40 EI ( A, B ) ,, A, B, A, B, ( ),,,,, A, B, AB 10. 9, F, d CD,, (a) F, Rd, E, CD CD,,,, X1, X, F ; CD,, FN, CD = - X, ( b),

188 171 1/ 4 ( ( c) ),, M( ) = X1 + F Rsin- X R(1 - cos ) M ( ) = 1 X1 M ( ) = - R( 1 - cos ) X, (1 ) B, V X 1 X1 + EI F 0 ( ) B, X1 (- sin ) - = S X1 - FR cos 0 X1 + EI F X1 M ( ) M ( ) d S = 0 EI X 1 Rsin- X R(1 - cos ) 1 Rd= 0 FR X1 + V X = S - X R(- sin) 0 = 0 - X R - 1 = 0 ( 1) M () M ( ) d S = 0 EI X Rsin- X R(1 - cos ) R( 1 - cos ) Rd= 0 + FR sin- X R(1 - cos ) ( 1 - cos) d= 0 FR (cos- cos ) 0 X1-1 + FR 4 ) - X R(- sin+ + 1 sincos 0 = 0 - X R = 0 ( )

189 17 1 ), ( ), CD FN, CD = - X = X = F (- 4) - 8 F ( ), 1/ 4, B, ABCD 10. 1( a), AB, BC CD E I l, BC M, F (1 ) :, 10. 1( a), 10. 1( b),, (c) ( b), A, D, M FN = F,, ( c) A, D (c), M,, X1,, 10. 1( d) M,

190 173 X1, 1 X1 + 1 F = 0 = 1, (e), ( f), 1 1 = EI ( l l 1 F = - l + 1 l EI ( 1 l F l X1 = - 1 F 11 l 3 l ) = - Fl 3 4 EI = 3 F 7 l ) = 7 l3 1 EI 10. 1( b ), (c), ( g), 10. 1( h ) ( ) M :, M B, F, (i),, M w M = wb = MC E I = 1 EI 1 l 3 Fl Fl 14 3 l - l 3 Fl 14 1 l = 5 Fl3 84 EI (), M,, ; ( ),,, ( a) () F, ( b), ( c), ( d), ( e), 10. 1

191 B, C? , F AB C, F w C = 3.33 mmab : 10. E = 00 GPa, CD l0 = 0.8 m, A = 10 mm ( a), ( b), (c), ( d) 11, 1, 1,, 1 F, F EI, Me, l, AC B BD,, B

192 AB( EI ) B F, EA, 10. 7, B M A = - MB,? ( ) ( F = kn, a = 1 m, E = 10 5 M Pa, I = 855 cm 4 )? , AB, F, AB = BC = l, AB I, BC I, EB , AB C, A, C, B, AB, BC l, AB q, : ; B B, EI l d A B, C AB CD, l/, D - ( ), D T E, G , a, BD F,

193 176 AC ,, B H, D, F = 8 kn, d = 0.1 m, [ ] = 150 M Pa, E = 10 5 M Pa, G = MPa : ( 1) ; ( ) () , ABCDE,, d = 4 cm, B = D = 90, q = 500 N/ m, E = 00 GPa, G = 0.4 E, a = 1 m, b = a : (1 ) B M B ; ( ) wc A, B ( ), ACB E I, ADB E IC M C D M D,? , AB, BC, d = 40 mm, B, = 1 3, [ ] = 60 MPa, BC ABCD, , q :

194 177 1 ) ; ( ) B B, EI , EI, ( )= a3 3 EI B FS : EI, q , EI C AB CD 4 m BC,, AB CD E = 00 GPa, I = mm 4, E = 00 GPa, A = 60 mm, = , A, B, C, D,

195 178 AB F B, I, A, E , L A B B, A CD, CD 1, AB a, 1 L0, L0 e E G, AB E I GI p, E0, 1 () E0 A0 1

196

197 (1 ), ( ), (3 ), (4 ) (5 ) (1 ) ; ( ) (3 ) (4 ). (1 ) ( ),, (3 ) (4 )

198 (1 ) ( ) (1 ) :,,,,,, ( ) :,, ;,. (1 ) ( ) c r = E = l,, = 1;,,= ; i,= 0. 5;,,= 0. 7;,,,= 1 i Fc r ( ) ( ) = EI ( l) c r = a - b c r = a1 - b1 :, ;, a, b, a1 b1

199 18 3 ) ( ) : c r = s, u,,,, ( ), P, p s, s,,, :, p = E ;, s = a - s ; p b, s = 0, 3. (1 ), = FN A [ cr ] = cr nst cr, n = c r = Fcr F nst :, nst ( ) = FN A [ ],,,,, ; [ ] :, :,,,,,,,,,,,, ;

200 (a), ABCD, Q35, p = 00 M Pa, s = 40 MPa, b = 400 M Pa, E = 00 GPa d1 = 1 cm, L1 = 100 cm, d = cm, L = 100 cm (1 ) F M A = 0, - F3 a + FN1 sin30 a + FN cos30 a = 0 ( 11. 1( b ) ) FN1 = 3 F - 3 FN ( 1) wc = w B wc = L1 L = L1, wb = sin30 cos30 = 3 3 L L1 = 3 3 L, L1 = 3 3 L FN1 EA1 L1 = 3 3 FN EA L A = 4 A1, L1 = L FN1 = FN = 3 6 FN ( )

201 184 1 ) ( ) ( ) [ F],,, FN =.6 F FN1 = 0.75 F [ ] = s n = 40 = 10 ( M Pa) [ FN1 ] = A1 [ ] = 4 1 [ ] = 9.45 kn [ FN ] = A [ ] = 4 [ ] = 37.7 kn [ F] = [ FN1 ] 0.75 = [ F] = [ FN ].60 (3 ) [ F] Fc r = [ F] = 1.6 kn p = E 100 p = l = i d/ 4 = EI = ( l) [ FN ] = Fcr nst (4 ) = 1.6 kn = 14.5 kn = 00 > p = 7.75 kn [ F] = [ F N ] = 15.5 kn =.98 kn,,,,,, ( a),,,,, C,, : (1 ) ; ( ) A F (1 )

202 ( FN1 ) cr = EI =.04 EI ( 0.7 l) l ( FN ) cr = ( FN3 ) cr = ( FN1 ) cr ( FN ) cr =.7 EI = 0.75 EI ( l/ cos30 ) l,, ( 11. ( b ) ) Fx = 0, FN = FN3 ( 1) Fy = 0, FN1 + FN cos+ FN3 cos= F FN1 + FN cos= F ( ) ( 11. ( c) ) ( ) ( 3) FN1 = FN = l1 cos= l FN1 l E A cos= FN l/ cos E A FN1 cos = FN ( 3) F 1 + cos 3 = F Fcos 1 + cos 3 = 0.36 F FN1 FN = 1.33, FAB A D,, AC, ( ) F Fcr AB AD A C, AB AD, F A C,, Fcr = ( FN1 ) cr + ( FN ) c r cos=.04 EI l + (0.75 EI )cos30= l

203 EI l = 3.96 EI l,,,, AB AD, AC,, F C, A, B, C, CF D = 10 cm, d = 6 cm, q ( kn/ m),, q n = 3, Es = M Pa; Ec = MPa, p = 30 M Pa, b = 600 MPa I 36C I x = cm 4, Iy = 61 cm 4, A = 90.7 cm F,, C L, F = 1 + Es ql Ec ( 5/ 8) ql wcq - wcf = L ql 4 Es I x - 48 HI x A C L 3 = 1 48 = ql FL 3 Es Ix = FH Ec AC 5 8 ql ( 10-6 ) , q (1 ) : = F A C [ ] = b n = = = 00 M Pa 0.611qL ( 10-6 ) 10-4 q 05.6 ( kn/ m ) ( ) : I = 64 ( ) = m 4 = i = p = Ec p I AC = = D + d = = 80.3 =.9 cm

204 187 H i = ,, Fcr = Ec I (H ) = 171. > p = = 53 kn 5 F = ql Fc r n q 17.3 kn/ m, [ q] = 17.3 kn/ m = 3,, Fc r ( EI ) m - n, EI d d w = M 0 d x EI M( x) = M0 - Fw w = M( x) = d x M0 - Fw - Fw E I k = F E I = k M 0 F - k w d w + k w = k M0 d x F w = asin kx + bcos kx + M0 F w= akcos kx - bksin kx x = 0, w= 0, a = 0 x = 0, w = 0, b = - M0 F w = M0 F ( 1 - cos kx ) x = l, w = 0, 1 - cos kl = 0 cos kl = 1 kl = n n = 1,, ( n = 0, F = 0, ) k = n = l F E I F = ( n) EI l

205 188 n 1, F = Fc r = 4 EI = EI l (0.5 l),,,,, (a),,, EI, 11. 5, 11. 5( b ),, M0 ( 11. 5( c) ), M( x) = Fw - M0 EI w= - M( x) = - Fw + M0 w+ F E I w = M0 EI F E I = k w+ k w = k M0 F w = Asin kx + Bcos kx + M0 F w= kacos kx - kb sin kx x = 0, w= 0 = 0 + B + M0 F B = - M0 F

206 189 x 0, w = 0 = ka - 0 A = 0 w = M0 F (1 - cos kx ) w= km0 F sin kx x = L, w= km0 F sin kl = 0, w = = M0 F sin kl = 0 kl = n ( n = 1,, 3) ( 1 - cos kl ) n = 1, Fcr k = L = F E I = EI, = M0 L F ,,,, AB CDE d BD ( (a) ), [ ] = 80 MPa, AB : b = 30 mm, h = 40 mm, CDE : b = 30 mm, h1 = 60 mm, BD a = 0.6 m, d = 1 mm, l = 1 m F ( 1) :, 11. 6( b ) BD FN, BD,, B, D FN = F + I AB I CE F + ( h h1 ( F - FN ) l 3 3 EIA B = ) 3 = = F + bh3 / 1 bh 3 1/ 1 FN ( l) 3 48 EI CE = F + ( ) 3 = F ( ) : AB,, M max = ( F F) l = 0.19 Fl

207 190 max M W = 0.19 Fl bh / 6 = Fl bh F bh [ ] l = [ ] = 4.96 kn CE,, Mmax max = FN = Mmax W l = Fl Fl = bh 1/ 6 = = Fl.616 Fl bh 1 [ ] F bh 1 [ ].616 l = BD = l = 4 l = i d = = 00 = FN A [ ] FN [ ] A = , [ FN ] = 1.63 kn [ F] = [ FN ] = = 1.87 kn = 3.3 kn = 1.63 kn ABCE BD,,,,

208 (a), AB BCD DE,, E = 00 G Pa, [ ] = 160 MPa, p = 00 M Pa, nst = 3AB d AB = 0 mm, BCD DE d, F D, E, d F D, E, AB, F D, AB, AB, (1 ) AB [ F] AB p = E p = l = l = 4 l = i d AB d AB 4 > p, AB Fcr = EI = l = = = = 6 kn 0.5 [ F] = Fcr nst = 6 3 = 0.67 kn ( ) df DE, F D, C, F DE,, MC max = [ F] 0.5 = 0.5 [ F] M.max = [ F] 4 = 0.5 [ F], FDE, DE C, 3 d max 16[ F] = [ ] = Mmax W 3 Mmax = = d [ F] d = [ ] m = 8.7 cm D,,

209 19 AB DE 1. 8 AF, q = 4 kn/ m ( 11. 8( a) ), 40 mm( ), Q35, E = , s = 61, nst = 5, : (1 ) A B ; ( ) M Pa, p = (1 ) :, ( b ), Fx = 0, FA x = FB x MA = 0 FBx q.5 FBx Fy = 0, FA y -.5 q = 0 = 1.5 kn FA y D, 11. 8( c) = 10 kn Fx = 0, FN3 - FN cos45= 0 F N3 = FN cos45 Fy = 0, FN1 - FN sin45= 0 FN1 = FN sin45 FN3 = FB x = 1.5 kn ( ) : FN = FN1 = 0 FN3 = kn cos45 = FN sin45= 1.5 kn 1) ED i = d/ 4 = 10 mm, = 1

210 193 l = i = 141 > p Fcr = EI = (3.14) = 14 kn ( l) ( ) I = d4 64 = 3.14 ( 4) 4 64 n = Fcr F ) BD = l = i 10, 10-8 = m 4 = = 7 > nst = 5 = 50 <,,, CD, ( a) bh, (xo y, ; xoz, ), E = 00 GPa, p = 00 M Pa, l =. 3 m, : (1 ) b = 40 mm, h = 60 mm, ; ( ) xoy x Oz, b h (1 ) b = 40 mm, h = 60 mm, p = E p = xo y, iz = I z A = bh 3 1( bh ) = h 1 z = l = iz 1 l = h xoz, = iy = Iy A = b 1 y = l = iy : z > y > p = xo y, Fc r = EI z = E( bh 3 ) = ( ) 3 = 69 kn ( l) 1 ( l) 1( 1. 3 ) ( ) xoy x Oz, y = z

211 194 b h = 1 ( 0. 5 l) b = 1 (1 l) h ( ),, xo y,, z ; xoz,, y, xoy x Oz,,,,, , A, B, C, AB, d = 80 mm, BC, a = 70 mm, Q35, l = 3 m nst =. 5, : ( 1) AB,,, Fc r = l = i 0. 7 (1. 5 3) = > p = EI = ( ) ( ) ( l) ( ) 64 ( ) BC,, Fcr i = = l = i I A = a 4 1 a = 3 6 a (1 3 ) = > p = EI = ( ) (0. 07) 4 ( l) ( 1 3 ) 1 = 400 kn = 439 kn (3 ) :,, [ F] = Fcr ns t = = 160 kn AB BC B,

212 195, p, , EI, a = l ( a), ( b), 11. ( b),, (a), ( b )?? D, 11. 3,,, C( N/ m), (1 ) ; ( ) ; (3 ) ,,, p, A p,,? 11. 5, AB, BC, 11. 5, A, B, C, Q35, E = 10 5 M Pa,

213 196 p 00 MPa, ns t =.5[ F] (mm) ,, Fcr : c = 0.60 cm, A = 1.13 cm, x I x = 0.4 cm 4, x0 Ix 0 = 0.63 cm 4, l = 50 cm, E = MPa (11. 7 ),, (1 ) ; ( ) , 4 cm6 cm,, l = 160 cm, nst [ ] = 160 MPa : (1 ) ; = 3, a = 310 MPa, b = 1.14 M Pa, p = 00 M Pa, ( ),? Fcr

214 ,,, F,,, h b? , I1 I, F, F k1 = tan k1 l k l tan = k1 F, k = E I 1 k F E I AB, BC, A, B, C, F (

215 198 < < ) AB( R = 1 m) BC, A, B, C, BC 40 mm 80 mm, 3, E = 11 GPaBC F AB CD, E t(), t( ),, AB b, h, E, ( - 1 ) CD d t ( C, D ) ,,, d = 6 cm Q35 E = 00 GPa, [ ] = 160 MPa, p = 00 M Pa, [ ] = 100 MPa

216 , BC E I 1, L1, EI, L,, F AB A C A, , AC Fc r AB, CD, 0, ns t = 5, AB?, E = 00 GPa, = , a = 6 mm, b = 3 mm ( ) (a),, ( b ) c, m = c Fcr ( ) AB,

217 00 CD FG EI : (1 ) F? ( ), 1.5 F?

218 (1 ) ( ), (3 ) (4 ) (5 ), (6 ), (7 ), (8 ), (1 ); ( ) ; (3 ); (4 ); (5 ) ; (6 ); (7 ) S N. (1 ) ( ) ; ( ); (3 )

219 0. 1. (), ; ;. ; ; ,,,,,, :,,.,,, 3.,,, : (1 ),, ( ), (3 ) (4 ), 4. (1 ) :

220 03 Kd H s t ( ) : Kd = v g st :, Kd s t st F 5. (1 ),, ( ),, (3 ), (4 ),, ; 6. (1 ) 1. 1, max m in ( ) m m = 1 ( max (3 ) a + min ) a = 1 ( max - min ) (4 ) r r = min max 1. 1 (5 ) ( ) r (6 ) ( ) [ r ], (7 ) ( ) 7. (1 ) ( ) (3 ) :, 8. (1 ) : [ - 1 ] - 1 Kn f

221 04-1 ; n [ - 1 ] ; nf ; - 1 nf K max max, ( ) : () , 1. ( a), OO, A B(L, A), B ( F) q, E, G, W Wp 1.,, 1. ( b ), MA A = FLcos+ ql cos+ F g L sin cos+ FN A = - ( ql + F) sin+ F g Lcos + q g max = FN A A + M A W q g L 3 3 sin cos L cos sin,,, ( a) R, Oy,, A, D B

222 , ( 1. 3( a) ) qd ( ) = A g Rcos = A R cos g,, B, C,, B, C, X1,,, 1. 3 ( b ), 1/ 4, 1. 3 (c), B, 11 X1 + 1 F = 0, ( 1. 3( d ) ) dm( ) = - A g Rcos Rd R ( sin- sin ) = M( ) = d M() = - A 0 g - A R 3 g - A R 3 g - A R 3 cos ( sin- sin ) d g R 3 [ sin cos 0 cos ( sin- sin ) d= d- sin (0 ) cos sin d ] = 0

223 06 B ( 1. 3 (e) ) 11 = [ M( ) ] EI 1 F = M( ) M( ) EI - A R 4 X1 = - 1 F 11 B D (= ) 1 d S = 0 M( ) = 1 d S = 0 sin ge I 0 MD = - A R 3 g = A R 4 8 ge I R Rd= EI EI MB = X1 = A R 3 4 g sin ( - A R 3 EI g sin ) 1 Rd= d= - A R 4 8 ge I EI R = A 4 g + A R 3 4 g R 3 ( ) = - A R 3 4 g ( ),, 1, 1/ 4, M( ) (a), AB BC B, l = 1 m, a = 0.1 m DD A B, F = 1. kn, h = 1 cm D D,, Es = 00 G Pa, Ew = 10 GPa [ ] = 6 M Pa ( 1), FD B D, 1. 4 ( b), B A B (AB l AB ), w B = lab wb = la B FN B l3 3 Es I = FN A l E w A - FN B l E w A FN A = F - FN B FN B = FN B l 3 3 Es I = ( F - EN B ) l Ew A ( ) D D, s t = FN A l Ew A (3 ), - FN B l E w A 5 a F = 1 F = 54.5 N l + 10 a = ( ) = m

224 Kd = h = st (4 ) B (5 ) : AB, ( A D ) d = 4.8 ( FN B ) d = Kd FN B = = 333 N = ( FN A ) d A = Kd F N A A 4.9 M Pa < [ ] = ,,,, , F A, v, L E I, ( AB ) Kd = E0 Kd = E0 V E0 = 1 F g v + F L V, 1. 5

225 08 wc V A B C 1 FwC = 1 F F L3 48 EI Kd = EI ( v + gl ) gf L 3 ( st ) max = Mmax W z = FL 4Wz ( d ) max = Fl [ EI ( v + gl ) ] 4Wz gf L 3, F A B,, F,, 1. 5, F, ABC C ( 1. 6 ),, A, E = 00 G Pa,= 0.5, l = m, D = 100 mm, 1 = , = F a, Kd F = MA A = MA Wz =, = Fl, T = Fa = x, A = T W p x = 1 E [ x - ( y + z ) ] = x E = 1 y = 1 E [ y - ( x + z ) ] = - x E = - 1 y = z = 0 1 = x E = Fl W z E = = x + y + x - y x y = G x y x y cos = x y G = - A G = = a = ( m = 400 mm = kn - x y sin - Fa W p G Fa Wp G ) 1 = ( x y = 10-3 ) =

226 (h = 0 ), Kd =, ( a) ABC, B BD, H = 0.1 m,? F = 500 N, Q35, E = 10 5 I = m 4, W = m 3, d = 80 mm MPa, [ ] = 180 M Pa, 1. 7 (1 ) s t B F B 1. 7 ( b ) ), (

227 10 FB 37.3 F I I + 1 A = 0.88 kn ( ) Kd (3 ) : B M B, st M A, st st = 4 mm Kd = h = 8.1 st = 0.5 = 1 knm = = 0.5 knm max d (4 ) : = l = i, = Kd max, st / 4 = = 16 M Pa < [ ] = 50 BD, d = Kd B D, st = Kd FB A = 1.4 M Pa < [ ] C,,,, 1. 7, F, 1. 8 (a) F v L,,, : A, I, R, E L L = FL E A M M = s E I ds M M 1. 8 ( b) M = FR sin M = 1 R(1 + sin ) 1. 8

228 11, = FR3 EI 0 ( sin+ sin ) d= ( + ) FR3 EI = 3.57 FR3 EI C, st = L + = IL AR3 EI A F Kd = 1 + v g C, st = 1 + EI A v Fg( IL AR 3 ), = Kd= Kd 3.57 FR3 EI,,,, ( a) d = cm, h = cm, b = 4 cm, F = 50 N, cm,,, E = 10 GPa,, 1. 9 (1 ) :,,

229 1. 9 ( b ), FN = F,, X1, 1/ 4, 1. 9( c) B, X1 (1 ) 11 = ( M) d S EI 1 F = MF Md S E I 11 X1 + 1 F = 0 ( 1) = 1 MF = FR ( 1 - cos ) (0 ) M = - 1 = EI 1 0 = EI 1 0 X1, M( ) = MF + X1 M = ( - 1 ) Rd= R EI FR = - 1 F 11 (1 - cos ) ( - 1) Rd= - FR EI ( - 1) = FR ( 1-1 ) FR ( 1 - cos) + FR( 1-1 ) ( - 1) = FR ( 1 - cos ) ( ), C, D, =, Mmax = M = FR ( ), C st,, C, M( ), ( ), F = 1, st = M() M( ) d S EI M() = R = 1 - cos 4 FR ( EI cos ) R( 1 - cos ) Rd= 4 FR 3 EI 0 ( 1 - cos ) d= FR 3 Kd = h = st EI ( 4 - ) hei F R 3 ( 4 - ) = ( 4 - ) = ( 3)

230 13 st, max = M W = 6 FR = = Pa bh d, max = Kd st, max = = 99.4 MPa, ;, (a) AB, CD, CD D, F h, F = 100 N, d = 30 mm, E = 10 GPa, G = 0.4 E, l = 1 00 mm, h = 50 mm, AB (1 ) : CD D st, 1 = F( l ) 3 3 EI = Fl3 4 EI AB F l,, A, B, T A = T B = Fl ( b ), D st, = T A ( l ) GIP l = Fl 4 ( l ) 0.4 E I = 10 Fl3 18 EI AB, F D st, 3, AB w C, 1. 10( c), M A = MB, A = 0, A = M A l 3 EI + MB l 6 EI - Fl 16 EI = 0

231 14 st, 3 = wc = Fl3 48 EI, D st = st, 1 + st, ( ) : Fl 3 8 EI = 8 Fl3 Ed 4 = + st, 3 = Fl3 4 EI m =.59 mm MA M B = Fl 8 - MA l 16 EI = Fl 3 19 EI + 10 Fl3 18 EI + Fl 3 19 EI = = Kd = h = st.59 = 14.9 (3 ) : CD, AB,, CD d, max AB, = Kd s t, max Kd st = MC W st = = Kd 16 Fl d 3 = 14.9 T W P, MC F MC W = Kd l d 3 3 = = Fl 4 - Fl 8 = Fl 8 = M A = 4 Fl d 3 = = 4 Fl d = 5.66 M Pa = 337 M Pa = 5.66 MPa ( r3 ) d = Kd st + 4 st = = M Pa, AB C,,,, C, , E = 00 GPa, = 0.3, AB, CD K u v u = v = : (1 ) ; ( ) H = 0.1 m AB, AB CD B (1 ) CD FS = F, K,

232 15 (1 ) u = E ( 1 + ) v = - (1 ) E ( 1 + ) = E( u - v ) ( 1 + ) = [39 - ( - 39 ) ] 10-6 ( ) = 3 ( ) C FS bh = = 6 MPa ( ) F/ bh = 3 4 F = 6 M Pa ( 3) F = 60 kn st, C = ( F ) 13 3 EI = = m B = F 16 EI = C = - st, C ( F ) 1 = EI = rad = rad F3 48 EI = st = + st, C Kd = h = st Cd Bd = m = = 7. = Kd C = = rad = Kd B = = rad = m AD B ( C),,, ;

233 , ( a), ( b)?? ( a) AB, B F, H H B F ( 1. 3 ( b ) ), B 1. 3 (a), B 1. 3 (a) 1. 4,,, 1. 5 h A B, B K F H

234 17 B, E ( a), ( b), ( a) B, ( b ) C,, k: F,?? A max = 50 M Pa, ( ) - 1 = 00 M Pa, K= 1.6, = 0.8, = v (1. 8), ( )???

235 (a), ( b ), 1. 10( b ) 1 ( A),,,?? AB L, A, E D F, B H, B (1. 11 (a) ) : (1 ) ; ( ) B C, C P, D C H, (1. 11 ( b) ( a), ( b), F h,, ( a), ( b), ( b ),, F : (1 ) Kd??

236 19 )?? ,,, ABC 1. 16, F H = a C () GIP (1 ) ; ( ) C = 0.8 EIz, :

237 0. 17 m, v, (1. 17), ( ),, AFB,, CD, 50 mm,, [ ] = 100 MPa, E = 10 5 M Pa, G = MPa F = 10 N, B, H, Kd H/ st OO l, A, W, F, C, CC a, : E (1 ) BC ( ) BC, , (), F, 1 O1 O, 1 b =, C 1. 19, r l, l = 10 b, h = b, CD E, g ,, F v,, l(), EI, a, A, E, F 1. l (1. ), EI, W,, ( v), ( F), (, )

238 , BAB, AB A, E d, RC ( ) AB, CD (1. 4), l, EI,, CD A B,, F

239 h : (1 ) ; ( ) ; (3 ) (AB, CD,?) * 1. 5 m, v0,, 1. 5,, A, A, l,, : (1 )? ( ) , A, B, F h = l v D, E, G () F = 600 N, H = 100 mm 1. 7 B, E = 10 GPa, CD( ) D AB L = mm,, h = 60 mm, b = 600 mm,

240 , A, C, ABC, ABC d, EG F A, A A =?() [ ] = 140 M Pa, d = cm, l = 0 cm, F = 00 N,? , ABC, A, C A BC,, lab = lbc = l,, d, EI = GIp, k( )F, ABC () v B ( I, I p ) EI Z, h F F = 3 kn, H = 0.1 m C,, cm,, E = 10 5 M Pa ( )

241

242 1. 1.1,, ( a) a = ; ( b) b = ; ( c) c = 1. 1 ( 001 ) a = 0, b = -, c = -,, 1. 1 (a),, ; 1. 1 ( b ),, 1. 1 ( b) - ;, 1. 1( c) -.? ( 001 )

243 6., ( 001 ),,,,,,,,,,,,,,, 4. 1.,,,,, ( A) ; ( B) ; ( C) ; (D) ( 000 ) ( B),, ( E) ( A),,, FN3, ( ) E1 A1, E3 A3,, FN3 = 1 +, E1 A1 E3 A3, FN3 F E1 A1 5. ( A) ; ( B) ( C) (D) ( 00 ) ( B) E3 A3 cos 3 1.,,

244 , B, BO1 0 A, 0 O1,, O1 O ( 00 ) ; ;,,, 0 A 0O, O1 O,0 O1, (a), l1, l, d1, d E, C F, C C ( 00 ) 1. 3 (1 ) 1. 4 ( b ), FA + FB = F ( 1) ( ) lac + lcb = 0 ( ) (3 ) lac = - FA l1 EA1 = - 4 FA l1 Ed 1 l BC = F B l (4 ) EA = 4 F B l Ed FB l Ed - 4 FA l1 Ed 1 = 0, (5 )( 1), ( 3) (6 ) C FB l d - FB = FA = FA l1 d 1 F 1 + l d 1 F = 0 ( 3) l1 d 1 + l1 d l d 1 C = l AC = FA l1 EA1 = 4 Fl1 l E( l d 1 + l1 d ) ( )

245 8 FA F B F,,,,,,, AC, B C C C A C, A C, C ,, A1/ A = / 3, F, : (1 ) ; ( )F = 10 kn, A1 = 100 mm ( 00 ) (1 ) B, FN, BC = FN, AB = F sin ( ) F cos ( ) sin,, BC = AB = F 1 sina F cos sina1 F 1 = F cos sin A sina cos= A1 A = 3 = arccos 3 = 48 1 ( ) F = 10 kn, A1 = 100 mm AB, FN = Fcot = M Pa A 1 BC = AB = MPa,,= FN/ A, (a), E A, ( 001 ) (1 ) 1. 6 ( b), R, FN1, FN,, Fy = 0, FN1 sin45= F ( 1) Fx = 0, FN1 cos45= FN + R ( ) ( ) 1. 6 (c), A A,,

246 9 l = 0 FN l E A = 0 FN = 0 (3 ), FN1 = F 1. 6,, A C,, ( a), E = 00 GPa, = , A = 10 cm, B C 0, BD, ( 00 ) (1 ) 1. 7 ( b), B B, l1 l ( ) B, 1. 7( c), = cos30 ( 1) FN1 cos30= FN FN1 = 3 FN ( ) (3 )

247 l = FN l EA ( 3) (4 ) ( 3) (4 )( 1) l1 = tl1 - FN1 EA l1 ( 4) l1 = 3 l t l 3 - FN1 EA l 3 = 3 FN l EA t E A - FN1 = 3 4 FN ( 5) (5 )( ), ( 5), FN1 = kn ( ) FN = 6. kn ( ) B, B,,,,, BC, BD ,, ( 001 ) : ( A ),, = G, ;,,,, 1.,, 1. 9( a), t, D( td), l [ ], A, Me

248 31 n ( 001 ) (1 ), = Me R 0 t = Me D t ( ), ab (1. 9 ( b) ), FS = = = lt = Me D t Me lt D t = Me l D

249 3 (3 ) n, A, FS na [ ] n FS A[ ] ab,, 1. 9 ( b ), ab,, (a) d T, K 45 45, E, T = 45 ( 001 ) (1 )K, ( b) ( ) = 45= T W p 1 E ( = 16 T, 45=, d 3-45= ) = (+ ) = E E = E T = d3 16 = E 4 5 d3 16( 1 + ), 45 ( - 45 ),,, (a), F, A, B, G,, A BC d1 = 5 mm, DGF d = 30 mm, G = 80 GPa, A A ( 001 ) (1 )1. 11( b ), (c), A BC ( ( b) ), C D

250 Me C = 1 Nm ( ), F,, F0 = Me C F60 = Me D Me D = 3 Me C = 36 Nm (3 ) FGD (1. 11( c) ), D DF = EF + D E = 1 GIp T EF l EF GI p + TDE l DE GIp ( ) = rad (4 ) C D, CF C, CF 40 = DF 10 CF = 3 DF = rad A BC ( ( b ) ), A C = A AC = A H + H C = T A H l A H GI p1 0 + A = CF + AC GI p1 + T H C l HC GI p1 = rad = = rad =

251 34,,,,,,,,,,,, F, A A , l = 1 m, d = 0 mm, G = 80 GPa, = 0. 1 rad,, Me Me ( 00 ) (1 ) = GI p l = Me l G Ip = 0. 1 rad = ( Nm ( ) max = Me Wp (3 ) = ) 4 = ( ) 3 = Pa = 80 M Pa = max G max = G = = ,, (a) ( 001 ) ( b), ( c) (1 ) : ( )1. 13( b ) : E, (3 ) 1. 13( c) : E, rad FA = 6 kn(), FB = 19 kn( ) FS E = 6 - ( x - ) q= 6 - ( x - ) = 0 x = 5 m ME = ( 5 - ) q 1 = 11 knm, C, CD, E, (

252 35 B, 14 knm (a) FSmax Mmax ( 000 ) ( b ) ( c), FSmax = ql, Mmax = ql A C,, C,,, A, B, BC AC (a) ( 00 ) (1 ) : M A = 0, FC l + ql l = qll + qll FC = ql 1. 14

253 36 Fx 0, FAx = ql MC = 0, FAy l = ql l + qll + qll FAy = 3 ql ( ) ( )1. 15( b ), (c), ( d) A B BC, D ql,, BC, D, () B, B B,, (a) ( 001 ) (1 ) MA = 0 FB a = qa + qa 5 a FB = 7 qa 4 () MB = 0

254 37 FA a = qa + qa a FA = 3 4 qa( ) ( ) 1. 16( b )( c), A, B, C, BD,, (a) ( 001 ) (1 ) MB = 0 FC a + qaa = qa + qaa FC = qa( ) MC = 0 FB a + qa = qaa + qa3 a FB = qa( ) ( )1. 17( b )( c) D, FS = 0 D C x, qa - qx = 0 x = a BC ()

255 38 MC qa a - qa a = qa 1. T, 1. 18, [ t ] = 30 MPa, [ c ] = 60 M Pa, Z I z = m 4, [ F] ( 001 ) (1 ) M A = 0, FB =. 75 F M B = 0, FA = F ( ) 1. 18( b ), D, B, D t = MD Iz c = M D Iz B t = MB Iz c = M B Iz MD MB = F = - F = F [ t ] [ F] kn = F [ c ] [ F] kn = F [ t ] [ F] 4. 4 kn = F [ c ] [ F] 5. kn (3 )D,

256 39 F] kn T,,,,,,. A BC, A B = 6 l, BC = l,, ( a) F, [ t ] = [ c ]/, [ F] ( 00 ) ( 1) F, AB D, 1. 19( b), MD = 3 Fl C, 1. 19( c), MB = Fl ( ), z (1. 19( a) ), 4 bb b + b b( b + b) = [ ( b b) + (4 bb) ] yc z (3 ): Iz = 4 bb3 1 ( b - yc = 5 4 b + ( 5 4 b - b ) ( 4bb) b) ( b b) = 37 6 b4 b( b) 3 1 +

257 40 c = t = MD 7 4 b I z = [ F] MD 5 4 b I z = 3 Fl 7 4 b [ c ] 37 6 b4 b 3 l [ c ] 3 Fl 5 4 b [ t ] 37 6 b4, [ F] 148 b3 45 l [ t ] t = MB 7 4 b I z = [ F] 74 1 Fl 7 4 b [ t ] 37 6 b4 b 3 l [ t ] c = MB 5 4 b I z = Fl 5 4 b [ c ] 37 6 b4 [ F] 74 b3 15 l [ c ] (4 ), [ F] b 3 l [ t ],,, ( 1 ), (a) II, = , l = 1. 5 m, h = 160 mm, E = 00 GPaF ( I y = mm 4 ) ( 00 ) (1 ) 1. 0( b ), II ( C ), MC = F 4 ( ) C,,, = E= (3 ) C, = MC h/ Iy = F/ 4 h/ Iy = 80 M Pa = F =

258 F 10 3 = Pa F = 45. kn,,,,, ( a) T, M, T (1000 )( 1000) M ( 00 ) 1. 1 (1 )C, z y1 [ (100 0 ) + (100 0 ) ] =

259 4 I z = 0( 100) 3 1 y = 40 y = = 80 + ( ) ( 1000) + 100(0) 3 (40-10) ( 1000) = mm 4 ( ) 1. 1 ( b ) z M = y (d A A = y 1 M 100 Iz 40 y 3 0 y d y = M = 35% M 1 y M y (100 d y) = I z % ; 65 % + M = d A, ( ), d yy( d A) d A,,,,,,, Iz ( a) No. 18 ( W z = 185 cm 3 ) F,, a b [ ] = 160 M Pa ( 00 ) (1 ) F,,, ( ), ( ) BC, ( 1. ( b) ) Mmax = F 1 - ( a + b) =, F[1 - ( a + b) ] 4 (3 ) D, ( 1. (c) ) MC = Fb (4 ) A, ( 1. ( d) ) MB = Fa (5 ), F[ 1 - ( a + b) ] 4 = Fb = Fa 1.

260 43 (6 ) :, a b = m max = Mmax W z [ ] F [ ] W z = = 9. 6 kn F kn,,,, (),,, (a), ( 001 ) (1 ) ( 1. 3 ( b ) ), AC, CD, ( ): A A = 0, w A = 0 B wb = 0 C wc= wc (3 ) 1. 3( c),,,, 1. 3 ( b), A C, CD E I w= M, M, w> 0, ; M, w< 0,, M = 0, w= 0,, 1 = M,, E I (a) OA, O, w = c x 4, c E I, b, ( 001 ) (1 ) EI w= - M( x) w, M( x) - EI w= FS ( x) - EI w= q( x)

261 44 ( ) w = cx 4 - E I w= - 1 E Ic x = M( x) x = b, FS - E I w= - 4 EIcx = FS ( x) - E I w= - 4 E Ic = q( x) = - 4 EIcb M = - 1 EIcb q( x) = - 4 E Ic 1. 4 ( b) w( x), w ( x) = ( x), E I w= M ( x), E I w= M ( x ) = Fs ( x ), E I w= F S ( x) = q( x),, x, w, (a) q, E I, q l,, A () ( 001 ) FA, M( x) = FA x - qx A x0, dm( x) d x = FA - qx0 = 0 x0 = FA q FA Mmax = FA x0 - qx 0 = F A q - q ( FA q ) = F A q, Mmin = ql - FA l 1. 6,,,

262 45 FA q = ql - FA l F A + ql F A - q l = 0 FA, = FA = - ql ( ql) + 4 q l FA l3 3 EI - FA ql 4 8 EI = ( - 1 ) ql() = ( - 1) ql4 3 EI - = ( - 1 ) ql ql 4 8 EI ql4 EI,,, (a), B B = Fa( l - a ), 6 E Il 1. 7 ( b) C w C ( 001 ) (1 )1. 7( b ), d x q( x) = q0 x l d F = q( x) d x = q0 x d x l Bq ( ) 1. 7 (a) A B F, B B = Fa( l - a ) 6 EIl (3 )1. 7 ( b ), C w C B Bq, wc = 1 Bq 5 q0 l EI = l 0 = 5 q0 l4 768 EI d Fx ( l - x ) 6 EIl = l 0 q0 x 6 EIl ( l - x ) d x = 1. 7 q0 l3 45 EI, q0,, d x q( x) d F, F,, B Bq (a) AB C E I, C, k = 3 E I, : a 3 (1 ) C ; ( ) A

263 46 00 ) (1 ) FC, 1. 8 ( b), C 1. 8 (c) 1. 8 ( d) wc = B a = wc1 = qa4 8 EI - FC a 3 3 EI ( qa ( )C, qa 4 8 EI - FC a 3 3 EI FC = A = wc1 + wc = FC/ k 7qa 4 4 EI + qa4 6 EI - FC a 3 3 EI - FC a3 3 EI = FC k = FC/ k 7 kqa 4 4 EI + 16 ka 3 = 7 4 qa (3 )1. 8( d ), A qa - FC a a = 6 EI 1 EI qa 3 + kqa 6 6 EI ( 4 EI + 16 ka 3 ) - FC a) a a = 3 EI = 5 qa3 144 EI, A B, BC ; A B BC,, 31., 1. 9 (a), 1,, 3 (1999 ) qa4 6 EI - FC a 3 3 EI

264 ( b), 1 = 80 MPa = x, = y, x y = 0,= 50 M Pa, = 50 M Pa = cos ( - 10 ) = 40 MPa, 1 = 80 M Pa, 3 = 0,, : 1. 30, OA = 80 M Pa ( O, A 80 M Pa), OB = 50 MPa(B 50 MPa) B A A D, B AD = 30AD B D A D, C, C C, CA, A, E, OE = 40 M Pa = ( OA = 1 = 80 MPa, 3 = 0) (a) d T, K, 45 45, E, T = 45 ( 001 ) (1 )K, ( b)

265 48 5 ( - 45 ), ( ), 45= 1 = 3 = - 1 E ( 1-3 ) = 1 E = T = T Wp (+ ) = 1 + E = 16 T d 3 d 3 E 16( 1 + ) 4 5,, + 9 0, 45-45,,,,, (a), t = 5 mm, D = 100 mm, F T, K 100 M Pa, 30, F T ( 001 ) 1. 3 (1 )K 1. 3( b ) ( ) x = F A = F rt = x y = - F Dt, y = 0 T r t = - T D t max = ( x - 0 ) + F x y = ( Dt ) (10 8 ) = F + 4 T 4 D t D 4 t (3 ) 30,, 30= + ( T D t ) = F T ( 1) x - 0 sin( 30 ) + x y cos ( 30 ) = x 3 + x y

266 49 = 3 4 F Dt - 1 T D t 0 = 3 F - 0 T ( ) (4 ) ( 1), ( ), F = 157 kn T = 6. 8 knm, K, x x y F T,, 30, ; max 100 M Pa,,, 34., (a), AB, x y, ( 00 ) (1 ) x = - 15 M Pa, y = - 15 M Pa ( ) AB x = 135 = x + y + x x y = 0 (3 ) : max mi n - y cos- x y sin= cos( 135 ) - x y sin( 135 ) = x y = 15 M Pa = x + y ( x - y ) + x y = ( ) + 15 = 0-30 MPa

267 50 1 = = 0, 3 = - 30 MPa tan 0 = - x y x = - - y = = -, x y, x y, ( x A B ),, x 45 A B,,,, 1. 33( b ) 0 A B,, d, a x, b y 35., (a) d = 0 mm, E = 00 G Pa O a = , b = , c = , F T ( 00 ) (1 )O, ( b) ( ) O c F = E cd 4 a c, = F A = 4 F d = T W p = 16 T d 3 = E c = 4 F d = (010-3 ) 4 = a c b,, b = 1 E = = ( - + ) E b = ( 1 + )+ (1 - ) = 0. 1 kn

268 = = 16 T d T = ( ) = Nm,,,,,, 45 b x = c, y = a,= 45, b = x + y + x - y cos- x y sin b = c + a + c - a cos90- x y sin90= c = = x y, = x y = x y G, + qa - x y, x y = x y G = E x y = ( 1 + ) ( ) 16 T d 3 = T = ( ) 3 = Nm = (a)d, F 45,, ( 00 ) (1 ) A x y z, 1. 35( a) F y x Fx = Fsin= F Fy = Fsin= F ( ) : A B x A z y A z ( ), B Mx = Fy 10 d = 10 My = Fx 10 d = 10 BC, y A z x A y C (1. 35( b ) ) Fd Fd

269 FN = Fy = F T = Fx 10 d = 10 M x = Fy 10 d = 10 Fd Fd C Mx M z, M z = Fx 0 d = 0 Fd M = (5 Fd) + (10 Fd) = 5 10 Fd = FN A + M W = 4 F d = T Wp = r3 = + 4 = 16 5 Fd = 80 F d 3 d K (1. 35(c) ) Fd = d 3 F d ( ) F ( ) + 4( 80 ) = 557 F d d sin= 10 Fd 5 10 Fd = = arcsin = 63 6( M x ), BC, B, BC,

270 53,, (a) CDE d A d B ( A B ), ( b ) C, D, CDDE, E F, F CDE A 3 E, 3 G, [ ] B E, G, [ ], : (1 ); ( ) ; (3 ), ( 00 ) (1 ) CD ( ), C, T = F L Mz = F L ( ) C A 1, B 3, 4, 8. 1 ( b ) (c) (3 ) : 1, : = = ME1 y E 1 I z1 + E Iz TG1 G1 Ip1 + G Ip r3 = + 4 = r3 = = FL 3 Ed 3 E 15d E d4 64 FL 3Gd 3 G 15d FL d 3 + G d4 3 [ ] = = 19 FL 3d 3 48 FL 3d 3

271 54 3, 4 : r 3 = + 4 = = ME y E1 Iz1 + E Iz TG G1 Ip1 + G Ip = = r3 = FL Ed/ 3 E 15d E d4 64 FL Gd/ 3 G 15d FL d 3 + G d4 3 [ ] = 3 FL 3d 3 = 8 FL 3d 3,,,, (a), F1 = 1 kn, F = 0. 8 kn, d = 40 mm, l1 = 500 mm, l = 700 mm, [ ] = 160 M Pa, : 1. 37

272 55 1 ) ( ), ; (3 ) ( 001 ) (1 ): F1 F, ( b) ( ) : x Oy,, AB,, (c), ( d), (e), A, K, (f), = FN A + M W = ( ) M Pa (3 ) : = T Wp ( ) 3 = = ( ) 3 = 1. 7 MPa r3 = + 4 = ( ) + ( 1. 7 ) = M Pa < [ ],,, A B, ( a) F, F O, r, [ t ] = 30 M Pa, b = 150 mm, h = 00 mm, r = 60 mm = - (1 ) F K, [ F] ; ( )F,? [ F] min =? (3 )F,? [ F] max =? ( 001 ) (1 )F K,, FN = F My = F A - Mz = F F bh + ( F ) Iy F + ( F ) Iy F + 48 F + 48 F = 6. 7 F [ t ] + ( F ) Iz + ( F ) Iz = =

273 [ F] = kn ( )F,, M, B ( ( b) ) t, ma x = - t, max = - t, max - ( Frsin ) h F A + Iz + ( Frcos ) b F bh + ( Frsin ) 6 + ( Frcos ) 6 bh b h = Fr bh cos- 6 Fr b h sin= 0 b h cos = sin h b = tan= = 36 5 = 16 5 F + ( F ) 6 + ( F ) 6 = F + 36 F + 64 F = F [ t ] [ F] min I y = kn (3 )F C( y ), ( ( b) ) t = - - F A + Fr 6 bh = - F 6 h + 6 Fr = bh F F = =

274 F + 60 F = 6. 7 F [ t ] [ F] max = kn,,, xo y x Oz, F, F, ; F, ( a),,, E1 > E,, e ( 000 ) (1 ) FN1, FN,, FN1 + FN = F ( 1) FN1 l E1 A = FN l E A (1 ), ( ) FN1 = E1 E FN ( ) FN1 = E1 E1 + E F FN = E1 E + E F ( ) FN1 ( b - e) = FN ( b + e) ( 3) e = ( FN1 - FN ) b( FN1 - FN ) ( FN 1 + FN ) b( E1 - E ) ( E1 + E ) = b b = e( FN1 + FN ) ( E1 - E ) F E1 + E E1 + E ( E1 + E ) F =,, O, F,,, FN1, FN e (a) ( b) A B,, ( A) FC w C + FD w D = M A A + M B B ; ( B) FC w D + FD w C = M A B + MB A ; ( C) FC w C + FD w D = MA A + M B B ; (D) FC w D + FD w C = M A B + MB A ( 001 )

275 : C,,,, FC, FD, MA, MB w C, w D ; M A, MB, FC, FD A, B, FC w C + FD w D = MA A + MB B (a), E I, A ( 001 ) (1 )A, 1. 41( b) ( ) A B M( x1 ) = Fx1 M( x1 ) = 1 BC M( x ) = 4 Fa Fx, FN ( x ) = 3 5 F M( x ) = 1, FN ( x ) = 0 CD M( x3 ) = 4 Fa - F x3 M( x3 ) = 1 (3 ) A A = EI 1 4 a 0 M( x1 ) M( x1 ) d x1 + EI 1 5 a 0 1 EI 4 a M( x3 ) M( x3 ) d x3 = 0 M( x ) M( x ) d x +

276 59 EI 4 a 0 1 EI 4 a 0 6 Fa EI Fx1 d x1 + EI 1 5 a (4 Fa - 0 ( 4 Fa - Fx 3 ) d x3 = ( ) 4 5 Fx ) d x + Z,,,, ;, 43., 1. 4 A w A () E A, A, B F ( 001 ) (1 ), FN i (9 )A F1, B F ( )F1 FN i, ( 1 ) F1 (3 ) FN i l i FN i ( 1) E A F1 (4 )F1 = F = F, wa = FN i l i FN i E A F1 wa = F1 a E A + ( F1 + F ) a E A ( F1 + F1 ) a + F a E A + F1 a E A = = (3 + ) Fa E A l i F Ni FN i F 1 FN i li FN i E A F 1 1 a F1 1 F1 a E A a F 1 + F 1 ( F 1 + F ) a E A 3 a - F1 - F1 a E A 4 a a 0 0 0

277 60,, A B,, A,, A F1, B F F1, F1, F F, A (a) C w C C ( 001 ) ( 1 ) ( ( b ) ) ( )C, ( ( c) ),, wc = 1 EI ( - 1 aqa a qa a a qa a3 a 4 = qa 4 8 EI ( ) ( 3 ) C, ( ( d ) ),, C = 1 EI - 1 aqa qa a qa a1 = qa3 6 EI ( ), 1. 43,,, qa q,, (a) AB B C,, E A, EI,, B w y ( 1999 ) (1 )F, A B BC ( (c) ): A B FN, AB = F( ) BC FN, BC = F ( ) M( ) = ( F ) lsin- ( F ( )( ( b) ), BC A B FN, AB = 1 ( ) ) l(1 - cos ) = F lsin- F l(1 - cos )

278 BC (3 ) FN, BC = M( ) = lsin- l(1 - cos ) w B = 1 ( F1 ) l + 1 EA Fl EA + Fl EA EI Fl3 EI EI 0 M( ) M() ld= [ Flsin- Fl( 1 - cos ) ] [ lsin- l(1 - cos ) ] ld=,,, B, C, A B, B (a), E I ( 001 ) (1 ), Me, C, C FS ( ( b) ) ( ), C FS = X1,, 1 F = 11 = 11 X1 + 1 F = 0 ( l/ ) 3 3 EI = ( Me/ ) ( l/ ) EI l 3 4 EI ( ) = l 3 4 EI X 1 - Me l 16 EI = 0 X1 = 3 Me l Me l 16 EI () 1. 45

279 6 (3 ) : A F A = FS = 3 Me l C (), MA = Me/ 4 Mmax = Me/,, Me,, (a) A CB A B, E, E I, A, B ( 001 ) (1 ) AB, X1,, 11 X1 + 1 F = 0 A B EA,, 11 = 1 1 a E A X1 1 F = - = - 1 F = EI a ( 0 x) ( EI a ( 0 ( ) A B AB AB = l = x) dx = a E A + Fx ) ( x) d x = - Fa 3 3 EI FA a 3 3 Ia + Aa 3 = X1 a EA = FA a 3 I + Aa Fa 3 3 EI + EAa, AB,,,, AB C, A B, A, B A B A, B A, B,,, a3 3 EI

280 (a), E I,, A () ( 001 ) (1 ),,, ( ( b) ), FS F S ( )1. 47( b ),,, (3 ) 1. 47( c) FS = F S = qa (4 ), A,,, ; (a) A BCD, A D, E I, ( 00 ) (1 ), ( b),, B, 11 X1 + 1 F = = EI ( 1 l l 3 l) + 1 ( lll) = 5 l3 EI 3 EI 1 F = - 1 EI ( 1 ql l 3 l) - 1 EI ( ql l l) - 1 EI ( 1 ql ll) - 1 EI ( 1 3 ql l 3 4 l) = - ql 4 3 EI - ql 4 EI X1 = - 1 F 11 - = ql 4 4 EI - ql 4 8 EI = - 9ql4 4 EI 9 ql4 EI 3 = 9 4 EI 5 l 3 40 ql()

281 64 ( ) 1. 48( e), ( f), ( g),, B,, (a) q(n/ m), A, E I ( 00 ) (1 ),, C, D FN = qr = qr

282 C, D,, A ( ), X1 = 1, 1 1 F = 0 M( ) = M( ) = 1 q( R - Rcos ) - qr ( R - Rcos ) 1 11 = 0 EI M ( ) M( ) Rd= 1 o EI (3 ) A X1 = - IF = qr EI MA = qr - qr 4 EI M ( ) M( R ) Rd= EI q( R - Rcos ) - qr ( R - Rcos ) Rd= - qr3 8 EI EI R = qr 4 ( ) - qr R = qr 4 ( ),, C, D,, FN C = FN D = qd = qr,,,, , A B AC, A B 80 mm, AC 100 mm, Q35, p = 00 M Pa, s = 40 M Pa, b = 30 M Pa, E = 00 GPa, a = 304 M Pa, b = 1. 1 M Pa, ns t F = 3, A, B, C, ( 00 ) (1 ) A, FN, AC = 3 FN, AB 1. 50

283 66 FN AB + 3 FN, AC = F FN, A B = F ( ) ( ): A B = l i A C = l i = p = = 173 = = 80 s FN, AC = 3 F ( ) E = = p = a - s = b = 57 A B, A C (3 ): A B, Fcr = EI = ( ) 4 = 330 kn ( l) 64 (1 3 ) A C, Fcr [ F1 ] = Fc r ns t = 0 kn = cr A = ( a - b) A = ( ) 10 6 ( ) 4 = kn [ F ] = Fc r 3 nst = 648 kn [ F] = 0 kn,,, AB, , A, B, BD W = mm 3, [ ] = 160 MPa, A B, b = 0 mm, h = 40 mm, E = 00 GPa, p = 100, s = 61, nst = 3, Me [ M] ( 001 ) BD, A B, MC = 0, FN = Me ( ) Mmax = Me max = M e W

284 67 ( ): = l = i Fcr = EI = ( l) 1 1 b 3 h 1 1 bh Me W [ ] = = 1. 8 knm = 3 = 173 > p ( 0 ) = 1( 1 1 ) 5. 6 kn [ Me ] = Fcr nst = knm (3 ) [ Me ] = knm 1. 51,,,, () , F = 0 kn, AB D = 50 mm, d = 40 mm, Q35, E = 06 GPa, p = 00 MPa, s = 35 MPa, a = 304 MPa, b= 1. 1 MPa, nst =, A B ( 000 ) (1 )AB : F( ) = FN FN ( ) A B : = kn ( ) = l = i p = E p = = = > p, A B, Fcr = EI = ( l) ( ) = 1 kn 64( ) [ Fc r ] = Fc r ns t FN < [ Fcr ] = 61 kn, AB,, p

285 A B AC, BD, ( ) AC,, a = 45 mm, BD B, D,, D = 50 mm, d = 40 mm, E = 10 5 MPa, cr = ( M Pa), c = 13, nst = 3, F A B, : (1 )AB, x = 1. 5 m, [ F] ; ( )x,? [ F] max? (3 )x,? [ F] min? ( 001 ) (1 )F A B, x = 1. 5 m,, Fcr 1 Fcr = c r A = 1 = l = i FN1 = FN = F 1 3 = > c = 13 = EI = ( ) 4 = kn ( l) 1( 1 ) = l = i ( ) 10 6 ( [ F] = nst = = < c = 13 ) ( ) 4 = kn = kn ( ),,, Fcr, 1 = kn Fcr, = kn

286 69 Fcr + Fc r = F = kn = x = 1. 3 m [ F] max = (3 )x = 3 m, F B, F = 19. 9, FN [ F] mi n = = F = kn = kn, F,, F AB,,, F F B,,,,,, (a) A BC I = cm 4, W = 508 cm 3, CD, d = 40 mm, E = 00 GPa, [ ] = 160 MPa, l = 1 m, nst = 3, [ Me ] ( 001 ) (1 ), ( b), Me l EI - X1 l 3 3 EI - ( X1 l) l EI = X1 l E A ( ): X1 = 0. 7 Me Mmax = 0. 7 Me l = 0. 7 Me ma x = 0. 7 Me W [ ]

287 70 (3 ) : e ] W [ ] 0. 7 = CD, Fc r (4 ) = knm = EI = ( ) 4 = kn ( l) 64( 1 1) Me = Fcr 0. 7 [ Me ] = 344 nst = = 344 knm = knm [ Me ] = knm,, 56. 6, 1. 55( a), E,, a= 1 m, d = 50 mm,,? F Q35, E = 00 GPa, p = 00 M Pa, s = 40 M Pa, a = 314 MPa, b = 1. 1 M Pa ( 00 ) (1 ), A C, X1 11 = F N i F N i l i E A 1 F = F N i E A X1 FN i l i = - 1 F 11 = a(1 + ) EA = - Fa E A (1 + ) = 0. 7 F (1. 55 ( b ),

288 71 F Ni F N i l i F Ni F Ni l i F Ni F Ni l i F F F F / a / a / a / a - Fa - Fa - Fa - Fa a a a a 5 F - 1 a - Fa a a 0 a ( ): ( AC ),, > p, Fcr FN p = = F + 0 = F = l = i = 113 E = = p = EI = ( ) 4 = 30 kn ( l) 64 (1 ) F = 43 kn,,,,,, AC, (a), F C H, R, a= R, E I,,, : (1 ) C st ; ( ) C d ; (3 )Fd ( 001 ) (1 )C : C, ( ( b ) ),

289 BC M( x) = F x A B ( 0xa) M( x) = x ( 0xa) M ( ) = Fa+ Fasin ( 0 ) M( ) = a + asim (0 ) st = EI 1 a 0 M( x) M( x) d x + EI 1 M ( ) M() Rd= v Fa3 3 EI + Fa3 (3+ 8) 4 EI st = Fa3 Fa3 (8 + 9) = EI EI ( ) C :, (3 ) : Kd = H st = HE I Fa 3 d = Kd st = ( HE I ) Fa Fa 3 EI Fd = Kd F = ( HE I Fa 3 ) F, Kd Kd, (a) F, v C, A B BC, d, E, ( 001 ) ( 1 ) : Kd = ( b ) ) BC M( x1 ) = F x1 ( 0x1 h) A B M( x1 ) = x1 ( 0x1 h) M ( x ) = Fh (0x a) v, s t ( g st

290 M( x ) = h ( 0x a) st = EI 1 h 0 M( x1 ) M( x1 ) d x1 + EI 1 a 0 M( x ) M( x ) d x = Fh 3 3 EI + Fh a E I = Fh3 + 3 Fh a 3 EI ( ): Kd = 3 EIv g( Fh Fh a) d, max = Kd st = Kd Fh 3 d 3 = 3 EIv g( Fh Fh a) 3 Fh d 3, st,,, st F C ( ), C (a)d A BC d0 CD C, F, H B, CD Q35, b = 380 M Pa, s = 40 MPa, p = 00 MPa, E = 00 GPa, G = 80 GPa, d = 50 mm, d0 = 10 mm, L = 1 m, F = 00 N, H = 0 mm, n =, ns t = 3 ( 00 ) (1 ), CD ABC X ( b) C ( )B st = FL3 3 EI FL 3 3 EI - X1 L3 3 EI X1 - X1 L3 3 EI - X1 L 3 GI p - = N ( X1 L) L L GI p = X1 L E A0, st = ( F - X1 ) L3 3 EI = m Kd = H = = 7.74 st

291 (3 ) Fcr = l = i Kd X1 = = 68 N p = 1 L 4 d0 E p = = = 400 > p = EI = ( ) 4 = 969 N ( l) 64 ( 1 1) Kd Fcr X1 = = 3. 6 > nst = 3 CD, = Kd X1 A0 = 68 4 ( ) s = = > n = = 3. 4 MPa,,, Kd,, CD, ( a) 1 kn,, W = 30 cm 3, F = 00 N, L = 1 m, A t, A r max min m a ( 001 ) (1 ),, st = = MPa

292 d = ( ) 103 L W ( ) t ( b) : max = 40 MPa a = = 6. 7 MPa = = 40 MPa m in = = 6. 6 MPa m = max + min = M Pa r = mi n = = max 40,,,, A, A,, A (a) l, z d,, A B ( 00 ) (1 ),, 1. 60( b ) A C,, CB,, q( y) = ( 1 d 4 ) y, ( 0 y l) q = ( 1 d 4 ) l ( )( (c),,, B

293 X1, 1 F = - 1 EI l qx 0 1 d x - 1 X1 FS = 0, FN = 0 = - 1 F = l E I EI l ql 0 1 d x = - ql 3 = ql 3 = d 1 l 3 6 EI - ql 3 EI = - ql3 3 EI, B MB A M A = ql 3 ( ) = ql - ql 3 = ql 6 = d 4 l 3 ( ),,,,,, A,,, ; B,,

294 77 ( 10,, 0 ), 4, 1, 1. y = f ( x) x, y A ( 1. 1 ), x I x, d A, Ix = A y d A, ( ( A) 1 4 (B) 1 ( C ) (D) f( x) ) ,, F H, st ( ) Kd = H st ( A) A ( B) A ( C) B (D) A B 3. ()W1 W ( W1 > W ) ( 1.3 ), ( ) ( A), ( B), ( C) (D) 4. a - m ( a, m ), C1, C 0 ( 1.4), C1, C r1, r, max1, max, ( ( A) r1 = r, max1 ( C) r1 r, max1 ) > max ( B) r1 = r, max1 < max > max (D) r1 r, max1 < max

295 (1.5), 3, z ( ) ( A) z I z1 Iz = 3 ( B) A1 A = 3 ( C) z () Sz1 Sz = 3 (D) y1 y = (1.6),? ( A) 1 ( B) ( C ) 3 ( D) ,, F (> ), F ( ) 1. 7

296 79 A) OEBi ( B) OEB ( C) OEB3 (D) OEB (a) ( b ), F Me,, ( ) ( A) wc1 = wc ( B) B1 = B ( C) wc1 = B (D) B1 = wc ( ) ( A) ( B) ( C) (D) ,,, ( ( A) 1, ( B) 1, ( C) (D) ) ( 10 ) q, a, ( 1.10 ) ( 0 ) 1. 11, d = 100 mm, Me = 4 knm, F = 400 kn, e = 15 mm, E = 00 G Pa, s = 00 M Pa, n = : (1 ) ;

297 80 ) ( 0 ) 1. 1, E = 00 GPa, I = mm 4, A = mm, l = m, q = 300 N/ m, A BC 3 ( 15 ) ,, (15 ) 1.14, l = 100 mm, d = mm, p = 00 MPa, s = 50 M Pa, p = 100, s = 50,,, a = 304 M Pa, b= 1.1 M Pa : 1999 ( 0 ) (1 ), ; ( ), ( 0 ). 1,, ( 0 ) A B BC B, AB (

298 81. ( a) ), E1, I1, BC a a, (. ( b ) ), E q, ( 0 ). 3 AB BC, B C CD, A, CD q,, d, E, G, B ). 1 ( 0 ). 4,, B ( E I : ( 5 ) 3 1. (4 )3. 1( a) w1 = 5 ql4 ( E I ), 3. 1 ( b) 384 E I w =. (7 ) 3. ( MPa ),,

299 (4 ) 3. 3, Me1 Me, C A L/ 3, Me1 Me 4. (6 ) 3. 4 F = 40 kn, L = 1. 5 m, a = 3 cm, d = 14 cm, d1 = 1 cm,, m =, a =, r = (4 ) 3. 5, F = 40 kn, h = 10 mm, b = 80 mm, a = 350 mm, e = 50 mm, b s =, = 3. 5

300 83 75 ) 1. (15 ) 3. 6, A, C, D, G, H,, E, A,,, F, A B ( 15 )3. 7, A, B, C, F =. 88 kn h = 6 cm AB, BC (1 ) A B : E = 00 GPa, I = 100 cm 4, L = m ( ) BC : E1 = 7 GPa, A1 = 1 cm, I1 = 65 cm 4, a = 1 m, p = 6. 8, cr = a - b, a = 373 MPa, b=. 15 MPa, s = 36. 3, nst = 3 3. (15 ), 3. 8 A, B, C, D E A, I, CD q, AB E ( A BCD, ) (15 ) 3. 9, E1, E,, (

301 84 E1 > E,? 5. (15 ) 3. 10, 100 kw, 00 r/ min,, 0 () F1 ;,,, [ ] = 80 M Pa ( sin0= 0. 34, cos0= ) : ( 15 ) (4. 1 ), l = 1 m, d = 0 mm, G = 80 GPa, = 0.1 rad Me

302 85 15 ) 4. Me FS, M ( 10 ) 4. 3, E;, 3 a a l = 70 a,, t = , 100 ( 0 ) 4. 4, A B T, q 4. 3 CD, F 0x3 l/ F [ F] : d = 30 mm, [ t ] = 35 MPa, [ c ] = 140 M Pa; [ ] = 180 M Pa(, c ) ( 15 )A B BC, 4. 5 E AEI B w y ( 15 ) 4. 6 d = 0 mm, My T x A 0 = 610-4, B 45 45= , E = 00 GPa,= 0.5, [ ] = 160 MPaMy T x,

303 86 10 ) F C H ( 4. 7 ), E I, [ ], a> b, W, F : (1 ) 5. 1 t = 8 mm, D = 00 mm, d = 0 mm, [ ] = 60 M Pa, T = 30 knm, s 5. 1 ( 1 ) k g, G A E 38 mm38 mm, A, E A B, BC, CD ( 15 ) 5. 3 d = 65 mm D = 70 mm AB, A, B (y ) a = 300 mm BC, C ( x Oz ), x 30 F = 800 N E K r

304 87 15 )5. 4 K, x 45, 45= , E = 00 GPa,= 0.3 F (15 ) 5. 5, AB, BC, CD d = 0 mm, l = 30 d [ ] = 150 M Pa, E = 1[ ] p = 100, nst = 4 q [ q] ( 0 ) 5. 6 A C, A, C G E G H, E F, G H, EF A C, AC d1 = 100 mm, G H, EF d = 0 mm,, G = 0.4 E B Me = 7 knm, A C : 5. 6 (0 ) 5. 7 A B CD l, EI, CD, A B A, B

305 88 F, B 5. 7 ( 11 ) 5. 8 A, B E I, :

306 1. 00 ( 6, 3 ) ,( ) 1. 1., 4? ( A) ( B) ( C) ( D) ( ) ( ) ( 6, 3 ) 1.,,. 1.,,,

307 90. ( 10 ) 1. 3, l1, l, d1, d, E, C F,C C 1. 3 (10 ) 1. 4,, l = 1 m, d = 0 mm,g= 80 GPa, = 0. 1 rad, M e 1. 4 ( 10 )

308 91 10 ) 1. 6 II, = , l = 1. 5 m, h = 160 mm, E = 00 GPa, F ( Iy = mm 4 ) 1. 6 ( 10 ) 1. 7 F, d = 100 mm, a = 400 mm, E = 00 GPa,D k D = , r ( 10 ) 1. 8,EI, A w A

309 9 10 ) F,v C, 1. 9, A B BC, d, E, ( 10 ) 1. 10,,,, d = 40 mm, E = 00 GPa, [ ] = 10 MPa, 90,n st =, [ F] ( 8 ) 1. 11, A BCD a,ei, q,ac BD, E, F B. B 1.,. - 1,100 MPa 4 F l 1 l C = E( l d 1 + l1 d ) = rad, max = 80 MPa, M e = k Nm F = 45. kn r3 = 13 MPa wa = 10 Fa3 3 EI 3 Fh 3 EIv d, max = d 3 g( Fh Fh a) [ F] = kn M = 0, F s = q a, EF = 0

310 (15 ) 1. 1, E = 10 GPa, p = 00 MPa, s = 35 MPa, a = 304 MPa, b = 1. 1 MPa, 3,5 000 mm, 3 F cr 1. 1 ( 0 ) 1. 13, D= 80 mm, d = 0. 5 D Me = 15 k Nm E = 00 GPa, = 0. 3, : x y ; ( 1) A x y ( ) (0 ) 1. 14, d, A, a F C, E, G= 0. 4 E ( 1) K d ; ( ), [ ] 1. 14

311 94 15 ) A B BC ( ),, A B d 1 = 0 mm, BC d = 50 mm, [ ] = 160 MPa, F = 5 kn, a = 0. 6 m, ( ) (15 ) T, M, T (100 mm0 mm) ( 100 mm 0 mm)m (15 ) 1. 17, A, D, EI, EI, F, a, E I (a) F cr = 959 k N ( b) F cr = k N (c) Fcr = kn (1) x = , y = () = 40 mm

312 95 1) k d = E I 11 Fa () r3 = 3 5 Fa d 3 K d [ ] AB = MPa < [ ] BC = MPa < [ ] 65 % 35% ( 5,3 ) 1., 1. 18, A, B,,, ( ) ,, ( ) 3. 1,, D 1 D,G 1, G, D 1 > D, G 1 > G, ( ) 4. min = MPa, a = 40 MPa,( ) ,,, l, E A,k, ( ) ( 5,3 ) 1.,10, 5, 10 5,, ( ) ( A) 10 > 5 ( B) 10 < 5 ( C) 10 = 5 ( D)

313 , ( ) ,, R, t( Rt), A,, 1. 1 ( )1. 1 ( D)m , A B, A B, 1. ( ) 1. 5., F cr1, 1,, F cr,f cr / F cr1 ( ) ( A) 4 (B)8 (C) 16 ( D) 1. ( 10 ) ( 15 )1. 4,10,100 r/ min, D,

314 97 C ( 1) ; ( ) ; ( 3) 600 mm, F1 > F, F = 1. 5 kn, [ ] = 80 MPa, : ( 0 ) 1. 5,A BC E I, C, k = 3 EI a 3, : ( 1) C ; ( ) A 4. ( 15 ) 1. 6, CD No. 14, A B, D = 50 mm, d = 40 mm Q35, p = 00 MPa, s = 40 MPa, E = 00 GPa, a = 304 MPa, b = 1. 1 MPa, n = 1. 5, nst 1. 5 =, Fmax ( No. 14 W y = cm 3, W z = 10 cm 3, A = 1. 5 cm ) 5. ( 10 ) 1. 7, B, C, D, E,a, r F, : ( 1) B CD ; ( ) A

315 98. max = F ta d 3 1. B. D 3. B 4. B 5. C 1.. d6. cm 3. F C = F max = 6. 8 kn qa a = 5 qa3 144 EI ( ) 5. ( 1) FBx = F, FBy = F, FN, CD = F ( ) FAx = F, FA y = F, MA = 5 Fa + Fr ( 4,3 ) 1 3,, A, B, C D, 1. = F N A ( ) ( A) ( B) ( C) ( D). 1. 8,( ) ( A) y 1 - z 1, y - z ( B) y 1 - z 1, y - z ( A) y1 - z1, y - z ( A) y 1 - z 1, y - z 3., 1. 9, ( )

316 99 ( A) (B) ( C) ( D ) ,, 1. 30( ) ( F ), ( ) ( A) FS, M ; ( B) F S, M ; ( C)F S, M ; ( D) F S, M , A l/ 3, Me1 / Me = ( ) ( A) 1/ ( B) 1/ 3 ( C) ( D) 3 7., ( ) ( A) ( B), ( )

317 300 ( C), ( D), 8. 4, ( ), ( A) ( B) ( C) ( D) ( 6,68 ) 1. ( 10 ) ( 10 ) No 18 ( W z = 185 cm 3 ) F,, a b, [ ] = 160 MPa 3. ( 1 ) d, F, ,, ( 10 ) 1. 37, 5. ( 1 ) 1. 38, q( N/ m) A EI 6. ( 14 ) 6,1. 39, E, a = 1 m,d = 50 mm,,? F Q35,E = 00 GPa, p = 00 MPa s =

318 MPa, a = 314 MPa, b = 1. 1 MPa B. B 3. D 4. B 5. C 6. C 7. D 8. D 1.. a = b= m F14. 8 kn 3. r3 = 557 F d 4. l = l 6 E 5. M A = qr 4 6. AC, F = 43 kn (0 )1. 40, A, B, C, D,, A B, A AB = A BC = A BD, A B, (15 ) 1. 41, OA, O, y = cx 4, c E I, b,

319 (0 ) A B BCD, Q35, E = 06 GPa, p = 00 MPa, [ ] = 160 MPa, A B 1. 5 m, 50 mm60 mm BCD m, C, D Me,150 mm00 mm, 1. 4, n st = 3,M e 1. 4 (0 ) CDE d A d B ( A B ) C,D, C DDE, E F F CDE, CD L, DE L, A 3 E, 3 G, [ ], B E, G,[ ] 1. 43

320 303 ( 1) ; ( ) ; ( 3), (5 ) 1. 44, A, B, D, EI, A B, DE b, CB, CD b/,,, : ( 1) A, E ; ( ) C, F N, AH = 7 10 F, F N, BH = 3 10 F, F N, BC = F N, BD = 3 10 F q = 4 EIC, F = 4 EICb, M C = 1 EIcb M e 10 knm r3 = 9. 3 Fl d 3 [ ] F Bx = 9qb 8 ( ), F By = 7 4 FAx = qb 8 ( ), FAy = 3 4 qb( ) qb( ) M A = 3 4 qb C = 157 qb 3 qb E I ( ) ( 5 ) 1. ( 4 ) 1. 45, f, 1. 45,

321 304. (4 ) 1. 46, F = 00 kn, t = 0 mm, [ ] = 80 MPa, [ b s ] = 00 MPa,, d = 3. ( 6 ) 1. 47, F A B, max =, max = ( 5 ) 1. 48,l,d, A B, m, G, A A = ( 6 ) 1. 49, 45= 75 MPa, 45= 5 MPa, 1 =, = ( 75 ) 1. (15 ) 1. 50,,R, E 0, 1. E 0 F ( ) ( 5 ) F = 100 N H = 5 cm,, a = 0. 4 m, l = 1 m, d = 4 cm, b = 1. 5 cm, h = cm, E = 00 GPa, G = 0. 4 E, [ ] = 10 MPa,

322 ( 15 ) 1. 5, BC, I,BC A,,E A B q, : ( 1) BC ; ( ) BC,q? ( 0 ) D, dd( 1. 53),,, ( ), 1. 0 O1, O1 O. d = 5 cm 3. max = 3 Fl bh, max = 3 F bh A = 3 ml 8 G I p 5. 1 = 100 MPa, = 50 MPa 3 ( R + 0. r) 1. r = 3. 4R 3 F. d = 67 MPa > [ ]

323 FN, BC = Aqa3 3 Aa + I r3 = 113 MPa < [ ] q= EIBC (3 Aa + I) Aa 5 4. max = Ed 3D + Ed 1D (0 ) 1. 54,,E,, d, C, AC l, A F ( ) (0 ) A B 1. 55, d = 40 mm, F1 = 1 k N, F = 0. 8 kn, s = 40 MPa, n = ( 1) ; ( ) ; ( 3) (15 ) 1. 56,E = 00 GPa, = 0. 3, [ ] = 160 MPa, A BCD ( 1) EC ( (a) ( b), ) ; ( ) A BCD 1. 56

324 ) 1. 57,F H, C, B (15 ) : ( 1) ; ( ) (15 ) A BCD, A B, E I F = 1. 6 Ed4 l ( 1) A M z = 640 Nm, T = 16 Nm FN = 1 kn, FS ( ) = MPa = 1. 7 MPa = 0. 8 k N ( 3) r3 = MPa < [ ] B = 4 Ga3 + 3 Gla 4 EI H ( EI 4 Gd Ga l ) F Bx = 9 40 ql, F By = ql

325 308 F Ax = ql, F Ay = ql ( 5,3 ) ,,F (> ), F ( ) ( A) 0 E B 1 ( B) 0 E B ( C) 0 E B 3 ( D) 0 E B , ( ) ( A) 1 ( B) ( C)3 ( D) 4 3. ( ) ( A) ( B) ( C) ( D) Iy, Iz ( ) (1. 6 > < ) W, A,F T M e,, ( ) ( A) F A + 1 W M e + T [ ] ( B) ( F A ) + ( M e W ) + ( T W ) [ ]

326 309 ( C) ( F A + M e W ) + ( T W ) [ ] ( D) ( F A + M e W ) + 4( T W ) [ ] ( 5,3 ) ,, , , max = ,, 1. ( 13 ) 1. 69, E = 00 GPa,= A = 10 cm BC 0, B D,

327 ( 14 ) CD,( )A, B F Ay = 40 kn (), F By = 8. 5 kn () ( 1 ) T, A ; B, F = 5 kn, I z = cm ( 1) F, t, max,; ( ) F, c, max, ; ( 3) max ; ( 4) B [ ] = 100 MPa, d = 0 mm, 4. (15 ), 1. 7 d = 0 mm, E = 00 GPa O a = , b =

328 , c = F Me 5. ( 16 ) d A BC CD (,d 0 ) C, F, H B, CD Q35, b = 380 MPa, s = 40 MPa, p = 00 MPa, E = 00 GPa, G= 80 GPa, d = 50 mm, d 0 = 10 mm, L = 1 m, F = 00 N, H = 0 mm, n =, n st = B. D 3. B D 1. cb, b( h - a). 3. max = FN, BC = kn () FN, BD = 6. kn (). F s, max = 10 kn M max = 0 knm 3. ( 1) F A B, t, max = MPa ( ) F A B, c, max = MPa

329 31 F ( 3) max = 6. 6 MPa ( 4)= MPa < [ ], c, max = MPa 4. F = 0. 1 k N, T = Nm 5. CD n = 3. 6 > n st = 3

330 = = CD 1. 3 u, v, du d x, d v,+ d y 1. 4 ( a) A = 0, B = L,= L ( b) A = B = L 1. 5 = rad ,= L 1. 8 AB = l 1 cos + l sin l 1 l. 1 [ l] = [ ], [ l = ] E. FN, BC = 60 kn, FN, AC = - 40 kn BC = 300 MPa > s, AC = - 00 MPa < s AC = BC,. 5 = BC = l BC l BC AC l AC = lbc = ( 1) E ; ( ) ; ( 3). 7 ( 1) F N1 = 0 ; ( ) F N = FA. 8 p = , lp = p l = 5.63 mm. 9 = 0.3, E = 08 GPa, G= 80 GPa. 10 1,3, L 1 = L + L V = ( F 1 + F ) l 1 E A. 1 5 > w = > + F ( l - l 1 ) E A

331 F 7.7 kn. 16 F. 17 w = ( - 1 ) FL (), w = Fl E A E A ( ). 18 F = 10 kn. 19 (1 ) A = 3.1 MPa( ), B = - 6. MPa() ( ) A = MPa( ), B = MPa( ). 0 w A = cm, w B = cm. 1 DB = MPa(), DC = MPa( ). A 1 = A = A 4 = A 5 = 3.09 cm, A 3 = A 1 = cm = F eb, F b s = b( h - a) l d = [ ] 8[ bs ] 3. 7 D= 130 mm, 1max = 97 MPa, max = 0.8 MPa 3. 8 AB = - 64 M e Gd max = 14 Me1 d = 3 T Rt, F S = T l R x4 mm 3. 1 M e = E d3 8(1 + ) (1 ) = 44.4 MPa[ ], ( ) Me = 74.6 Nm (3 ) d = D = m (1 ) : A D max = / m < [ ] C D max = 0.66 / m < [ ] : A D max = 60.5 MPa > [ ] C D max = 35.1 MPa < [ ] ( ) A B ( 3) n M e l D A[ ] max = MPa, max = / m

332 Fs, max = 5 6 qa, Mmax = 5 6 qa Fs, max = 94 kn, Mmax = knm 4. 8 F s, max = 100 kn, M max = 10 knm D Ed [ ] - d 5. 8 = 0,= max = qx bh, max = - 4 qx bh, max = q b ( ), = 3qx bh, max = 59.3 MPa 5. 1 max = 1.7 MPa, m max =.096 MPa,B 1 cm t = 31 MPa < [ t ], c = 43 MPa < [ c ], = 10.5 MPa < [ ] M a / M b = M4.5 knm F max = bh [ ] 9 l ql EI ( 1) F = kn ; ( ) F = 81.4 k N 6. 6 w A = w = - 7 ql 4 4 EI q 0 x 10 E I L ( x3-3 L x + L 3 )

333 w = ql 4 EI x w = ql 1 E I x3 x < l q 4 E I ( x - l) 4 x < l - ( 5 qx 10 E Il ( - 4 l3 + 8 l x - 5 l x + x 3 ) A = qa3 6 E I, w C = wd = F l3 6 E I ( ) M e = ( T - T1 ) EI h Fla F C = 16( a 3 + EI k l ) M max = 3EI AT 3 I + A l 3 qa 4 EI ql k + 7 ql 3 4 EI ) ( x - l) + 5 ql 1 E I ( x - q l)3 + 4 E I ( x - l) 4 x< 3 l = 10 MPa, = 7. MPa, 3 = -. MPa, max = 71.1 MPa = = 80 MPa, = 40 MPa, 3 = 0, max = 40 MPa ( 1) max = MPa ( ) = 1.7 ( 3), n 1 n, 1 = = n n = 1.13 MPa, = 0, 3 = MPa, 0 = = , d max = cm, d min = cm AC = AB cos, = = - AB sin T = 3.58 k Nm, = = 3 Fl F 8 Ebh, 45 = 16 Ebh [ ( 1 - ) 3 l h 90 = x = y = 3 F l 8 Ebh E 3(1 - [ (3 - ) ) x + ( E 3 (1 - ) [( ( 1 + ) ] 60 ) ] 60 ) - ( 1-3 ) x ]

334 317 xy E 3(1 + ) ( (1 ) x = 100 MPa, ) x y = 49 MPa, ( ) r3 = 14 MPa < [ ] r4 = 17 MPa < [ ] (1 ) M e = Nm y = 80 MPa, y x = - 49 MPa ( ) A 1 = , 3 = , 0 = -.5 B 1 = , = , 0 = - 45 (3 ) = kn, = MPa, = MPa r3 = ( F 1 A + F l W ) T + ( W ) p 8. 5 max =.78 Fa d ( 1) max max = 1.55 ( ) ; ( ) = 1.9 ( ) ( 1) F = 40.8 kn, e= mm, () F = 4 k N, e= 39 mm 8. 9 a = 0 F d E ( ), A = MPa(), F = 17.4 kn, w C = 0.54 cm 8. 1 max = F b = - d E () F d, min = F d F = 1 57 N, e= 0.0 mm r3 = 105 MPa < [ ] E F = ( 1 - ) abh r3 = 151 MPa < [ ] = ( ) d = 5.1 cm B = MPa() V F = w 1 + w 9. 6 w A = 5 Fa3 6 EI ( )

335 V = AG L, v = G 9. 8 w y = 48 F R3 Gd ( 1) = 3.11 F R3 0 E I ( ) ( ) AB = 1.11 FR3 0 EI, A, B w = Me 6 EI ( l x - x 3 l ) (1 ) Mmax = EI 3R e; ( ) d 0 d = (4 +) FR 0 4 E I = e(4 +) 1 R w= F R3 EI ( ) w = 0.56 cm w = cm( ) w D H = 0 F Eb (), w DV wc = 4 Fl3 43 EI + F 9 k w C = Fa3 3 E I + 8 Fa E A C = 5 Fa 6 EI + 4 F E A F R3 w= ( +) EI = 300 F Eb ( ) (e) 10., max = MPa F N1 = F N = F ( I A l ) B = 0.78 mm wb = Fl3 33 EI w B = T = d4 4 ql 4 16 E I ( ) B = 3ql3 3 E I ( ), B= - = B + B = ql3 6 EI l ( EG 4 E + G ) w AC = Fa3 4 E I ( ) 7ql 3 96 E I ( )

336 ( 1) r3 = 147 MPa < [ ] ( ) w= cm() ( 1) M B = 74.1 Nm ; ( ) w C = 9.3 mm = 3 (- 3 3 ) = r4 50 MPa < [ ] B = qa3 8 EI ( ) F Ax = 6 3 F, F Ay = 15 3 F, F Cy = 15 3 F M A = F s = 5 8 qa F s = 7 16 Fa, = Fa3 3 E I qa, M = qa = 7.4 MPa() 10. F N = F N1 = e 5 a A F (5 a A + 3 I) FN = e L0 E 0 A 0 L0 1 E 0 A 0 + L3 3 EI L3 3 E I + L0 E 0 A 0 L0 E 0 A a L GI p 1 + a L G I p Fcr = E I l 11. ( b) ; ( F cr ) b = 9( F cr ) a ( 1) EI w = - F( w - ) - R( l - x) ( ) x = 0, w = 0, w = 0 x = l, y = R C, ( 3) [ F] = 160 k N F cr = 3.53 kn F N, max = 8.1 k N, F N, max = kn (1 ) F cr = EI 4 l ; ( ) F cr = 4 E I l (3 ) Fcr = 9 E I l ; ( 4) Fcr = E I l (5 ) F cr =.04 E I l

337 h b = = [ F] = 3.45 kn t = 3 hd 4 l 3l 3 ( bh 3 + d ) max = MPa < [ ], max = 5.44 MPa < [ ] max =.1 MPa < [ ], F cr = 78.5 kn > F N,BC kltankl = 6 I1 L I L Fcr = 1.4 E I l t = w = - F cr EI w ( 1) F = 9 E I 16 h ( k = F E I ) M x, w = Asin k x + Bcosk x + M L EI LFcr ( ) 1) CD A 1.5 l, FG A 3l ; ) FG,; x (a) 1. 3, 1. 4, - 1 n = n k f max 1. 5 dmax = ( H ( Eh3 b + 6 kl 3 ) 6 F l 3 ) st st = 6( F - F B ) l bh 1. 6 (a) 1. 7 n= 1. 8 max = 3 F EIv glw ( b) ( 1) max = ( H E A FL ) F A ; () max = P A + ( H E A F L ) F A

338 31. 1 : d, 1 = Fh F l E A F A : d, = Fh F l E A F A ( b) (a) K d = ( H + v g ) =.1 Fa E I ( W z 50 Fa ) 3 = Fa E I ( W z 50 Fa ) wc = 5.5 Fa3 EI ( E I 50 Fa ) H1.01 m x = [ F( l + a) + W l ( l - x ) ] ga l = [ F( l + a) + Wl 3 ] W l E Ag GE 1. 0 max = 15 gb 1. 1 d = st ( dmax = v W v g( ql3 3 EI + F l E A ) ) 3 E IF lg 1. 3 w = h,d, A B,F d = F( C h Fl 3 / 48 EI )

339 3 max 3 3 l g( 9 CA + 5 l v 0 E ) 1. 6 r3 = h + v g ( 13 E + 16 G ) F l3 d d 3 F l 1. 7 dmax = 1.08 MPa 1. 8 A = 3 F l3 d 4 ( 4 3 E + 1 G ) r3 = MPa 1. 9 F d = klv 3 EI lf g (3 EI + 4 kl 3 ) (3 E I + 5 kl 3 ) M d = ( EhI 33 Fa 3 )3 Fa K d = 31.7, d = 1.6 MPa

340 C. B 3. A 4. B 5. C. D. B 8. C 9. B 10. A Fs, max = qa, M max = qa r3 = MPa > [ ], F N, BC = N M A = 67.4 Nm, F Ay = N 1 = 80 MPa, = 0, 3 = 40 MPa F cr = N F s max = 5 q 0 l, M max = 1 15 q 0 l q 5 a (3 l E a + 3 I1 E1 ) 63 l 5 w B = 7 ql3 1 E I, B = ql3 EI, B = ql3 GI p B = ql3 3 EI 3 1. w = 5ql4 768 EI. 1 = MPa, 3 = MPa, 0 = 13 17

341 34 max MPa 3. M 1 / M = 1/ 4. m = 0, a = 34. MPa, r = b s = 10 MPa,= MPa 1. F N1 = 3 5 F - 5 E A l F N = 6 5 F + E A 5 l. F Bd = k N < [ F] = kn BC 3. F N = qal 3 A 1 I L + 8 Aa Aa L M E = ql 8 - qa L 3 A 1 I L + 8 Aa Aa L 4. t = c = E 1 M y E 1 I 1 + E I E M E 1 I 1 + E I y 5. d1 mm 4 = 10-3 rad, = 80 MPa, M e = 15.6 Nm F s, max = qa, M max = qa t7.3 [ F] 10.3 kn wy = 0.14 F l3 E I + F l E A M x = Nm, M y = 94. Nm, r4 = MPa > [ ] max = Fa 3 b ( a 3 + b 3 ) W H EI( a3 + b 3 ) Fa 3 + b 3 [ ] 5 s= 39.5 mm

342 35 A B = 3.39 MPa BC max = 03.6 MPa CD max = 07 MPa r4 = 8.1 MPa F = 667 N [ q] = 15 N/ m max = MPa wb = 3 Fl3 144 EI A - B = 11 Fa3 40 E I

343 36,.. :,1983,,.. :,1987 3,.. :, , :, :,1984 6,.. :, 198 7,.,. :,1985