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1 1 1. 1 1 1. 1. 1 1 1. 1. 1 1. 1. 3 1. 4 6 1. 5 8 10. 1 10. 1. 1 10. 1. 10. 11. 3 11. 4 14. 5 5 3 30 3. 1 30 3. 1. 1 30 3. 1. 30 3. 31 3. 3 31 3. 4 35 3. 5 45

50 4. 1 50 4. 1. 1 50 4. 1. 50 4. 50 4. 3 51 4. 4 5 4. 5 60 5 64 5. 1 64 5. 1. 1 64 5. 1. 64 5. 64 5. 3 65 5. 4 67 5. 5 77 6 83 6. 1 83 6. 1. 1 83 6. 1. 83 6. 83 6. 3 84 6. 4 85 6. 5 96 7 100 7. 1 100 7. 1. 1 100 7. 1. 100 7. 100 7. 3 101 7. 4 104 7. 5 114 8 119 8. 1 119

8. 1. 1 119 8. 1. 119 8. 119 8. 3 10 8. 4 11 8. 5 134 9 140 9. 1 140 9. 1. 1 140 9. 1. 140 9. 140 9. 3 141 9. 4 143 9. 5 154 10 158 10. 1 158 10. 1. 1 158 10. 1. 158 10. 158 10. 3 159 10. 4 161 10. 5 173 11 180 11. 1 180 11. 1. 1 180 11. 1. 180 11. 181 11. 3 181 11. 4 183 11. 5 195 1 01 1. 1 01 1. 1. 1 01 1. 1. 01 1. 0

. 3 0 1. 4 04 1. 5 16 1 5 77 89 1. 00 89. 00 93 3. 00 95 4. 00 98 5. 001 301 6. 00 303 7. 00 306 8. 00 308 313 33 36

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

. (1 ) ( ) (3 ) (4 ) 1. 3 1.,,,,,,.,,, ( ),, 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,

3, 1. 1 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,

4 1. 3 1. 4 ( ), 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 ),,, ;,,,, 1. 5 1. 6 5., A ( ), AB, x, x( 1. 6( a) ), x + u,u AB, ( 1. 6( b ) )

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. 8 1. 9 1. 10,, 1. 9 (a) ( b),, 1. 9( a), 1. 9( b), F m = FL, F,,, 1. 10( a)

6 BC, F A B, B F M = Fa( 1. 10( b) ) ; BC, A F 1. 4 1. 1, 1. 11 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) 1. 11 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, :,, 1. 1. 13 (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,

7 My Mz,, Fx = 0, FN = F Mx = 0, Mx = Fa My = 0, My = Fa 1. 13,,, F A C, D 1. 3 1. 14, BC ( A), (B), ( C), (D), B, BC A B (),, 1. 14 1. 15 1. 4 1. 15, F, ( A) a (B) b ( C) c (D) D, a(b, c), (),,,

8. 5 1. 1 1. 1 R, R R, R = 80 mm,r = 3 10-3 mm, 1.,,? 1. F C E,?? 1. 1 1. 1. 3 P P ACB (1. 3 ), P A C B, P x, y, PA x, PB y, P x P y 1. 4 1. 4( a), ( b) A, B 1. 5 A A B, AC 60 ( 1. 5),, 59.5, = 1. 3 1. 4 1. 6 1. 6, AB C, F A B C, (1 ) AB, BC? ( ) AB, BC?

9. 7 (1 ) ; ( ) ; ( 3) 1. 5 1. 6 1. 8 1. 8, l1, l, l1 l, AB 1. 8

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

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

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 = - =,,

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 ),,,

14. 4. 1. ( 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

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,,,,

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 = 5 10 3 = 6.5 10-4 00 10-6 00 10 9 = = 6.5 10-4, ( ) B (. 4( b ) ) A = 0 By = l1 = 6.5 10-4 m A y = l3, A A B = B y = 6.5 10-4 m A x = Bx = 1 3 Ay = 3.61 10-4 m = 3 Ay = 7. 10-4 m (3 ) : n = s FN1/ A = 80 106 00 10-6 =.4 5 10 3,,,,,,

17. 4. 5, 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,,, ;,,,,. 5. 6 (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 =

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)

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, = 1.5 10-6 - 1,. 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

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 ) = 1 10-4 +.5 10-4 - FN1 EA = BB= 3 7 10-4 - 4 FN1 EA FN l EA - tl = 4 3 FN EA - 5 3 10-4 = 7 10-4 - 4 FN1 EA = 3 4 FN 3 EA - 5 3 10-4 (1 ) ( ) 4 FN1 EA + 4 FN EA = 1 10-4 FN1 + FN = 3 10-4 EA ( ) 3 FN1 + FN1 = 3 10-4 EA 1 = FN1 A = 3 10-4 3 + 1 E = MPa = FN A = 3 FN1 A = 38.1 MPa,,,,,,,,,. 7. 8( a) A, B d = 1 mm, C F, = 0.003 5, C F. 8( b ), E =.1 10 5 AC l = l0 (1 + ) l = 1 000 + = 1 000 (1 + 0.003 5 ) M Pa,

1 000 + = 10 6 (1.003 5) C, = 1.003 5 10 6-10 6 83.74 mm = E0.00 + 0.1 E(0.003 5-0.00 ) = F = FN 0.00 15.1 10 5 = 451.5 MPa l + l = A l( 1 + ) = 451.1 10 6 10-6 59.1 N 4 83.7 1 000 ( 1 + 0.003 5) =. 8,,,. 8. 9( a), B F,. 9

(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. 9.10 (a), ( l) l ( 1), 5, AB 4, 1.10 ( b) A B A: Fx = 0, FN1 = FN ( 1) Fy = 0, FN3 = FN1 cos60 ( )

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)

4 FN = FN = FN3 = 6 3-4 F ( ) 3 FN4 = FN5 = 9 3-6 3 F ( ) A B, 4, 5, 1, A B ( AB, ), AB. 10.11,,,,, 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 = 0.055 EsT 4 Es = 0.109 EsT ( ) ( 3) ( 4)

5 4 ) 0, s 0 s0 0 A = s0 A = s 0 A T, 0 = s0 = s0 ( 1) 0 + 0.109 EsT s0 + 0.109 EsT = 0 + 0.109 EsT s0+ 0.055 EsT = + 0.055 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. 3. 3 A, F, A.. 3. 4. 4, F1 = 0 kn, F = 55 kn, q = 10 kn/ m, a = 1 m,. 5. 5, E = 00 GPa, B, 3 10-3, 140 MPa, =?. 6,. 6, : (1 ) E ; ( ) ; (3 )

6. 4. 5. 7. 7, A F, : (1 )? ( ) A??. 6. 7. 8,. 8, E = 00 GPa, l = 6 mm,?. 9,,, F 3 kn, 1 = 1010-6, = - 3610-6, E, G,. 9. 8. 9. 10. 10

7. 11 F1, F (. 11) A, E, F1, F, V 1 V, V= V 1 + V = F 1 l1 EA + F l EA. 10. 11. 1, 5 (l0 = 5 d(. 1) ) 10,. 1. 13. 13, C, EA. 13. 14. 14. 14( a) ( b ), A1 = A, L1 = L,

8 F = F, C1 C 1, ( A) 1 = ; ( B) 1 < ; ( C) 1 > ; (D). 15. 15, H K, AB CD, A, A = 4 cm, [ ] = 160 M Pa, AB, CD, F. 16. 16, A, B,,. 15. 16. 17. 17, AD, BD CD E A,, F, = = 45, D,. 18. 18 ABC,, 15, C F, ABC, F? AD, BE, : : Es =.0 10 5 M Pa, s = 1 10-6 - 1, As = 6 cm, : Ec = 1.0 10 5 M Pa, c = 16 10-6 - 1, Ac = 4 cm. 17. 18. 19. 19, 50 mm, 15 mm, 50 mm, 45 mm,, EB = 70 GPa,, EA = 100 GPa

9 0, 50, 15 kn, ( B = 10-6 - 1, A = 18 10-6 - 1 )?. 0 a. 0, ( ), A B,, [ ] = 10 MPa, E = 10 5 M Pa, F = 60 kn, a = 0 cm. 19. 0. 1. 1, DB, DC, E = 10 GPa, DC = l 3 10-3 AC, DB DC ( ).., a = 1 m, F = 150 kn, [ ], [ ] = 160 M PaA1 A A3 A4 A5 = 11 11,. 1.

30 3. 1 3. 1. 1 (1 ), ( ), (3 ) (4 ) (5 ) (6 ), (7 ) (8 ) (9 ) (10) 3. 1. : (1 ), ( ), ; (3 ), (4 ), (5 ) (6 ) (7 ) (8 ) : (1 ) ( )

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

3. :,, :,, = FS A [ ] [ ],, FS, u, u = FS, u A u [ ], [ ] 3. 3. 1( 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 (

33. 3), p,, G, Pa = G 3. 3. 3 :, 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 [ ]

34., (1 ) : n P, Me = 159. P n ( Nm) ( P k W, n r/ s ) Me = 9 549 P n ( Nm) ( P kw, n r/ min) Me = 7 04 P n ( Nm) ( P, 1 = 735.5 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 ),,,,

35. 4 3. 1 3. 5( a), F = 40 kn, 5, d = 0 mm, 3. 5 (1 ) F, 3. 5 ( b) M = Fa = 40 0.5 = 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 = 0 4 0.1 = 50 kn (4 ) 3. 5 (c), m in m in = FS1 d / 4 = 4 8 000 = 5.5 MPa (0) 10-6, FS FS y = FS1 + FS 3 5 = 8 + 50 3 5 = 38 kn FS FS x = FS 4 5 = 40 kn FS = F S x + F S y = 38 + 40 = 55. kn max = FS A = 4 55. 103 ( 0 ) 10-6 = 175.6 MPa, F ;,,

36. 3. 6( 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 = - 50 000 cos30 + 8 16 150 MPa = [ ] (3 ) = FS A b s = FbS AbS - 50 000 400 4 50 000 4 = = 79.6 MPa < [ ] = 50 000 8 = 31.3 M Pa < [ b s ] 6 8 16 =,,,, 3. 3 3. 7( a) d0 = 5 mm D = 50 mm, d = 5 mm, 0 mm, 50, Es =.1 10 5 M Pa, s = 11 10-6 - 1 ; Ec = 1.05 10 5 MPa, c = 17 10-6 - 1

37 3. 7 (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) 10-6 50.1 4 5 1.05 4 (50-5 ) 10 5 18.56 kn (5 ), 4 ( 50-5 ) 1.05 + 4 5.1 = Fs = FN s = 9.8 kn Fs A = 9.8 10 3 4 0 10-6 = 9.5 M Pa,, 3. 4 3. 8, L = 510 mm, D = 50 mm d1 = 5 mm, d = 38 mm, 70 M Pa, : (1 ) T 3. 8 =

38 ( ), L? (1 ) T Wp1 [ ] = 16 503 10-9 T Wp [ ] = 16 503 10-9 1 144 Nm 1-1 - ( ), 1 =, L1 L = Ip1 Ip = T L1 GI p1 5 50 38 50 = T L GI p 3 ( 504-5 4 ) 3 ( 504-38 4 ) L1 + L = 510 mm 4 4 70 10 6 70 10 6 = 1.407 L1 = 98 mm, L = 1 mm = 1 610 Nm = 1 144 Nm,,, L,,,,, 3. 5, 3. 9, Me, : l, R, t1, t, G (1 ) ( ) 3. 9 q (1 ) : q1 1 ;

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,,,,, 3. 6 3. 10, 5 mm, A B, 600 mm, 50 mm mm,, 00 Nm,, G = 80 G Pa, 1 t1 + 1 t 3. 10 ( 1) T = 00 Nm, T, M = M = M ( ) T, = Tl GIp

40 T,, + = (3 ), Ip Ip M = = Ip = d4 3 = 54 3 T 1. = 00 1. M r t Ml + Ml GI p GI p Tl GI p = Ml GIp, Ip = D4 3 3 50 4 1-46 50 = = 163.93 Nm Ip Ip Tl GI p + 1 (1-4 ), = 46 50 4 = 0. = 163.93 103 4 =.65 N/ mm =.65 MPa,, ;,, 3. 7 = B( 3. 11 (a) ), B, : (1 ) v( ) ; ( ), V ( max ), R, l( 3. 11 ( b) ) 3. 11 (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

41 3. 11( 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 0 3 7 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 3 3 1 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 =,,, 3. 8 3. 1 (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

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

43,,, 3. 9 3. 13( a) = 8 mm, D = 00 mm,, d = 0 mm, [ ] = 60 M Pa, [ b s ] = 160 M Pa, Me, s = 30 knm 3. 13 (1 ), = T R 0 = Me D = 30 10 3 (100 10-3 ) 8 10-3 = 59.7 M Pa ( ), 3. 13 ( b),, (3 ), FS FS = = 59.7 M Pa l = l s FS = s = 59.7 ( 8 10-3 ) s, l (4 ), (5 ), A = s [ ] d 4 FS s d 4 [ ] 1 = 0.039 5 m = 39.5 mm b s = FbS AbS 39.5 mm = FS d = s d [ b s ] s d[ b s ] = 0.053 6 m = 53.6 mm,,,

44. 10 3. 14( a), R, ABE, CDF ABCD,, 3. 14 ( b),? 3. 14 (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

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. 5 3. 1 (), 3. 1,, 3.,,,, 3. 3. 1 3. 3. 3 3. 3 3. 3 3. 4 3. 4, Me = 0 knm, me = 5 knm/ m, l = 1.5 m,

46. 5 3. 5, [ ], [ b s ],, L/ d? 3. 4 3. 5 3. 6 3. 6( a) ( b ) 3. 6 3. 7 3. 7, d = 75 mm 1 Me, D G = 80 M Pa, G = 10 GPa, Me = 16 knm, 3. 8 3. 8, B A A B ( A), Me, a, G, d, m 3. 7 3. 8

47 3. 9 3. 9, Me1 = Me, a = c = L/ 4, b = L/, d, 3. 10 L, R, t, 3. 10 (a),, R( R t), 3. 10( b) 3. 9 (1 ) T, ; ( ), 3. 10 (c), T, :?? 3. 10 3. 11 3. 11, [ ] = 0.6 MPa, a = 4 cm, b = 6 cm, F = 10-3 MN, x? 3. 1 3. 1 d, 15, E, (), ( ) 3. 11 3. 1 3. 13 d1 = 44 mm d D = 1, Me, 3. 13 60 60= - 5010-6 [ ] = 50 M Pa,

48 E 10 5 M Pa, = 0.3 : (1 ) ; ( ) ; (3 ) d, D 3. 13 3. 14 3. 14 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. 14 3. 15,, 3. 15,, D, l; [ ], A, Me, 3. 16 3. 16 ABC, d1 = 100 mm, A, B Me = 7 knm, C d = 0 mm EF G H, G = 0.4 E, G = 80 GPa ABC

49 3. 15 3. 16

50 4. 1 4. 1. 1 (1 ), ( ) (3 ), (4 ) (5 ) 4. 1. (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) :,

51. 3 1.,,,, (1 ) ( ), 4. 1( a), ( ), 4. 1 ( b) (3 ) 4. 1( c), 4. 1 :. 90, ; 4. (a) : (1 ) 4. ( b ) ( ),, 4. ( c) (3 ), 4. :,,

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. :, 4. 4 4. 1 4. 3, 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 = 75 3.5-10.5-80 + 1 30 1.5 = - 83.75 knm

53 MG 5 1.5-1 0 1.5 = 15.65 knm 4. 3 ) 4. 4. 4( 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 1.013 m, FS,, ME = - 15.013.013 + 30. 1.013 + 15 = 15. knm AD, A, A, MA AD, AD, 4. 3 4. 5( a),,,,,,,

54 4. 4, 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 - 1 18 q0 L = 7 q0 L 16

55. 5( c), ( d) 4. 5,, ( FS),,,, 1/ 3 4. 4 4. 6( a) 4. 6 ( b), ( c), C,, AB A 1. 8 m,, M = 9 1.8 + 4-1 5 1.8 = 3.1 knm, ( AC CE ) C F1, C, AC CE, 4. 5 4. 7( c),, :,, ;,,,,, d M FS =d x, d FS = q( x) d x,, FS M, FS, M, M, FS 4. 7( b), 4. 7 (a),,,

56,,, 4. 6 4. 7 4. 6 4. 8( a) ( ), 4. 8, FA = FC = F

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 4. 7 4. 9 (a), = d FS d x = q( x)?? 4. 9 FS ( x) = 0 4. 9 ( b) d M = d x d FS ( x) d x M( x) = qx h Mmax = ql h = q( x)

58, q( x),,,, qh, 4. 8 4. 10 (a), F = F1,, ( FS ) 4. 10 4. 10( b ) (f), C D,,, AB, F1, F B, BC ; B C, CD,, 4. 9 4. 11 (a) ABC,

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) 4. 11 4. 11( a) AB BC,, AB, F C B 4. 10 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)

60, x, x,,,,, 4. 1 4. 5 4. 1 4. 1 M, FN 4. 4.,, FS, max Mmax 4. 1 4. 4. 3 4. 3 ( FN, FS M), q, D 4. 4 4. 4, FS M 4. 5 4. 5, Me, q0 BC 4. 6 4. 6 CABD ( ), A, B FA y = 40 kn( ), FBy = 8.5 kn() 4. 7 4. 7, FS, max M max

61 4. 3 4. 4 4. 5 4. 6 4. 7

6 4. 8 4. 8, FS, max M max 4. 8 4. 9 4. 9( a), ( b), 4. 9 4. 10 4. 10, 4. 10 4. 11 4. 11( a) ( b )

63 4. 11 4. 1 R 4. 1, q0 M 4. 1 4. 13 AB 4. 13, B 1 m, 4. 14 4. 14, ABC, R, B Me 4. 13 4. 14

64 5. 1 5. 1. 1 (1 ), ( ) (3 ), (4 ) (5 ), (6 ) 5. 1. : (1 ) ( ) (3 ), (4 ), : (1 ) ( ) (3 ) 5. (1 ) ( )

65. 3 1.,,,,,,. (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 :, ( )

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 ( ),,,,,,,

67. 4 5. 1 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 = 03 1 3 969 cm 4 + 0 ( 10-8.) + 10 3 1 + 10 (8. - 1 ) = 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 = 40 103 (0-8.) 10-3 969 10-8 = 118.9 M Pa 40 10 3 ( 0-8. ) 1 10-6 10-3 969 10-8 = 7.01 MPa = 40 103 14 7. 10-6 14 10-3 969 10-8 = 1.45 M Pa = 40 103 14 7. 10-6 4 10-3 969 10-8 = 5.08 M Pa

68,,, z, ( ),, ( b),, 40 mm, 140 mm 5., 5., Iz 170 MPa, 6 m, B, : (1 ) B ; ( ) q, ( : AB M max ) = 1 184 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 = 1.514 q = Mmax ymax I z [ ] 1.514 q7 10-1 184 10-8 170 10 6 q 19 kn/ m ( ) MA = 0, q6 3 - FB ( 6-1.74) = 0, B, FB = 80.8 kn FS, max = - FB + q1.74 = - 47. kn

69 max = FS, max S* z max Iz b - 1.74 MPa = - 47. 103 [ 7 6 + 5.5] 10-6 10-1 184 10-8 =,,,,, 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 = 0.04 0.1 6 = 96 10-6 m 3 [ F] = 4 [ ] W z1 = 4 100 10 6 96 10-6 = 38.4 kn ( ) :, 1 [ F], A, A x, 5. 3( b ) x MB = 0, C FA = 3.5 - x [ F] 4 Mx = FA x = [ F] 4 ( 3.5 x - x )

70 Mx (3 ) : d Mx d x = [ F] 4 ( 3.5 - x) = 0 x = 1.75 m Mma x = [ F] 4 ( 3.5 1.75-1.75 ) = 9 400 Nm max = Mmax W z = 9 400 = 98 MPa < [ ] 300 10-6,,,,,, D 5. 4,, 5. 4,, E = 00 GPa, E = 10 G Pa 5. 4 q = 10 kn/ m, Mmax = 1 8 ql = 1 8 10 4 = 0 knm Mmax = M+ M,, M E I = M E I I = 1 1 1 303 = 7 000 cm 4 I = ( 1 1 0.6 303 ) = 700 cm 4 M = 40 3 M = M knm, M = 0 3 knm

71 max = M, max W = M W = = 40 3 103 15 10-700 10-8 = 74.07 M Pa 0 3 103 15 10-7 000 10-8 = 3.70 MPa,,, Mmax = M+ M,, MM 5. 5 ( 5. 5 ), l = 10.5 m, 36 a, I z = 15 760 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) 103 10.5 4 = 16.75 knm : Iz = 157 60 + 10 1.63 1 + 18.8 10 1.6 = 7 077 cm 4 max = M max ymax I z = 16.75 103 7 077 10-8 196 10-3 = 117.8 MPa < [ ] ( ), Mmax [ ] W z = 140 10 6 875 10-6 = 1.5 knm x, x, Mx = l - x ( 50 + 1) 10 3 x = 1.5 10 3 l 6 x - 651 x + 1 86 = 0 x = 651 651-4 6 1 86 6 = 7.86 m.64 m

7 L 10.5 -.64 = 5. m,,, ; x,, x 5. 6 5. 6, T, : (1 ) ; ( ) ; (3 ) 5. 6 (1 ) I z : Iz = 8 3 1 + 8 4. + 13 1 + 1.8 = 763.7 cm 4 ( ) : A,,, t = 5 103 8.8 10 - = 57.6 10 6 Pa 763.7 10-8 c = 5 103 5. 10 - = 34 10 6 Pa 763.7 10-8 B,,,, (3 ) max : t = 6 103 5. 10 - = 40.9 10 6 Pa 763.7 10-8 c = 6 103 8.8 10 - = 69.1 10 6 Pa 763.7 10-8 tmax = 57.6 M Pa ( A ) cmax = 69.1 M Pa ( B )

73 max 11 10 3 8.8 4.4 10-6 763.7 10-8 10 - = 5.58 10 6 Pa = 11 103 3 4. 10-6 = 1.8 10 6 Pa 763.7 10-8 10 -,, S * z *, 5. 7 5. 7( 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

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 3 + - q 4b = - 0.5 q b ( ) y = 4 cm, = 1 6, = 0; y = - 4 cm, = - 1 6 5. 7( c) ; (3 ) y = h, = 1, = q b ; y = - h, = - 1 1 4 = - 0.5 M Pa, 5. 7( b ) ;, = - 0.333 q/ b = - 0.333 M Pa,, = 0 5. 7( d ),,,,, 5. 8 5. 8,, M, 5. 8, : Ew, Es (1 ) ; ( ) :,, 5. 8 (1 ) = y ( a)

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 5. 9 5. 9( a), l = 300 mm, F = 500 N,, Ew Est = 10 GPa, = 10 GPa, (1 ),, z,= Est b1 Ew = 10 10 ( ) ( 5. 9( b ) ), = 1, = 1 0 = 40 mm

76 y = y.5 40 1.5 + 0 50 7.5 0.5 + 0 50 = ( 50 +.5) - 14 = 38.5 mm = 14 mm I z = (3 ) : w, max st, max = = 40.53 1 56. 10 4 mm 4 Mmax y Iz M max y1 Iz + 40.5 1.75 + 0 503 1 + 0 50 13.5 = = 500 0.3 38.5 10-3 56. 10-8 = 10.3 10 6 Pa = 10.3 M Pa = 1 500 0.3 14 10-3 56. 10-8 = 78.7 10 6 Pa = 78.7 M Pa 5. 9 5. 8,,, z,= Est,,,,, st, max = Ew Mmax y1 I z 5. 10 5. 10 T, A ( ), B, F = 5 kn, I z = 1 367 cm 4 (1 ) F, t, max, ; ( ) F, c, max, ; (3 ) max ; (4 ) B [ ] = 10010 3 kpa, d = 0 mm, (1 ) F A B,,,,

77 t max = 5 103 4 8.5 10-4 1 367 10-8 = 155.4 10 6 Pa = 155.4 MPa ( ) F A B, F, F AB, F, c, max c, max = 5.5 8.5 t, ma x = M M t, max = 0.8 1 t, max, F, 14.4 MPa = 100.6 M Pa = 14.4 M Pa (3 ) F A,, FS = F,,, max = FS S* z I z b = 5 10 3 4 8.5 8.5 10-6 4 10-1 367 10-8 = 6.606 M Pa (4 ) F B, FS F,, = P A = 5 10 3 = 39.8 MPa < [ ] 4 0 5. 10,,,, 5. 5 5. 1 5. 1 A - A, 5. 5., 5. 3 Z, 5. 3( a), ( b ),

78 5. 1 5. 5. 3 5. 4 5. 4( a), T ( ) 5. 4 5. 5 5. 5, O, A,, 5. 6, a = l/ 4 (5. 6 ) 5. 7 5. 7 d, D, [ ], E, D 5. 8 h, b, Me 5. 8( a),?, h/, b (

79. 8( b) ) 5. 8( a)?? 5. 5 5. 6 5. 7 5. 8 5. 9 5. 9, q(n/ cm),,, x, 5. 9 5. 10 5. 10( a),, (1 ) x ( 5. 10( b ) ) ;

80 ) 5. 10 5. 11 AD, 5. 11 (1 ) ; ( ) q = 60 kn/ m, a = 1 m,? 5. 11 5. 1, m, q = 6 kn/ m, 1 m,,, 5. 1 (1 ) ; ( ), 5. 1

81. 13 ABC 5. 13,, [ t ] = 3 MPa, [ c ] = 80 M Pa, [ ] = 5 M Pa, z, I z = 35 10 6 mm 4 (1 ) ; ( ) Iz ( ) ; (3 ) ; (4 ) ; (5 ), T?? 5. 13 5. 14 10 cm, 0 cm, 1 cm, 5. 14,,, E = 0 E 5. 15,, 5. 15 E1 [ ] = 1 M Pa = 11 GPa, [ 1 ] = 14 M Pa; E = 8 GPa, 5. 14 5. 15 5. 16 5. 16, l, b, h, h 6, h 3, h,, F E, [ ], 5. 17 5. 17

8 E, E, ( ) E1 > E,? 5. 16 5. 17

83 6. 1 6. 1. 1 (1 ), ( ) (3 ) (4 ) 6. 1. : (1 ) ( ) (3 ) : (1 ), ( ) (3 ) 6. (1 ) ( ) wmax [ w] (3 ) max [ ] (4 )

84. 3 1. (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.,

85 (1 ), ( ), 1 = M EI, 5. 6. w max [ w] max [ ],,,,,, 6. 4 6. 1,, 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, )

86, w = w= M( x) E1 I1 + E I M( x) E1 I1 + E I ( ) wc = - 5 ql 4 384 EI = - 5 ql 4 384 E( I1 + I ) = - 5 ql 4 3 Eb( h 3 1 + 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 ) ; ( ),

87 FA = 1 l ( 1 ql 1 3 M( x) = ql 6 x - 1 6 EI w= - M( x) = - EI w= - EI w = - l) = ql 6 () q l x3 ql 6 x + 1 6 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 = 0 6. 3 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 4 + 7 l 4 ) EI= - ql 1 x + q 4 l x4 + 7 ql3 360 = 0 - l x + x 4 + 7 15 l4 = 0 x = 0.519 l wmax = 0.006 5 ql4 EI, ;,, w, 6. 4 6. 4( 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)

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 8 + 1 ( 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 ( )

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) 6. 5 6. 5 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

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, 6. 6 6. 6 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

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 3 + 1 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

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 - 1 6 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 - 1 6 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

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

94 EI w x = 0, A w A = qx 3 4 FL 3 384 EI ( L - x) - ql3 96 x + ql4 384 wa = Fa3 48 EI,,,, C,, 6. 9 6. 9, A, C ;, B F, = 600 10-6, 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

95 wb l 3 3 EI 3 l E I h = l h = 600 10-6 ( 60 10-3 ) = 54 10-5 10-3,,, 6. 10 6. 10( a), AB CD BD, AB CD EI, l, F m 6. 10 (1 ) AB CD, 6. 10( b ), 6. 10 ( 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 ( 6. 10 ( b) ),, F - FS = FS F = FS F = 4 EI l 3 AB CD, B D,,

96. 5 6. 1 6. 1 (a) w1 = 5ql4, 6. 1 ( b ) 384 EI w = 6. 1 6. 6.,,,,,, 6. 6. 3 6. 3( a), ( b ), (c), ( d ), ( ) 6. 3

97. 4 6. 4, EI,, y = - ax 3,,? 6. 5 6. 6, AB b = 40 mm, h = 60 mm, E = 10 G Pa, : (1 ) S 1 ( 1/ 100 mm), F? ( ) AB = 8.06 10-6, F? 6. 4 6. 5 6. 6 ABC 6. 6, AB BC E I, AB q, A w A () 6. 7 6. 7 ( ), EI = 6. 6 6. 7 6. 8 6. 8 ( EI = ), B, k 6. 8 6. 9 6. 9, AB, EI, l,, 6. 10 6. 10 w, l, t, : w ( ) :

98 w t l 6. 9 6. 10 6. 11 AB CD, C, 6. 11 (1 ) ; ( ) EI, A A w C 6. 1 ABCD 6. 1, AC I, CD I, E, D 6. 11 6. 1 6. 13 6. 13, E1, h1, 1, b = 1, E, h,, b = 1, 1 >, t,, B wb t 6. 14 6. 14, (l), h, T1, T ( T > T1 ), (, E, ),, 6. 15 6. 15 AB, EI, B BC, C, k, FC

99. 16 6. 16, EI, EA,,, 6. 13 6. 14 6. 15 6. 16

100 7. 1 7. 1. 1 (1 ), ( ), (3 ), (4 ), (5 ) (6 ), (7 ) 7. 1. : (1 ) ( ),, : (1 ) ( ) (3 ), 7. (1 ),

101 ) (3 ) (4 ) 7. 3 1. (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 :

10 ; ;,, 1, 1,,, 1, 3 ; 0, 180, 0 90 7. 1 ( ) : 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

103,,, =, E 5. v= 1 1 1 + 1 + 1 3 3 v= 1 E [ 1 + + 3 - ( 1 + 3 + 3 1 ) ] vd 6. = vv = 1-6 E ( 1 + + 3 ) = 1 + 6 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 [ ], : [ ] [ ],

104 8., (1 ) ( ) : r1 = 1 [ ] ( ) ( ) : : r = 1 - ( + 3 ) [ ], 5 % ;,,, 9. (1 ) ( ) : r3 = 1-3 [ ] ( ) ( ) : () : r4 = ; 1 [ ( 1 - ) + ( - 3 ) + ( 3-1 ) ] [ ] 7. 4 7. 1 7. ( 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),,

105 7. 7. 7. 3 45 = 3.5 10-4, = - 5.63 10-4, E = 00 GPa,= 0.3, d = 10 cm, Me 7. 3, = = 1 [- E ( - ) ] = E ( 1 + ) E 00 103 = 1 + 1 + 0.3 3.5 10-4 =, E = - 86.6 MPa 1 + = 50 M Pa = - sin ( 1)

106 (1 ) ( ) sin (45+ ) = cos ( ) ( ) + ( ) = = ( ) + ( ) = 100 MPa Me = Wp = 100 1003 16 = 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 = - 100 MPa 7. 4( c), 7. 4( d),, 1 = max = 100 M Pa = y 3 = - max = - 100 MPa = x x = 1 E [ x - y ] = 1 E [ - max - max ] =

107 100 10 6 00 10 9 (1 + 0.3) = - 0.65 10-3 y = - x = 0.65 10-3 ( ) ( ) z, ( ), z = 1 E [ - ( - max + max ) ] = 0 z= 1 E [ - ( - + ) ] = 0,, 10 mm, + 45-45,,,, 7. 4 7. 5( a) D, Me F, Me F,?FMe E, G, 7. 5, 7. 5( b ) 0 4 5 (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

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

109 1 = x + y ( x - y ) + 3-30 + 30-30 - 30 x y = + 30 = 30 = 4.43 M Pa = 1 - x y arctan ( x - y = 1 arct an - 30-30 = 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 () 7. 7 7. 7 (c), max = 36 103 = 144 MPa < [ ] 50 10-6 F( m - m ), F = 144 100-11.4 100 = 17.6 MPa F = 60 103 ( 10 11.4 ) ( 100-5.7) 10-9 = 9. MPa 500 10-8 9 10-3 r 4 = 17.6 + 3 9. = 137.3 M Pa < [ ]

110 max = 60 10 3 16.9 10-9 10-3 = 39.4 MPa r4 = 3 39.4 = 68. MPa < [ ],,,,, ; m - m, ; ( ),,, 7. 7, q ( 7. 8 (a) ) 7. 8

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),,,,, 7. 8 7. 9, 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 ( 3 4-1 4 )

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 - ) 7. 9 7. 10, E,, A, 90, F 7. 10 E= E= - - E(+ ) = ( 1 - ) ( + ) + = = F A F = A(+ ) = EA 1 - ( + ),

113. 10 A60, A 7. 11( a), F A 7. 11 7. 11( b ), - ( 1 0 - = F = 1 + + 1 - cos ) = F = 1 + + = 1-3 F = 1 - sin cos [ - (10 - ) ] 1 = 5 F, = F, = 60 7. 11( 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 ) = - 60 30 a( F, 3 F) b( F, - 3 F), 60, ab bac = - 60, C, C, Ca, 7. 11 ( d): 5 F F 1 = 5 F, = F, 1 = - 60, = 30,,,,,

114. 5 7. 1 7. 1, 1,, 3, max 7. 7.,,, p,?? p = 100 10 4 Pa 7. 1 7. 7. 3 7. 3 7. 3 7. 4, 7. 4, a 7. 5 7. 5 A, ( : M Pa) 7. 4 7. 5

115. 6 M FS (7. 6),,, 7. 7 7. 7 D = 1 cm, t = 4 mm, p = 6 MPa, Me = 4 knm, : (1 ) ; ( ),?? (3 ),? ( )?0 mm, 1 000 7. 6 7. 7 7. 8 7. 8,, F FN, E = 10 5 M Pa, = 0.3, A, D 3 0= - 03 10-6, 6 0= 343 10-6 (1 ) D ; ( ) D 7. 8 7. 9, D = 5 cm, t = 5 mm, p = 8 M Pa, T = 15 knm d = 5 cm, 7. 9, E = 00 GPa, = 0.3, 7. 10 7. 10 AB, AC 7. 11 7. 11, l, 45, = 34 10-5, D = 80 mm, d = 60 mm, l = 80 mm, E =.0 10 GPa,= 0.3, : (1 ) T =? ( )

116 7. 9 7. 10 7. 11 7. 1 7. 1,, A ( ), E G = E, F,?(E,, b, h, l ) ( 1 + ) 7. 1 7. 13 A x, 60 1 0,, x, y, x y x 60, 1 0 (7. 13 ) 7. 13 7. 14 7. 14 O,, 45 7. 14, :

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, 7. 16 7. 16 Me, Me, Me 7. 15 7. 16 7. 17 7. 17 (a), D = 8 cm, d = 4 cm, H - H A, B, 7. 17 ( b) Q35, E = 00 GPa,= 0.3, : (1 ), ; ( ) A, B ; (3 ) B, 7. 17( c),,,? ( M Pa) 7. 18 45, x y = u - ( x + y ) (7. 18) 7. 19 cm, 5 cm,, 7. 19,, F ( F = 80 kn), FN ( FN = 30 kn), = 0.3, : (1 ) ; ( ) AA (= 30 ),

118 7. 17 7. 18 7. 19

119 8. 1 8. 1. 1 (1 ), ( ) ( ) (3 ) 8. 1. : (1 ), ( ) ; (3 ), : (1 ) ( ) ( ) ( ) 8. (1 ) : xoy Mz ( xoz My, ) ( ) ( ) (, )

10 (3 ) (, ) r 8. 3 1. (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 [ ] [ ],,,

11 r = 1 W M + T [ ] : r4 = 1 W M + 3 4 T [ ] (1 ), ( ) ( ) (3 ), M 8. 4 8. 1 8. 1( a), A = 80 10-4 m, W = 10010-6 m 3, Wp = 0010-6 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 = 10 + 8 = 1.8 knm W = MW W 1.8 103 = = 18.1 M Pa 100 10-6 N = FN A = 0 103 80 10-4 =.5 M Pa = W + N = 130.6 M Pa = T Wp 1 = ( 3 ) + = 1.93%, = 4 10 3 00 10-6 = 0 MPa 130.6 130.6 ( ) + (0) = 65.3 68.3 r3 = 1-3 = 136.6 M Pa > [ ] = 134 MPa AB,,, r3 = + 4 = W + N = 130.6 M Pa

1 8. 1 8. ( ), 8. (a), 4 m, 1 m, 6 mm, 0.36 M Pa, 1 500 N/ m, A, B, F = 4 1 500 = 6 000 N q = 1 500 N/ m F1 = FN = F sin = 5 F F t an = F t an= 1, sin= 5 5 AB

13 M F B = pd 4 t - FN A B 1.5 - = 0.36 106 1 4 6 10-3 - 1 = pd t A, = pd 4t A - q 4 + FN 0.5 = 3 4 F = 4 500 Nm 6 000 3.14 1 6 10-3 = 14.68 M Pa () = 0.36 106 1 6 10-3 = 30 M Pa () FN A - M W = 15-0.318-0.97 = 13.71 MPa W = 3 D3 ( 1-4 ) 1 = pd t = 30 M Pa A, B 8. ( b) 8. (c) 8.,, B, 1 = 14.68 MPa, = 30 MPa, 3 = 0 AB C 8. 3 8. 3, F T, F

14 e AB a b, a = 50 10-6, b = - 9.5 10-6 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 = 0010 9 ( 5010-6 - 9.510-6 ) (100 10-3 401 kn (1 ) - ( ) 64 Fe d 3 = E( a - b ) 8 ) = e = E( a - b ) d3 64 F = 0010 9 (5010-6 + 9.510-6 ) ( 100 10-3 ) 3 64 401 10 3 = 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

15 Ip d 4 3 = 8cm4 I = bh3 1 = 1 cm4 Wp = d3 16 = 4cm3 8. 4 (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 < [ ]

16 3 ) C w C : wc1 = wc = Fal GI p Fl 3 3 EI z = 0.16 cm a = 0.078 cm wc3 = Fa3 3 EI = 0.10 cm wc = wc1 + wc + wc3 = 0.306 c m, r4 = 1 W M + 0.75 T ; C, 8. 5 8. 5 (a), 100 kw, 00 r/ min,, 0 () F1 ;,, [ ] = 80 M Pa( sin0= 0.34, cos0= 0.94 ), T = 9 549 P n = 9 549 100 00 F1 ( 8. 5 ( b) ), = 4 774.5 Nm F1 F1 F1 = F1 cos0 D1 = T T 4.77 = D1 cos0 0.6 0.94 = 16.9 kn F1 y = F1 sin0= 16.9 0.34 = 5.79 kn F1 z F, = F1 cos0= 16.9 0.938 = 15.9 kn ( F - F ) D F 8. 5( c) = T D = = T 4.77 1 3 F = 3 9.54 = 8.6 kn = 9.54 kn

8. 5 17

18 My, Mz Fz 8. 5 ( d), MA = 0, = 0 8. 5( f), M B Fy FAy = = 0, FBz = F1 z 0.5 = 15.9 0.5 = 3.98 kn FAz = F1 z + FBz = 15.9 + 3.98 = 19.9 kn = 0, FAy -.5 F1 y - 3 F 1 = 0 3 F +.5 F1 y = 8.6 +.5 5.79 FBy - 3 F + FA y - F1 y = 0 = 1.54 kn FBy = 3 F - FA y + F1 y = 8.6-1.54 + 5.79 = 1.85 kn M8. 5 (e), ( g), ( h ),, M = M y + M z = 3.98 + 1.85 = 13.45 knm T = 4.77 knm 1 W M + T [ ] W = d3 3 M + T = 13.45 + 4.77 = 14.7 knm d 3 3 14.7 106 80 d 1 mm = 1.8 10 6 mm 3,,,,, ( z ) ( y ),,, 8. 6 8. 6 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 (50 + 150) 10-3 = 4 10 3 400 10-3 = 1 600 Nm, x ( ) F x, FN = 4 10 3 400 400 + 50 = 3 390 N

19 T F 150 10-3 400 400 + 50 = 17. Nm My = F 400 + 50 10-3 + 150 10-3 50 400 + 150 = 551 Nm (3 ) (4 ) M = M y + M z = 1 69 Nm r3 = + 4 = M W + FN A = 1 69 3 ( 80 10-3 ) 3 1 - = 3 390 4 (80 10-3 ) 1 - T Wp = 70 80 17. 16 ( 80 10-3 ) 3 1-70 80 4 + = 84. 10 6 Pa 70 80 4 = 3.06 10 6 Pa r3 = 84. + 3.06 = 84.4 MPa < [ ] 8. 6,,,, ( ), r3 = 1 W M + T,,,, 8. 7 8. 7( a) AB,

130 Fx Fsin = 5 sin30= 1.5 kn ( 8. 7 ( b) ) Fy = Fcos= 1.6 kn N = Fx A = 1.5 10 3 = 0.6 MPa () 30 16 10-4 Mma x = 1 4 Fy l = 1 4 1.6 300 10 - W = Mmax bh C, 6 3 = 18.7 knm = 18.7 103 6 16 30 10-6 = 7.8 M Pa c, max = - (7.8 + 0.6) = - 8.05 M Pa C, t, max = 0 + 7.8 = 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, 400 10-6, 100 10-6 FN, E = 00 GPa, = 0.3 T, 8. 8 ( b) FN, 8. 8 (c), R1 T 1 3, 1 ; R 3 1,

131, R1 1, R1, R, t = t (1 - E ), t = FN D 4 1 + t, R t - 1 8. 8 : : : = 1 + t - ( t - 1 ) = 1 = 1 + t + ( t - 1 ) = t = 400 10-6, = 100 10-6, 1 = 1 (1 + ), E T = E 1 D 3 1 + 16 1 = 00 10-6 t = 50 10-6 1 = = T W p = 386.7 Nm

13 FN E t D 1-4 = 35.9 kn,,, ;,,, 8. 9 8. 9 (a) M T, A 0= 5 10-4, B 45 4 5= 4.510-4 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= 600 10-9 00 10 9 5 10-4 = 60 Nm ( ) B 8. 9 (c) T = 45= 1 E ( 45- - 45) = 1 + 1 + T = E E EWp 45 1 + = EW 4 5 1 + = 00 109 600 10-9 1 + 0.5 (3 ) Wp 4.5 10-4 r4 = 1 W M + 0.75 T = 159.8 M Pa < [ ] = 86.4 Nm,,, 45, (),,, 8. 10 ABC, 8. 10 (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,

133 A My = FL, Mz = FL, T = FL ( = Mx ) BAB : My = FL, T = FL ( = Mx ) 8. 10 ( ) 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 =

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

135. 5 d 8. 5, 8. 6, F = 90 kn, 10 mm, : (1 )? ( ) ( 8. 6 ),???( ) 8. 3 8. 4 8. 5 8. 6 8. 7 AB ( 8. 7( a) ) CD (8. 7( b) ),? 8.8, ( ), F, 8. 8 (a) E1 = 1 10 5 M Pa, E = 0.7 10 3 M Pa, b = 10 mm, h = 40 mm: (1 ) m - m, = 60010-6 (8. 8 ( b) ),, F e ( ) m - m ( 8. 8 (c) ),, F e 8. 9 8. 9, d A B, B m = Fd ( ) F() E, ( ) = 1 3 O a 45O b a b 8. 10 8. 10, Z, Fy = 4 kn,

136 8. 7 8. 8 8. 9 Iy = 83 10-8 m 4 ; I z = 1 93110-8 m 4 l = 3 m

137 8. 11 8. 11,, 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? 8. 10 8. 11 8. 1 8. 1,, F, 8. 13 8. 13 d = 4 mm, E = 00 GPa, a = 480 10-6, b = 50 10-6 F e 8. 14 8. 14, AB, d = cm, l = 0.3 m, a = 0. m, [ ] = 140 M Pa AB 8. 15 8. 15,, A = 45, E, b, h F 8. 16 8. 16, d = 8 cm,

138 8. 1 8. 13 8. 14 [ ] = 160 MPa 8. 15 8. 16

139. 17 8. 17, Me = 3 Me1 = 900 kn mm F = 0.5 kn, Me1, Me C, B F d = 50 mm, l = 1 m, E =.1 10 5 M Pa, = 0.8 a 45a B 8. 17 8. 18 8. 18 (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

140 9. 1 9. 1. 1 (1 ), ( ) (3 ) (4 ) 9. 1. : (1 ) ( ) (3 ) (4 ) : () 9. (1 ) ( ) ( ) ( ) (3 )

141. 3 1. (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 ) ( ),,

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

143. 4 9. 1 9. 1( 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 + 1 0 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 9. 9. (a), AB C F, AB BC, EI, C F, 0 <

144, 9. F, FF = 1, F M M, 9. ( b) ( c) C = 1 EI - - 1 FL sin ( 3 Lcos ) - FL sin ( Lcos+ 1 Lsin ) + 1 FL cos ( Lcos+ 3 Lsin ) = 0 1 3 sin cos- sin cos- 1 sin + 1 cos + 1 3 sin cos= 0 cos - sin - sin cos= 0 cos- sin= 0 tan= 1, = 4 = 8 ( ), F,, F, F 9. 3 9. 3 (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

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 9. 3 9. 4 9. 4( a) A, EI( )

146 9. 4 9. 4 (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 + 1 0 EI ( - Fx ) ql 4 EI ( 1 1-1 8-1 16-1 16 ) = - 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 9. 5 9. 5 (a) D,

147 EA a 9. 5 D, D, 9. 5(b),, FN,,, 1 a a, 9. 5 (c),, FN 9. 5( a), FN 9 1 9 1 F N l F N F N F N l F N F N F N l - - 3 F a - 3 F a - 0 a 0 a - 1 3 F a 1 3 F a 1 3 F a - 1 3 1 3 1 1 3 1 3 3 1 3 1 3 3 Fa - 3 Fa - 1 3 1 3 1 a 1 a 3 F 3 F 0 0 0 0 0 0 1 6 Fa 3 1 6 Fa 1 3 1 3 Fa - 3 1 a 1 a 1 a 3 F 3 F 3 F

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

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 9. 7 9. 7 (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

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, 4 9. 8, 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 =

151 qh l 8 EI + ql EA = - 3 ql Ebh + ql Ebh = - ql Ebh ( ),, A, A,, 9. 9 9. 9( a), ABC t1, t, C wh, wv ( h) t > t1 9. 9 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),

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) =,,,,,,,,,,, =

153. 10 9. 10 (a), r1, r, b,,, A ( ) G 9. 10 r,, r, 9. 10 ( 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,,

154. 5 9. 1 9. 1, 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 ) 9. 1 9. 9. 3 9. 3,, M, V( M), T, V( T), V( M, T ), V( M, T) = V( M) + V( T )? 9. 4 9. 4,? 9. 3 9. 4 9. 5 9. 5 V F? 9. 6 wa EI, F, a (9. 6 ) ) 9. 7 abcd FS, 9. 7,, G, AFS (1 ) ; ( ), :

155 9. 5 9. 6 9. 8 d 9. 8, R, O F, OA, O 9. 7 9. 8 9. 9 9. 9: (1 ) a ; ( ) EI, 9. 10 9. 10, Me, EI 9. 9 9. 10 9. 11 9. 11 B F wb = F E I E ; ; I ; 1 3 ( a3 + b 3 ) + C( a + b ) + (1 + ) a b + C I A

156 A 9. 1, R0, ( ), e, 9. 1, E,, x 9. 11 9. 1 9. 13 9. 13, A, EI, C F C ( ) 9. 14 d = 1 cm, 9. 14 3/ 4, OA, r = 10 cm, O F = 100 N, G = 85 GPa,, O? 9. 13 9. 14 9. 15 9. 15, F = 500 N, L = 1 m, a = 4 cm, E = 00 GPa B,

157 9. 15 9. 16, C F, 9. 16, b h, l = 10 h, ED 9. 16 9. 17 AB E I, B, 9. 17, k, F C 9. 18 9. 18, BC AD, BC EI, AD EA, C F, C 9. 17 9. 18

158 0 10. 1 10. 1. 1 (1 ), ( ) (3 ), (4 ), 10. 1. : (1 ) ( ) (3 ) : (1 ) ( ) (3 ) 10. (1 )

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

160., (1 ) :,,, ( ) :,,, 1 = 11 x1 + 1 x + + 1 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 = 0 10. (a),, 10. ( b), ) 10. 4. (1 ),

161 ) (3 ) 10. 4 10. 1 ABC, d = 0 mm, C CD, ( C, D ), d0 = 1 mm, 10. 3( a) t = 80, K, : E = 00 GPa, G = 84 GPa = 1 10-6 - 1 10. 3, X1 X1 ( 10. 3 ( b) ) t, 1 1 X1 + 1 t = 0 = 1 10. 3( 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 ( 0.6 3 + 0.3 3 ) 3 00 10 9 0 4 10-1 + + 1 l1 EA 4 4 00 10 9 1 10-6 = 8.94 10-5 = 3 ab Gd 4 + 4 l Ed 0 3 0.6 0.3 84 10 9 0 4 10-1 + m/ N =

16 t = - lt = - 1 10-6 4 80 = - 384 10-5 m X1 = - 1 t = 384 11 1.01 = 43 N K 10. 3 ( d), = M W = = T Wp X1 a d 3 3 = X1 b d 3 16 = = 3 43 0.6 0 3 10-9 16 43 0.3 0 3 10-9 = 3.87 MPa = 8. M Pa,,, X1, C, C w C,, wc = lt - 10. 10. 4( a) EI a E A, F, X1 l E A ( ) 10. 4 10. 3( b ) F X, 10. 4( c), ( d )

163 F 1 F = 1 EI - ( aa ) 5 6 ( Fa) - ( aa ) Fa = - 11 1 EI Fa3 11 = 1 EI, ( aa ) 3 ( a) = a3 3 EI 1 F + X( 11 + a EA ) = 0 X = 11 4 + 1, 10. 4( e), I Aa 10. 4 (c), ( d) w = 1 EI Fa 3 EI ( Fa a) a - X( 4-11 4 1 + 3 I A a F aa ) 1 6 ( a) =,,,,,, 10. 3 ABCDE, C, F, 10. 5 (a) (1 ) ; ( ) CD ; (3 ) ( 1), C X 1, X, 10. 5 ( b), C (), C, C l ( lx 0 1 + 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 3 3 + ( F - X1 ) l l - X l l 4 X1 + 8 3 X = - X 3 9 X1 + 4 X = F - X1 + F - X ( 1)