,, : ;,,, (CIP) /. :, 005. ISBN TB301 CIP (005) : : 17, : : ( 09 ) : : : 787 mm1 09 mm 1/ 16 : 5.75

Transcription

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2 ,, : ;,,, (CIP) /. :, 005. ISBN TB301 CIP (005) : : 17, : : ( 09 ) : : : 787 mm1 09 mm 1/ 16 : 5.75 : 630 : : 8. 00

3 ( ) 1,,,,,,, 80100,,,,,, ;,,,,,,,,,,,,,,,,,,,,,

4 ( ) 9 3 ( ) 13 4 ( ) ( ) 7 ( ) 5 8 ( )

5

6 ( ) *

7

8 1 1,,,,,,,,, :, ;,,,,,,,, ;,,,,,,,,,,, : (1 ),,, ( ),,, (3 ),,,,,,,, ;,,,,, 1

9 ,,, 1,,,,,,,,,, (1 ),,,,,,, ( ),,,,,,,,,,,,,, (3 ),,,,,,,, (4 ),,,,,,,,, 1 3,,

10 . (1 ),, ( ),,,,,,,,,. (1 ),,,,, ; ( ),,, ;,, 1.,,,,,,,,,,,,.,,, 1 1,,,,,, FR M ( 1 ), x, y z, FR M x y z, Fx, Fy F z Mx, My Mz Fx, FN ; Fy F z ; Mx, T ; My Mz,,, 3

11 Fx 0, Fy = 0, Fz = 0 Mx = 0, My = 0, Mz = ,,, 3 (1 ),,, ( ) (3 ), 1 4,,, 1 3, K A,A F,F A, p, 4

12 p F A 1 3 p, A,,, p, pk ( 1 p = lim A0 p = lim A0 F A = d F d A A (1 1) 1),, A 0 p,, p = + (1 ) N/ m, 1 N/ m = 1 Pa ( ), 1 GPa = 1 G N/ m = 10 9 Pa, 1 MN/ m = 1 MPa = 10 6 N/ m = 10 6 Pa,,,,,, ( ),,, ; 1 4( a), AB x,, A x, B x +, [ (x + + ) - ] - x =, AB, AB, m = u x = lim u x0 x = d u d x A x,, 1 (1 3) 4( b), +,,, 5

13 ,, ( ) (), (1 5 ) ; 1 5,,, 4 : (1 ), ( 1 6( a), ( b) ) ( ), (1 6 (c) ) (3 ), (1 6 ( d) ) (4 ),, ( 1 6( e) ),,,,,, ;, 6

14 1 6 7

15 ( ),,,,,,,, 1, 1,,,, 3,, ;,, :

16 1 ) :,, ( ) : ( ) 1. 4( a),, mm,, FN,, FN Fx = 0, FN - F = 0 FN = F 4,, FN, FN,,, mm,,, FN :, FN, ;, FN,, : (1 ),, ( ),,,.,,,,,, 9

17 ,,,,, 1 5( a),, (1 ) AC : 11, ( 5( b ) ) Fx = 0 FN1 = F1 = 5 kn ( ) 5 CD :, ( 5( b) ), FN Fx = 0 FN + F - F1 = 0 FN = F1 - F = - 10 kn ( ) FN ( ),,, ( 5 (c) ) 5 (c) CB, FN max = 10 kn, CB : (1 ), (),,, ( ),, ( ),,,, ;,,, (),,,,,,, 10

18 , 6,, abcd,, abcd,, a b c d, :,,,,,,, 6 FN = d A = A A = FN A ( 1),, FN ( 1 ) FN, A :,,, ( ( x) = FN ( x) A( x), ( x), FN ( x) A( x),, ( max = FN max A 1) ( ) 1 ), ( 3), 7, AB cm, F = 130 kn, = 30AB (1 ) AB A, Fy FN A B sin30= F = 0, 11

19 ( ) A B FN AB F = 60 kn ( ) A B = FN A B A = = M Pa (a), A1 = 3 cm, A = 4 cm ; l1 = l = 50 m A F = 1 kn = 0.08 N/ cm 3,, max (1 ) AB : 11, FN1 FN1 BC :, FN = F + A1 x1 (0 x1 l1 ) ( a), FN = F + A1 l1 + A ( x - l1 ) ( l1 x l1 + l ) ( b) ( ) (a) ( b ) x1 = 0, FN A = F = 1 kn x1 = l1, FNB = F + A1 l1 = = 1.4 kn x = l1, FNB = F + A1 l1 + A ( l1 - l1 ) = 1.4 kn x = l1 + l, FNC = F + A 1 l1 + A l = 1.98 kn 8( b ) (3 ) (a) ( b), AB B, BC C ( 1 ) B = FNB A1 = = 41.4 M Pa C = FN C A B, C, max = 41.4 MPa 1 = = 36.8 MPa

20 3 ( ),,, ( ),,, mm ( 9 ) 9 F, A, ( 1 ), = FN A = F A mm A, AA A= A cos, p mm, p A cos - F = 0 p= F A cos= cos p,,,: = = pcos= cos ( 4) psin= sin ( 5) : x n, ;:, ;:,, ( 4 ) ( 5 ),,, 13

21 4) ( 5 ),,, () ( 4 ) ( 5) : (1 ) = 0, max ( ) = + 45, =,= 0 ; = max, = ; (3 ) = 90, = 0,= 0 : ( ) ; 45 4 ( ), E,,,,, 10,, l, l d l = 10 d, l = 5 d,, l A l = 11.3 A, l = 5.65 A %,,,, F,, L, F L,, F A,,, L l,, 14

22 ( 11 ) 11, 1. ( O a ), a a, P,, = E ( 6) E,, E,, G Pa( 1 G Pa = 10 6 Pa)( 6) P, E oa E = = tan, a b,,, b e,, a, b,,,,,,. ( b c ),,,,,,,,,, s s 15

23 ,, 1 3. ( ce ) 45,,, e b, b e,,,,, 13, A, f, 5. l1, l, = l1 - l 100 % ( 7) l A, A1, = A - A1 A, : = 0% 30%,= 60% 100% ( 8), : 5% ;< 5% 6., Oa O ( 14), d,, ddd ddoa,,, dd, d, de f, d, d 14 Oabcde f d de f,, ( ), (,, d), 14 dh

24 14 15,, Q345,, 4,,, 3, 15, 0.%,, P 0. ( 16 ) 17, 17

25 ,,, 16 17, E,,,,, b,, h = (1.5 3 ) d 1., 18 : E s,,,,,, 18 18

26 ., 19 (a), 45 55, ( 19 ( b) ) b bc bc = ( 3 5) b,, 19 5,,, s,,, b, ;, b,,,,,,,,,, u, ;,,,,, [ ], [ ] = u n ( 9), n 1, [ ] = s ns 19 ( 10)

27 , ns, nb ] = b nb ( 11), :, ns 1.5.5;, nb.5 5.0,, ( ),, max (), nmax max [ ] ( 1) = FNmax A [ ] ( 13) (), 1. (),,. (),, (), ( 3. A FNmax [ ] 13 ) ( 14) (),, ( 13) FN max [ ] A ( 15), () max [ ], 5%, 4 0( a), AB, CD, d = 30 mm, Q35, [ ] = 160 MPa, F = 50 kn, (1 ) 0( b ), MA = 0 FN sin F3 000 = 0 FN = 150 kn 0 ( ) ( 1 ) CD

28 0 = FN A = FN d 4 = = 1.3 MPa (3 ), = 1.3 MPa > [ ] = 160 M Pa, CD, 5 4, CD, CD ( 13 ), CD A = d 1 4 FN [ ] d1 4 FN1 [ ] = , CD 34.6 mm = m = 34.6 mm 6 4, CD d = 30 mm,, FN = 3 F = FN A = 3 F d 4 [ ] F d [ ] = F 37.7 kn = 37.7 kn 7 4, CD A B ( 1 (a) ), F AB,, M A = 0 1( b ), CD FN, A x, FN = Fx 000sin 1

29 , x = ( F B ), FN 1 FNmax = 3 F sin, CD CD V AlC D = A FNmax = [ ] 3 F [ ] sin 3 F 000 [ ] sin cos =, CD V, V, sin= 1 = F [ ] sin 4 7,, : ; ; ; 6 ( ) ;, l, A FN, l l1, l = l1 ( ), l l, = l l - l

30 , = E, FN A = El l l = FN l E A ( 16) ( 16),, l FN l, A EA (), EA,, EA () ( 16), l FN,, ( ), FN, b b1,, b = b1 = b b - b, ( ),,, =, (, 17) ( 17) = - ( 18) ( 16) A FN,,, d x, ( 3 ;,,, d(l) = 16), FN ( x) d x E A ( x), FN ( x) A( x), x 3

31 FN ( x) l EA ( x) d x ( 19) , BD A1 = cm, AD A = 4 cm E = M Pa, F1 = 5 kn, F = 10 kn AB la B la B (1 ) BD, DC, CA FN1, FN, FN3 FN1 = - 5 kn, FN = - 5 kn, FN3 = 5 kn ( ) ( 16) lb D = l1 = ldc = l = lca = l3 = (3 ) FN1 l1 EA1 FN l EA FN3 l3 EA3 = = = = = = la B = l1 + l + l3 = m 9 5 (a), BD, d = 0 mm, l = 1 m, E = 00 GPa ; BC, a = 100 mm, E = 1 GPa F = 50 kn B 4 (1 ) B( 5 (a) ) Fx = 0 Fy = 0, FN1 = 50 kn ( ) FN = 70.7 kn ( ) ( ) 5 (a), l1 = l = 1 m, l = BC BD l1 = FN1 l1 E1 l = A1 = FN l E A l cos45 = 1.41 m m m m = m = = m

32 5 (3 ) B, l1, l B, BD B1 D, BC B DB1 C D C, CB, B3 B3 B, B1 B3 B B3, B1 D B C, B3, B, BB1 = l1, BB = l 5 ( b) B B B4 = l1 + l B1 B3 = B1 B4 + B4 B3 = BB + B B4 = B, B B B3 l + l1 + l = BB1 = l1 = m m BB3 = ( B1 B3 ) + ( BB1 ) = m,,,,,,, : ; ; ; ;, 7 ( ),, 5

33 ,,,, V() 6 (a),, F, l, 6 ( b), F1, l1 6 d F1, dl1, F1 F1 dl1, dw = F1 dl1 6 ( b), dw F d F1, F F W 6 ( b), F l, W = l F1 dl1 = 1 0 Fl ( 0),,,,, W, V= W = 1 Fl ( 1) 6 FN = F,,, = FN l E A V= 1 FNl = F N l EA J( ), 1 J = 1 Nm ( ) ( )

34 ,,,, d x, d y, d z, d x, d y, d z, ( 7( a) ), ( x ) ( ),,,,, 7( b ), 1 ( 1 d yd z), 1, d 1, d 1, d x d 1 d x, 1 d yd z d 1 d x, dw = dv= d yd zd 1 d x = ( 0 1 d 1 ) dv, dv = d xd yd z, ( v= d V dv = 0 1 d 1 ( 3) 3) 1 d 1 7 ( b),, = E, v= J/ m 3 ( / 3 ) 1 v= 1 ( 4) = E = E, ( 5) ( 5) 10 8, AB A C A, A F = 35 knab A C d1 = 1 mm d = 15 mm, E = 10 GPa A (1 ) A, 1 7

35 FN1 = FN1 = F ( ) F ( ) ( ) V= F N1 l1 EA 1 + F N l EA = 4 F l1 E(1 + 3 ) d F l E(1 + 3 ) d (3 ) A, F, W = 1 F 8 1 F= 4 F l1 E(1 + 3 ) d F l E(1 + 3 ) d 8 Fl1 16 Fl = + = m = mm E(1 + 3 ) d 1 E(1 + 3 ) d,, F 8 ( ),, 9 (a), AD ( 9( b ) ), 3,,, 3,, 9 8

36 ,,,,,,,,,, 9 ( b),,, 9( b ), 1 (), E1 A1, 3 () E3 A3, 3 l 3, FN3 ( ), 3, FN3, ( 30 (a) ) F F N3, 1 FN1 ( ), FN ( )A 30 ( b), Fx = 0, FN sin- FN1 sin= 0 Fy = 0, FN1 sin+ FN cos+ FN3 = 0 ( 6) 30,, F F N3 ( 30 (a) (c) ) 3 FN3 ( 30 ( d) ), F FN3 l; 3 FN3 l3 ( l = l3 ( 7) 7),, l1 = l = l3 = FN1 l1 E1 FN3 l3 E3 A3 A1 = E1 = FN3 l E3 A3 FN1 l A1 cos 9 ( 8) ( 9)

37 30 (c) ( 8) l = l1 cos = FN1 l E1 A1 cos ( 9) ( 30 ) ( 7 ), FN1 = E1 A1 ( 6) ( 31) FN1 = FN = FN3 = E3 A3 ( 30) cos FN3 ( 31) E1 A1 cos E1 A1 cos 3 + E3 A3 E3 A3 E1 A1 cos 3 + E3 A3,,, : (1 ), ( ), (3 ) () (4 ) ( ) ( 3), () 11 31( a),, B F, AB () EA 1, BC ( ) EA A, C F F 31 (1 ) F, A, C F A FC, 31 ( b) FA + FC - F = 0 ( a),, ( ) C, FC, FFC F FC l 30

38 ,, l = 0 ( b) (3 ) AB BC, la B = FN AB l1 EA1 = FA l1 EA 1 lbc = FNBC l EA = - FC l EA l = la B + lbc = FA l1 EA1 (4 ) (c) ( b), - FC l EA (c) l = FA l1 EA1 - FC l EA = 0 ( d) (a) ( d) FA = A1 l A1 l + A l1 F A l1 FC = A1 l + A l1 1 3 (a), () EA, F, 1 3 l F 3 ( 1) 3,, F, 1 3 FN1, FN FN3, 3( b ) B Fx = 0, FN1 - FN sin30= 0 ( a) Fy = 0, FN3 + FN sin30- F = 0 ( b) ( ) 3 (c), 1 3 l3 = l sin30 + l1 = l + 3l1 (c) tan30 31

39 3 ), l = l1 = FN1 l1 EA = FN1 l EA FN l EA = FN l E Acos30 = FN l 3 EA l3 = FN3 l3 EA = FN3 l EA ( d) ( e) (f) (c), ( d) ( e) ( f) (4 ) (a) ( b ) ( g) 1. 3 FN3 = 4 FN + 3 FN1 ( g) FN1 = FN = 3 4 ( + 3 ) F 3 ( + 3 ) F FN3 = ( + 3 ) F,,,,, 33,,,,,,,,,,, ;, 13, 34( a), 1 33 E1 A1, 3 E3 A3, 3 l, (1 ), 3,, 1, 34 (a) 1 3 FN1, FN FN3, 1 3 l1, l l3 A1 30 ( b), Fx = 0, FN1 sin- FN sin= 0 FN1 = FN ( a) Fy = 0, FN3 - FN1 cos- FN cos= 0 3

40 34 (a) FN3 = FN1 cos+ FN cos= FN1 cos FN1 = FN3 cos ( ) 30( c) ( b) (3 ) = AA1 = AA + A A1 = l3 + l1 cos l1 = l = ( d) (c), E1 = F N3 l E 3 A3 (4 ) (e) ( b ), FN1 = FN = FN3 = FN1 l FN3 l, l3 = A1 cos E3 A3 + E1 FN1 l A1 cos E1 A1 E3 A3 cos E3 A3 + E1 A1 cos l E1 A1 E3 A3 cos 3 E3 A3 + E1 A1 cos l,, ( ),.,,,,,,,, 35 (a) 35( b ), AB,, A, B,, 33 (c) ( d) ( e)

41 FA FB AB, FA = FB ( 3) 35 ( 3),,, FB l,, FB l = l T + lf ( 33),lT lf FB lt lf lt lf = lt ( 34) = FB l E A ( 35),, T, EA (),,, l = 0 ( 36) ( 33 )( 34) ( 35) ( 36 ), lt = FB FB l E A = EAT T = FB A = ET = /, E = MPa, T, T = E T = T =.5T M Pa T, T, :,, ;,, ; 34

42 , ; 5,,, ( ) ( ) (, ), 9,,,,,,,, 36,,,,,, 36,, Kt, n ; max Kt = max n, ( 37), F,, b, d, AA n = F ( b - d) ( ) ( ) 35

43 ,,,,,,,,,,,,,, ( ), ( ), 10,, 37,,, :,, ;, 37,,,,, nn ( 37, 3 : mm 38( a) ) ; ( 38 ( b) ) ; ( 38 (c) ) 38 36

44 37, 39 (a),,,, mm nn ( 39 ( b) ), mm nn,, 39( c),,, FQ 39,,,, = FQ AQ ( 38), AQ = FQ AQ [ ] ( 39), [ ],, ( 38 ) b, ( 38),,,,,, ( 39),, 38,,,,, Fb s,, b s,,,,,, b s = Fbs Ab s ( 40), Abs ( ),, 37

45 ), 40 ( b), d ( 40 (a), ( b max Fb s d 40 ), ( ), b s = Fb s Ab s [ b s ] ( 41), [ b s ],,, , 6, = 8 mm, b = 160 mm, d = 16 mm, F = 150 kn [ ] = 140 M Pa, [ b s ] = 330 MPa, [ ] = 170 M Pa 41 (1 ),,,, FQ = F 6 = 5 kn 38 = FQ AQ = 4 FQ d = = Pa = 14.4 MPa < [ ] ( ),,

46 b s Fb s Ab s = F 6 d = = Pa = 195.3M Pa < [ b s ] (3 ),, 4( a),, 4 ( b) 4(c) 11, 33 3, 3-3, = FN3 A3 = F b- d = ( ) = Pa = M Pa < [ ] 15 43( a) (, ) d = 70 mm, bh l = 0 mm 1 mm 100 mm, [ ] = 60 M Pa, [ b s ] Me = 100 MPa 4 (1 ) nn, ( 43( b ) ), nn FQ, FQ d = Me 43 39

47 FQ ( ) Me = FQ AQ = Me d bl Me d = Me bdl [ ] bdl[ ] = (4 ) 43( c) = 4 00 N = 4. kn Fb s = FQ = Me d Me dhl[ b s ] 4 b s = Fb s Ab s = Me d h l = 4 Me dhl [ b s ] = , Memax =.1 kn = 100 N =.1 kn, :, ( ),, ;,,,, ;, ;,, ( ),, (1 ), ( ) = FN A (3 ),, 40 (4 ) max [ ] 3 : (5 ) = E

48 (6 ) ( ) l FN l E A V= F N l EA v= 1 = E (7 ) () :, ; ; ; ; (8 ) : 1) ) = FQ AQ [ ] b s = Fb s Ab s [ b s ] 1 1, 1 11, , 33, A = 400 mm, , 33, A1 = 00 mm, A = 300 mm, A3 = 400 mm, 5 5 F = 10 kn, A = 100 mm, = 0, 30, 45, 60, , F,, 41

49 , a = mm, b = 0 mm, l = 70 mm F = 6 kn, l = 0.15 mm, b = mm, E ,, 3, 4 : 1, A1 = A = mm, [ w ] = 0 MPa, 3, 4 A3 = A4 = 800 mm, [ s ] = 10 MPa [ F] 4

50 9 9,, [ t ] = 50 M Pa, [ c ] = 60 MPa, 5 mm [ F] , 1,, B F d b F = 50 kn, [ s ] = 160 M Pa, [ w ] = 10 M Pa , F [ F] A, [ ] 1 1, F, [ ] A B,

51 13 13 [ ] = 170 MPa, AC CD 14 14, AB, A1 = cm, [ s ] = 160 MPa ; AC, A = 3 cm, [ c ] = 100 M Pa, [ F] A E D mm,, E = 10 GPa, : (1 ) ; ( ) ; (3 ) , F, f = ky, k F = 40 kn, l = 1 m, A = mm, E = 10 GPak, 18 18, F, l, b1 44 b, E

52 , AB, CD d = 0 mm, E = 00 G Pa, [ ] = 160 MPa, : ;, B , BC, 1 3, E = 00 G PaC F l = 1 m, A1 = A = 100 mm, A3 = 150 mm, F = 0 kn 1 1, A C, F EA, A C 1 CA, l1 = m, A1 = 00 mm, E1 = 10 5 MPa ; BD, l = 1 m, A = 800 mm, E = M Pa AB,, : (1 ) AB, F DB x ; 45

53 ) mm, F? 3 3, 3 4 4, 1 () EA, AB, F = 0 kn, [ t ] = 30 MPa, [ c ] = 90 MPa , L = 3 m, = 5 mm, d = 100 mm F [ s ] = 160 M Pa, Es = 00 GPa; [ h ] = 30 M Pa, Eh [ F] = 30 GPa 6 6, E = 10 G Pa, A1 = mm, A = 500 mm F = 180 kn: (1 ) = 0.6 mm ; ( ) = 0.4 mm 7 7, Es = 10 GPa, cm, = l, 46 (1 ) ( 7 ( a) ) ; ( ) 3 ( 7 ( b) )

54 , = /, E = 00 GPa 9 9 1, E1 = 10 GPa, 1 = l/, A1 = 30 cm ;, E = 105 GPa, = /, A = 30 cm F = 50 kn , F d, D, h,, [ ] = 10 MPa, [ ] = 90 MPa, [ b s ] = 40 MPa F, b, [ ], [ b s ] l a 3 3,, b = 50 mm, F = 50 kn, [ b s ] = 10 MPa, [ ] = 1 M Pa L 47

55 , a = 00 mm, l = 1 m F = 100 kn, 33, [ ] = 1.5 MPa,,? F, F = 80 kn, b = 80 mm, = 10 mm, [ b s ] = 30 M Pa d = 16 mm, [ ] = 160 MPa, [ ] = 10 M Pa, 48

56 34 49

57 ,,, , A, Oz y d A, ( z, y), Sy = A z d A, S z y z (3 = A yd A (3 1) 1 ),,,,,,, 3 1,,, d A d A,, Oz y yc zc yd A A = A = zd A A A yd A A = A z d A A = A, C (3, C ( 3 1) (3 ) (3 ) 1 ),

58 zc Sy A, yc = Sz A (3 3) S y = AzC, S z = AyC (3 4) ( 3 4),, yc = 0, zc = 0,, S y = 0, S z = 0 ;,, ( ),,,, Sz n = Ai yci, Sy i = 1 n = Ai zc i (3 5) i = 1, Ai yc i, zci n n (3 5 ) ( 3 3), yc = Sz A n Ai yc i = i = 1 n Ai i = 1, zc = Sy A n Ai zc i = i = 1 n Ai i = 1 (3 6) S y, Sz C R (1 ) y, Sy = 0 z d A, (3 Sz d A = Rcos d y d y = Rcos d, y = Rsin =yd A A = 0 d A = R cos d 1 ), z Rsin R cos d= 3 R3 ( ) (3 ), yc = Sz A = 3 R3 1 R = 3 R 3, zc = ( a) C ( b) Oy z, A1 = = m 51

59 3 3 y1 = 0.1 (3 = m A = = m y = ), C = 0.11 m yc = = 0.08 m = 80 mm zc = 0,,,,,,, A, d A, ( z, y), Iy =z d A, I z A =y d A (3 7) A y z (3 7 ), Iy I z, 5, I y = Ai y, Iz = Ai z (3 8)

60 iy = I y A, iz = Iz A (3 9) iy iz y x d A, IP = d A ( 3 10) A 3 (3 4 = y + z IP 3 4 = A ( y + z ) d A = Iz + Iy ( 3 11) 11),,,,,, 3 4 I y n = Iyi, Iz i = 1 I yz n = Izi ( 3 1) i = 1 = A y z d A ( 3 13) y, z ( 3 13 ), I yz, y z, Iy z, d A z yd A,, I yz =y zd A A 3 3 ( 1) 3, (3 10) IP 5( a), d, d d A = d = d/ 0, I y = Iz d= d4 3 (3 11), IP = I y = I z Iy = Iz = IP = d

61 3 5 ( ) d, D (3 5( b) ),, IP = D4 3 - d4 3 = 3 ( D4 - d 4 ) = D4 3, y z (1-4 ) Iy = Iz = D d4 64 = 64 ( D4 - d 4 ) = D4 64 ( 1-4 ),= d D , d A = hd z, ( 3 I y 6, d z h y 7) y =z d A A = b/ - b/, z z hd A = hb3 1 Iz = bh3 1,, I y n = Iyi, Iz i = n = Izi ( 3 14) i = ( a) z 3 7( b ) BH, BH z I z 1, z Iz, z I z Iz1 = Iz + Iz 54

62 Iz = I z1 - I z z Iz Iz1 = BH3 1 B - d = 1 Iz = BH h 3 = ( B - d) h3 1 ( B - d) h ,,, 3 8, C, yc zc,, Iy C Iz C Iy C z C = A z C d A = A y C d A yc zc = A d A ( 3 15) y yc, a; z z C, b, y z

63 3 8 (3 17) (3 16) I yz I y Iz =z d A A =( zc A =y d A A =( yc A I y I z I yz A z d A =y d A A =y z d A A ( 3 16) y = yc + a, z = zc + b ( 3 17) + b) d A =z C d A + zc A bd A + b A d A A + a) d A =y C d A + yc A ad A + a A d A A =y z d A A =( yc + a) ( zc + b) d A yc zc A = d A + yc A bd A + zc A ad A + A abd A A zc, A d A yc A d A yc zc, yc zc, A d A = A, ( 3 15 ), Iy = Iy C + b A Iz = Iz C + a A ( 3 18) Iy z = Iy C z C + aba ( 3 18) ( 3 18),, (3 3 ) T 3 3 ( b), z1, (3 I z = I z 1 + A1 a 1 = ), z ( yc ) = + ( ) = m 4 z, ( 3 I z = I z + A a = z Iz 18 ), z + ( yc ) = + ( ) = m 4 = I z + I z = = m , x I x = bh3 1, x1 x, x1 I x 1 56

64 ,, Ix I x 1, Ix C, x xc ( 3 18 ) I x = I x C + Ix 1 - Ix = h 3 I x 1 = I x C + h 3 h 3 - h 3 A A = bh I x 1 = bh3 6 bh3 + Ix = 6 + bh3 1 = bh3 4, :,, ;,,,,,,,, 3 4 A (3 I y I z I y z =z d A A =y d A A =y z d A A 10 ), y z, ( 3 19) O,, y1, z1, y1, z1 Iy 1 =z 1 d A, Iz A 1 3 =y 1 d A, Iy z A 1 1 =y 1 z1 d A A ( 3 0) 10, d A z1 (3 0), y1 z1 = OB = OF + DE = ycos+ zsin = CB = CE - BE = zcos- ysin 3 10 ( 3 1) 57

65 I y 1 =, ( 3 A z 1 d A =( z1 cos- ysin ) d A = A cos A z d A + sin A y d A - sin cos A y z d A = I y cos + I z sin - I yz sin= Iy + Iz + I y - Iz 0 ) cos- I yz sin ( 3 ) Iz 1 = Iy + Iz - Iy - Iz cos+ I y z sin ( 3 3) Iy 1 z 1 = I y - Iz sin+ Iy z cos ( 3 4) I y 1, Iz 1, I y 1 z 1, (3 )(3 3) (3 4) (3 18) (3 3) Iy 1 + Iz1 = I y + Iz ( 3 5), O,,, ( 3 4),,, 0 y0, z0, I y 0 z 0,,,, (3 4) = 0 I y z 1 1 = 0 I y - I z sin 0 + I yz cos 0 = 0 ( 3 6) (3 tan 0 = - Iy z I y - Iz ( 3 7) 7 ) 0, y0 z0 Imax, Imi n (3 ( 3 7) 0, ( 3 ) ( 3 3) 7 ) cos 0 = 1 = 1 + tan 0 Iy - Iz ( Iy - Iz ) + 4 I yz sin 0 = tan 0 cos 0 = - I yz ( I y - Iz ) + 4 I y z 58

66 3 ) ( 3 3 ), Iy 0 = I y + Iz Iz 0 = Iy + Iz ( I y - Iz ) + 4 I yz ( Iy - Iz ) + 4 I y z ( 3 8) ( 3 ) (3 3), I y 1 I z 1, 0 360, Iy 1 Iz 1 ( 3 5 ), Iy 1 Iz 1, Iy 1 I z 1 = 1, d Iy 1 = 0, d = 1 d Iz 1 = 0 d = 1 I y - I z sin 1 + I yz cos 0 = 0 ( 3 9) ( 3 9 ), Iy Iz 1 1 ( = 1 ), I y z 1 1 = 0,, : (1 ),, 3 11( a), ( b), (c) ( ), 3 11( d), ( e) (3 ),, 3 11( f), ( g) (4 ), 3 11 ( h ), (i)

67 8 3 1 L, yc (1 ) 3 zc, yc = Sz A 3 1 1, Oy z C, = zc = S y A = = 15 mm = 80 mm ( ) y, z yc, zc Iy C, Iz C Iy C z C I y C = = = mm 4 I z C = = = mm = I y C z C = ( - 15) ( - 0 ) = = mm 4 (3 ) (3 7) tan 0 = - Iy C z C I y C - Iz C = -, yc, zc 60 (4 ) (3 8) = = = =.8

68 I z = Imax = Iy C + Iz C mm 4 I y 0 = Imin = Iy C + Iz C mm 4 ( Iy C - Iz C ) + 4 I y C z C = + 1 ( ) + 4( ) = ( Iy C - Iz C ) + 4 I y C z C = - 1 ( ) + 4( ) = (1 ), S y = Z z d A, S z, ( ) zc = Sy A = Z yd A, yc = Sz A (3 ), Iy =z d A, I z A =y d A A (4 ), IP = A d A IP = Iy + Iz (5 ), I yz = A y z d A,, (6 ), Sz n = Ai yci, Sy i = 1 n = Ai zc i i = 1 I y n = Iyi, Iz i = 1 n = Izi i = 1 61

69 7 ), I y = Iy C + b A Iz = I z C + a A I yz = Iy z C C + aba (8 ), Iy 1 = I y + I z + Iy - Iz cos- Iy z sin I z1 = Iy + Iz - I y - I z cos+ I yz sin Iy 1 z 1 = I y - Iz sin+ Iy z cos (9 ), tan 0 = - Iy z I y - Iz I y 0 = Iy + Iz I z 0 = I y + I z ( Iy - Iz ) + 4 I y z ( Iy - Iz ) + 4 I yz

70 , b = 150 mm, h = 300 mm a, I y = I z, a

71

72 10 65

73 ,, ; ;,, ( a),, F, Me = Fd,, Me= Me, 4 1( b ) Me Me,

74 ,,,,, Me, Me, 4 3,, AB AB, AB P kw( ), 1 kw = Nm/ s, P kw W = P ( Nm ) Me AB, n ( r/ min), Me nme, Me ( Nm ), P1 000 = n 60 M e 4 3 Me = P n (4 1), P ( k W, ) ; n ( r/ min) 4, 4 4( a), nn, ( 4 4 ( b) ),,,, nn T, Mx = 0, T - Me = 0 T = Me, T nn,, nn 67

75 4 4( c) ), T = Me,,, T : T,, T ;, 4 4, nn,,,,, ( a), A 4 4, B, C, D PA = 60 kw, PB = 5 kw, P = 5 k W, PD = 10 kw, n = 300 r/ min (1 ) (4 1 ) 68

76 Me B MeC = PB n = = 796 Nm Me A = PA n = = Nm Me D = PD n = = 318 Nm ( ), AB : 4 5( b ), 11 T1, 4 5 ( b) T1 - MeB = 0 T1 = MeB = 796 Nm AC : 4 5( c), AD : 4 T + Me A - MeB = 0 T = MeB - Me A = Nm 5( d), T3 + MeD = 0 T3 = - Me D = Nm (3 ),,, 4 5( e), BC, T max = Nm (4 ), A, 4 6 (a), 4 6 ( b), T max = Nm,,, ( a), R( R ) 10,,, (4 7 (a) abcd),,, ( 4 7( b) a b c d ),,,,,,, (4 7 (c) ) Me, Me =Rd A A = 0 RR d= R 69

77 Me R (4 ) 4 7 4, d x, d y, 7 ( d),,,,, (4 ) 4 7( d ),,,,, (d y) d x,,,, Fx = 0,, (d y) d x, Mz = 0 ( 4 (d y) d x = ( d x) d y = (4 3) 3 ),,,,,, 4 7 ( d),,,,, (4 7 ( d) ) 70, l, 4 7 ( b),

78 , r l (4 4),, = G (4 5) (4 5 ) ; G,, Pa, E,, G,, E,, G G = E (1 + ) (4 6) 4 4, (a),,,,,,, :,,, d x ( ( b ) ), d, O b d, O b, ab, ab,, d d x, a cd, cd,, c 4 8 ( b) 71

79 , dd d x = d (4 7) = d d x d, (4 d x,. (4 8) 8 ),,,,, (4 = G = G d d x (4 9) 9 ),,,,, , d A, d F = d A, O d A,, (4 9 ) T = A d A IP, A (4 10) (4 8 ) 7 d A T = G d A d A d d x = = d x T GI P T IP ( 4 10) ( 4 11)

80 1. (4 11), = R,,, max = TR I P = T IP R ( 4 1), IP R,, WP, WP = IP R ( 4 13) (4 (4 1) max = T WP 14),,. ( 4 14) Tmax,, ( 4 14 ), max max = Tmax WP [ ] ( 4 15), [ ] [ ], u, n, [ ] = u n ( 4 16),,,, (4 45(4 11 (a) ) ;,, 11 ( b) ), s ;,, b s b,, u (a), AB d1 = 10 mm, BC d = 100 mm 73

81 Me A knm, Me B = 36 knm, MeC = 14 knm [ ] = 80 M Pa, AB, BC T1 T 4 = knm = - 14 knm 1 ( b), AB BC,,, ( 4 14 ) ( 4 15 ) AB BC 1 max = T1 W P1 = 103 = 16 ( 0.1 ) Pa = 64.8 MPa [ ] 4 1 max = T WP, = = (0.1 ) 3 Pa = 71.3 MPa [ ] 4 3, Me =.0 knm, [ ] = 60 M Pa, ; = 0.8, (1 ) d, (4 15) W P = d3 16 T [ ] = Me [ ] d = 5 mm 3 16 Me d = [ ] = m = 51.9 mm ( ) D, (4 15 ) 3 16 Me D = ( 1-4 ) [ ] D = 6 mm, d1 3 W P = 50 mm = D3 16 ( 1-4 ) Me [ ] ( ) = m = 61.9 mm (3 ),, 74 = A1 A = 4 ( D - d 1 ) = 4 d = 0.50

82 , 4 4 3,,, ( a) ( ( 5 ) ), F D, d, 4 13 (1 ),, (4 13( b ) ),,,, FQ T, FQ = F T = FD ( ), FQ, (4 13( c) ), = T 4 max= FQ AQ T W P = FQ d 4 = 4 F d 13( d), = FD d 3 16 = 8 FD d 3,, A,, d D, D d max = max+ = 8 FD 1 + d d 3 D ( 4 17) 10, d 1, D 75

83 ( 4 17 ) max = 8 FD d 3 ( 4 18) D d < 10,,,, max = 8 FD 4 m + d 3 4 m - 3 ( 4 19), m = D d (3 ), [ ] max [ ] 4 5, ( 4 d x d= Td x GIP, l = d= T GIP, lt, (4 GIP = Tl GIP 10 ), d x ( 4 0) 0 ) ( 4 1) ( 4 1), T l, GIP,,,, d d x, [ ] ( 4 10), 76, = d d x = T GIP ( rad/ m)

84 max T GIP max [ ] ( rad/ m) ( 4 ), max = Tmax GIP [ ] ( rad/ m ) ( 4 3), d rad/ m,, d x ( )/ m,, ( 4 ) ( 4 3 ), P , n = 500 r/ min, P1 = 380 kw, P = 160 kw, = 0 k W, [ ] = 70 M Pa, [ ] = 1 / m, G = 80 GPa : (1 ) AB, BC ( ) = 0.8, (1 ) : 1) : Me A MeB = P1 n = P n = 7 57 Nm = Nm Me C 4 ) : = P3 n = 4 0 Nm 14 ( b) AB : d1 d1 = 85.3 mm 3 max = T W t 16 T = [ ] max = 3 = 16 T d T G d4 1 3 d1 [ ] 180 [ ] 85.3 mm = 80.8 mm 4 14 BC :, d 67.4 mm; d 74.4 mm d = 74.4 mm ( ), D D 96.3 mm D 97.3 mm D = 97.3 mm, 77

85 d D = = 77.8 mm, A A 47% = 4 ( D - d ) 4 d 1 = ( a) AB,, C D Me, A B MA MB ( 4 16 ( b) ), Mx = 0, MA - Me + Me - MB = 0 MA = MB ( a) (a),,,, A B, A B A B,, 4 A B = AC + C D + DB = 0 ( b) 14( b), AC, CD DB T1 = - MA T = Me - MA (c) T3 = - MB, AC, CD DB ( d) ( b), - MA a GIP A C = T1 a GIP C D = T a GI P DB = T3 a GIP + = - = = - ( Me - MA ) a GI P MA a GIP ( Me - MA ) a GIP MB a GIP MA + Me - MB = 0 ( e) (a) (e), - MB a GIP = 0 ( d) 78 MB = Me 3 ( f)

86 MA MB = Me (c) ( ), 4 6,,,,,, ( 4 T (4 18), 16( a) ), T1, 1 d T1, d 1, T1, T1 d 1 4 dw = T1 d 1 17( b ), dw 0 T d T1, 0 T W 4 16( b ), T, 4 16 (4 1) = Tl W = T1 d 0 1 = 1 V= W = T1 d 1 = 1 0 GIP T ( 4 4) T ( 4 5), V V= T l GIP = GIP l ( 4 6) ( a), F D, d, G 4 13 ( b), FQ T, 79

87 FQ F T = FD ( a) F,,, s, (4 V= 6), T s GIP n, (a) ( b),, s = nd V= 4 F D 3 n Gd 4 F = 4 F D 3 n Gd 4 ( b) = 8 FD3 n Gd 4 ( 4 7) 4 7,, 4 17 (a),, (4 17( b ) ),,,,,,,,,,, ;,,

88 , K1, t n (4 18),, n, n = n n, n= 0,, n = 0,, t K, 1,, 1, 1,, ,,,, 4 19, ; max, 1 max = T W t = = T hb ( 4 8) 1 = max ( 4 9) Tl = Tl Ghb 3 GIt ( 4 30), It = hb 3, h b ;, h b, , h/ b

89 1, h b > 10, (4 0), = 1 3,,, ( 4 8 ) (4 30) = max = T ( 4 31) 1 3 h Tl G 1 = Tl 3 h 3 GIt 4 ( 4 3) , l, Me, d; h/ b = 3/ d b = Me 4 = bh = 3 b 6 d, cmax = 16 Me d 3, c = 3 Me l Gd (4 8) ( 4 30 ) 4 1, r max = Me = hb r = Me l Ghb 3 = Me 0.31 hb = Me l 0.196Ghb 3 = Me b 3 Me l 0.94Gb 4 4 1, 8

90 cmax r max c = r = = 0.81,,,,,,,,,,,,, ; ; ; (4 ) T,, T1,,, T i,, 1,,, i,, (4 1 = T1 l GIt1 3) = 1 = = = i = = ( 4 33) T1 l G 1, = T l 3 h1 3 GIt 1 T = T1 + T + + Ti + ( 4 34) = T l G 1,, i = T i l 3 h 3 GI ti = G 1, 3 hi 3 i Ti l (4 33) ( 4 34 ) (4 35) T = G l 1 3 h h h1 3 i + = G l It i ( 4 35) 83

91 Tl G = Tl GI t t i ( 4 36) T i = It i It T ( 4 37), It = It i = 1 3 hi 3 i, ( 4 i = (4 37) (4 38), (4 Ti = 1 3 hi i Ti i 1 3 hi 3 i i = T i It 31 ), = T i i 39),, max = T max It It i ( 4 38) ( 4 39) ( 4 40),,,, It,, It = 1 3 hi 3 i ( 4 41),, = 1.00, = 1.1, T = 1.15, = 1.0 (4 4 4),, 3,,,,,, d x, abcd, 4 5 ( b), b 1, 1 ; c,,, ab cd 1, Fx = 0, 1 d x 1 - d x = = i i = ( 4 4) i i (4 4),,, d s, d s ds, O d s, O, 84 T = d s = d s

92 4 4,O ; d s d0, d s A0 (4, T = A0 = T A0 ( 4 43) 43),,, A0,,, max = T A0 max ( 4 44) (a), ( b), 4 5 ( b), Me, b = 50 mm = mm ( a), 4 5 (c), (4 44), max= T = A0 mi n T = Me Me b = Me b 4 5 ( b), 4 5 ( d), (4 40), 85

93 max T max It = max T = 1 3 hi 3 i max = 3 b = Me = 3 Me 4 b 3 4 b = 37.5,, 37.5 (1 ), Me = P n ( ) = Me R (3 ),, ;,, = (4 ) :,, (5 ) : = G = T IP (6 ) : max = Tmax WP = Tl GIP [ ] 86 (7 ) : (8 ) : max = Tmax GIP V= T l GIP [ ] = GIP l

94 max T W t = T hb = Tl = Tl Ghb 3 GIt max = T max max = It T A0 min , , n = 500 r/ min, A, PA = 70 kw, BC D, PB = 10 kw, PC = PD = 30 kw (1 ) ; ( ) A C, r/ min,, A 70 k W, B, C, D, E 0 k W, 10 kw, 5 kw 15 kw, , T (a),, (4 5 ( b ) ), 87

95 n = 00 r/ min, P = 0 kw, [ ] = 80 MPa, d1/ D1 = 0.5 d, d1 D , AE, D = 88

96 40 mm, d = 80 mm; BC, d1 = 100 mm, Me A = 0 knm, Me B = 36 knm, MeC = 16 kn m [ ] = 80 M Pa, G = 80 GPa, [ ] = 1. / m , F = 1.5 kn D = 50 mm, d = 8 mm, [ ] = 450 M Pa, 4 9, d = 0 mm, Me = 150 Nm l0 = 100 mm = 0.01 rad, G 4 10, n = 300 r/ min, P = 80 kw, [ ] = 80 MPa, [ ] = 1.0 / m, G = 80 GPa 4 11, R0, R1 R, R1/ R = n; Me s Meh, Mes Meh = 1 - n 1 + n 4 1, Me d,, l, G, = 4 Me l Gd , GIP

97 d = 60 mm Me, [ ] = 50 M Pa, [ ] = 0.35 / m, G = 80 GPa[ Me ], , d, m mm100 mm 100 mm80 mm, Me, = 4 knm, Me d = 5 mm, D = 75 mm = 1.5 mm, Me = 73.6 Nm,,,, G = 40 GPa : (1 ),? ( ) , h/ b = mm60 mm, [ ] = 80 M Pa, G = 80 GPa, Me A 4 0 d d d d, Me ; 4 1 = = 300 Nm [ ] = 60 M Pa T, IP 90

98 (1 ) ; ( ), ; (3 ) ; 4 19 (4 ), 4, 1 max max, G1 G (1 ) 1 max > max ; ( ) 1 max < max ; ( ) G1 > G, 1 max > max ; (4 ) G1 < G, 1max < max 4 3 d1 d, D (= d/ D ), ( W1/ W ), (1 ) ( 1-4 ) 3/ ; ( ) ( 1-4 ) 3/ (1 - ) ; (3 ) ( 1-4 ) (1 - ) ; (4 ) ( 1-4 ) / 3 (1 - ) T, l = m, Me = 00 Nm, G = 80 GPa , ( a), 91

99 e

100 ,,,,,,, ( ),,,,, ( 5 1 (a) )(5 (a) )(5 (a) ) ( 5 3( a) ) ,, T 93

101 5 5 ), ( ),, (5 6), ,,,,,,,,, 1. ( ),,,,,., 94

102 ), q( ) N/ m( / ) kn/ m( / ) q, 5 1, 5 3,,, ( ), F N( ) kn( ) 5 5 4,,,, Me Nm( ) knm () 3.,,,,, : (1 ),,,,,,, 5 7( a),,, ( ),,,,,, 5 7 ( b),, (3 ), 5 8 (c),,,,, 5 7 (c) ,,, 95

103 ,,,, (5 1( a) ) ;,,,,, ;,,,, ( 5 1 ( b) ), (5 4 (a) ),,,,,,,,, (5 4 ( b) ),, (, ), l 5 1( b )5 ( b) 5 3 ( b)5 4( b),,, 5 7, Fx,, : (1 ) :, ( 5 8( a) ) ( ) :, ( 5 8( b ) ) (3 ) :, ( 5 8( c) ),,, 5 ( ), 5 9 (a),, Ab mm, mm, ( 5 9( b) ) F1 FA y, Fy = 0 MC = 0 ( C mm ), mm : FQ 96 M

104 FQ,, N () kn( ) ; M,,, Nm ( ) knm(), FQ 5 9 Fy = 0, FA y - F1 - FQ = 0 FQ = FA y - F1 (5 1), MC = 0, M + F1 ( b - a) - FA y b = 0 M = FA y b - F1 ( b - a) (5 ) M C, ;,,, mm FQ, M,,, :, FQ FQ (5 ( 5 10 (a) ), ; M, 10 ( b) ),,,,,,, 5 9 ( b) mm 97

105 5 1) (5 ),,, : (1 ) FQ (), FQ = Fyi( ) (5 3), ; ( ) M ( ) C, M = Me C i( ) (5 4),,,, ;,, ;,, ( 5 3 ) ( 5 4 ),, ( ), (5 10) ;, 5 10,,,,, (5 3 ) ( 5 4),,, (a), C F, C CCCF C, C, C (1 ) A B F A y, FB y,, MB = 0, FA y l - Fb = 0, FA y = bf l ; MA = 0, FB y l - Fa = 0, FB y = af l ; 98

106 5 11 : Fy = 0, FA y + FB y - F = bf l + af l - F,, FA y, FB y, 5 11( a) ( ) 5 11( a), C,, (5 3) (5 4 ), FQC = bf l MC = abf l FQC MC, FQ C MC ( 5 11( b) ) C,, (5 1 ) (5 ), FQ C = - bf l FC = - abf l FQC, FQC ; MC, MC 5 5 1( a), C Me, C, CA B (1 ) A B F A y, FB y A, B MB = 0, FA y l - Me = 0 M A = 0, FB y l - Me = 0, FA y = Me l, FB y = Me l 99

107 5 1 Me Fy : = 0, FA y + FB y = l - Me l = 0, FA y, FA y ; FB y, FB y FA y, FB y, 5 (5 1( a) ( ) 5 1( a), C,, (5 3) 4 ), FQ C = FA y = Me l MC = FA y a = FQ CMC, FQ C MC ( 5 1 ( b) ) Me l a C,, (5 1 ) (5 ), FQ C = FB y MC = - FB y b = - = Me l Me l b = - Me b l, FQ C, FQC ( 5 MC(5 1 (c) ) 1( c) ) ; MC,,,,,, A, A (5 (5 1( e) ) A, ( 5 1) (5 ), 1 ( d) ) ; B, B 100 FQ A = FA y = Me l

108 MA FA y 0 = 0 FQ A, MC,, FQ A (5 1 ( d) ), B, (5 3 ) (5 4 ), FQ B = FB y = Me l MB = - FB y 0 = 0 FQB MB, B, 5 1 (e) (1 ),, ( ),,, ( ) ;, ( ),, ( 5 ), ( ),, ( ) ( ), ( ) ( 5 ) ( ) 5 C,, C, C,(5 3) (5 4) C C, F QC = F QC = M C = M C - M e = - M e l F QC - F QC = 0 M C - M C = M e,:,,, ( ),,, ( ),, ( 5 3) (5 4 ),,,,,, ( ), ( 5 3) (5 4),,,, ( a), q CA B,,,, ( 5 3) (5 4 ) C,,, ql/ 4,, ql/ 4 Me b l 101

109 A l 8 (5 13 ( b) ) (5, ( 5 3) (5 4 ), MC = FQ C = - ql 4 ql 4 l 8 = - ql 3 FQC MC, FQ C MC 13( b ) ) A( ), (5 3 ) ( 5 4 ) (5 13 (c) ), FQ A, MC FQ A = q0 = 0 MA = q0 0 = 0, A, B( ), ( 5 3) (5 4),, ql,, ql A l/ (5 MB FQ B = - ql = - ql l = - ql 13( d) ), FQ B, MB, B 5 13( d) 5 4, 5 14 (a) EC D (1 ),, qa,, A a( ( b ) )

110 5 14 A B FA y, FB y, A, B MB = 0, q a 3 a - FA y a + q a a - q a = 0 MA = 0, q a a + FB y a - q a a - q a = 0 FA y = q a, FB y = q a Fy : = 0, - qa + FA y - qa + FB y = - qa + qa - qa + qa = 0, FA y, FB y, FA y, FB y FA y, FB y, 5 14 (a) ( ) E, E, E, 5 14( b ) ( 5 3) (5 4 ), FQ E = - q a + FA y - q a = - q a + q a - q a = 0 ME = - q a a + FA y a - q a a = - q a + q a a - q a = - q a FQ C, 5 14 (c) ; MC, 5 14 (c) C( C ), ( 5 3 ) ( 5 4) (5 14 ( d) ), FQC = - q a, MC = - q a 0 = 0 FQ C, MC,, FQ C 5 14 ( d) 103

111 D D ), ( 5 3 ) (5 4) (5 14 (e) ), FQ D = 0, MD = - q a FQ D, MD,, MD 5 14 (e) (1 ) ( 5 3 ( 5 4) FQC MC, ql, FQC MC, 5 3 ( ),5 4, A, B,,,, ( 5 1 ), ( 5 ),, : ( ),,,,,,, ( ),,,,, (5 3 ) (5 4 ),, ( 5 3) ( 5 4 ) 5 3,,, x, x, x, FQ = FQ ( x) M = M( x) (),,,,, 104

112 ,, FQ x M x,,,,,,,,,, FQ FQ x,, x, x,,,,, (5,, M x, x 10),, x, M,,, (a) AB, q, (1 ), A, B, 5 15 (a) FA y = FB y = ql ( ) x, A x, x, 5 15( a) x, x, ( 5 3) ( 5 4), x FQ ( x) = FA y - qx = ql M( x) = FA y x - qx x = ql x - qx (a), ( b ) - qx (0 < x < l) ( a) ( 0 x l) ( b) ( 3), FQ x M x, A ; x ; FQ (5 15 ( b) ) ; M (5 (a), FQ 15( c) ) x,, A B ( AB ) (a), FQ A = - FQ B = ql/,, 105

113 FQ 5 x 0, FQ A x l, FQB = - = ql x, 15 ( b) ( b ), M x,,, ( b ) AB C, ql, M 5 x 0, MA = 0 x = l, MC = q l 8 x l, MB = 0 x, 15 (c) ( b ) 5 15(c),, FQ max = ql ;, M max = ql 8 (1 ), (a), ( b), 5 1 5,,, x ( ), 5 15( b) 5 15 (c),, ; (5,, 10 (a) ),, ( 3),,,, ( 4), 5 15( c),,,, ( ), ( 5 ) 5 15 (b ) 5 : x,, ( 5 1) (5 ) x x,,, ( ), 106

114 , ( a) AB, F,,, B,,,, ( 5 3) (5 4) (1 ) x, B x, x, 5 16 (a) B x, FQ ( x) = F (0 < x < l) ( a) M( x) = - Fx ( 0 x < l) ( b) ( ) ( 5 16 (a) ) FQ x M x, B, x, FQ ( 5 16 ( b ) ), M (5 16 (c) ) 5 16 (a), FQ, x, ( a) AB,, x 0, FQ A = F x l, FQB = F FQ x,, 5 16 ( b) ( b), M x,, ( b) AB,, x 0, MB = 0 x l, MA = - Fl M x,, 5 16 (c) 5 16( b) 5 16( c),, FQ max = F;, M max = Fl ( 5 3) ( 5 4), ( ),,, () ( 5 3, 5 5, 5 6),, (), ( ), ( 5 1, 5, 5 4 ),,, 107

115 ( ) ( ),,,, ( ),, (a) 5 17 ( 1) MB = 0 MA = 0, A, B 5 17 (a) FA y = q a, FB y = q a ( ), A, D, CA, AD DB,, (3 ) AC A D, C( 5 3 ) ( 5 4 ) CA x1 AD x, CA : FQ ( x1 ) = - qx1 (0 x1 < a) ( a) M( x1 ) = - q x 1 ( 0 x1 a) ( b) AD : FQ ( x ) = - qx + qx ( a < x a) (c) M( x ) = - qx + q a( x - a) ( a x a) ( d) 108

116 x3 DB B 5 3) ( 5 4 ) DB, BD : FQ ( x3 ) = - q a ( 0 < x3 < a) ( e) M( x3 ) = qx 3 - q a ( 0 < x3 a) ( f) (4 ),, : CA, ( a) ( b),,, C A FQ C = 0, MC = 0 FQC = - q a, MC = - q a AD, (c)( d),,, AD FQ A = 0, MA = - q a FQ D = - q a, MD = - q a DB, ( e) ( f),,, D B FQ D = - q a, MD = - q a FQ B = - q a, MB = - q a,,,, x, x,,,,, 5 17( b ),,, 5 17 (c) 5 17( b ) 5 17( c), A DB, FQ max = qa; B, M ma x = qa (1 ), ( ) ( ) ( ),,,, 5, 7 ( 3) ( 5 3 ) (5 4),,,,,,, ( ),, x,,, 109

117 , (),,,, (, ),,,,,,,,,,, : (1 ), () ( (5 ) (5 4) ),,, ( ), (),, ( ),, ;,,, ;,, ( a), (1 ),, C,, ( ), BC AB (3 ) BC,,,, C, x1 ( ) (5 18 ( b ) ), ( 5 3 ) ( 5 4), x1, BC FN ( x1 ) = 0 (0 x1 a) FQ ( x1 ) = F ( 0 < x1 a) M( x1 ) = - Fx 1 (0 x1 a) AB,, B, x ( 5 18 (c) ), ( 5 3) (5 4), x, AB 110 FN ( x ) = - F (0 x a) FQ ( x ) = 0 (0 x < a)

118 5 18 M( x ) = - Fa ( 0 x < a) (4 ),,, 5 18( d), 5 18( e) 5 18( f) (a) (1 ), MB = 0, MA = 0 A, B 5 19 (a) FA x = q a, FA y = 3 q a, FB y = 3q a ( ), AB BC (3 ) BC, C, AB 5 9,,, B, x1, x () ( 5 3) (5 4 ), x1 x, CB : FN ( x1 ) = 0 (0 x1 a) FQ ( x1 ) = - FC y = - q a AB : FN ( x ) = FC y = q a (0 < x1 a) M( x1 ) = FC y x1 (0 x1 < a) (0 x < a) 19 ( b), ( c) ), (5 111

119 5 19 FQ ( x ) = qx (0 x < a) M( x ) = FC y a - qx x = q a - qx (0 < x a) (4 ),,, 5 19( b ), (c), ( d) (1 ),,,,() ( ),, ( 3) ( 5 18 (d ) ),,,,, ( 4) D, 5 0( g),,, (,, ),, 11

120 ,,,, ( a), A, BF, R, 5 0,,,, (1 ),, 5 0 ( b) ( ), ( ), (5 0), n = 0, FN () + Fsin= 0 t = 0, FQ ( ) - Fcos= 0 M = 0, M( ) - FR sin= 0 FN ( ) = - Fsin 0 < FQ ( ) = Fcos 0 < < 113

121 M ) = FRsin 0 < (3 ),, 5 0 (c), ( d), ( e),, A, FN max = F, M max = FR, B, FQ max = F (a), x, x AB, q = q( x), x x + d x, d x, 5 FQ 1 ( b )x M,,, ( FQ + d FQ ) ( M + d M), q, d x q, Fy = 0 MC = 0 ( C x + d x ), FQ + qd x - ( FQ + d FQ ) = 0 (5 5) M + d M - q d x - FQ d x - M = 0 (5 6) 5 1 (5 5 ), d FQ d x = q (5 7) FQ x q (5 6 ), q d x, dm d x = FQ (5 8) 114

122 M x FQ 5 8 ) ( 5 7), d M d x = q (5 9) M x q (5 7 )(5 8)( 5 9),,, ( 5 7 )(5 8 ) (5 9) x,,, (5 7) (5 8 ) q, ( 5 7) ( 5 8) (5 9 ),, ; ;, ( 5 7) ( 5 8 ) ( 5 9) x,,, (5 3) ( 5 4) (, ), : (1 ) ( q = ),,, q, FQ, M ; q, FQ, M, M q ( ),, ;, (3 ) ( q = 0 ), x,, FQ, M, FQ, M (4 ),,,,, () (5 ),,,,, ;,, (6 ), ( ),,, ;,,, ;,, 115

123 7 ) ( ),, 5 1, 5 1 ( ) ( ) FQ = 0 CC,,, : (1 ) ( ) (3 ), (5 3 )(5 4 ), (4 ) ( a) (1 ) MB = 0 MA = 0, A B 5 (a) FA y = q a, FB y = q a ( ), AC, CD, DE EB (3 ) 116

124 5 1), (5 3 ) AC :,, FQ A = q a, FQ C = q a - qa = q a CD :,, FQ C = FQ C = q a FQ D = q a - q a = 0 DE :,, FQ D = FQE = q a - q a - q a = - q a EB :,, FQ E = FQB = - q a,, 5 ( b) ), ( 5 ) AC :,, MA = 0 MC = q a a - qa a = 3 q a CD :,, MC = q a a - qa a - q a = a 117

125 MD q a a - q aa - q a = q a DE :,, MD = MD = q a ME = q a a - 3 q a = - q a EB :,, ME = q a a = q a MB = 0,, 5 (4 ) : (c) 1) FQ () AD, C,,,, A D qa, D qa,,, qa FQ, FQ, FQ ) M (), C q a,, qa ; D,, ; E 3 qa,, 3qa, DE, EB,,,, DE EB M, FQ, M ( a) (1 ),,, ( ), ( 5 3) (5 4), Fy = 0 MB = 0, 5 3 (a) ( ), AC, CD DB (3 ) FB y = 5 kn, MeB = 5 knm 1) (), ( 5 3) AC :,, FQ A = FQ C = 5 kn CD :,, FQC = 5 kn FQ D = = - 5 kn DB :,, FQ D = FQB = = - 5 kn 118

126 5 3,,, 5 3( b ), CD E, ),, (5 ) AC :,, MA = 0 MC = 5 1 = 5 knm CD :,, CD MC = 5 1 = 5 knm MD = = 5 knm,, E, d M d x = FQ, E, EC x0, x0, FQE = FQC - 10 x0 = 0,, ( 5 x0 = FQC 10 3) E, = 5 10 = 0.5 m 119

127 ME 5 ( ) = 6.5 knm DB :,, MD = = 10 knm MB = = 5 knm,, 5 (4 ) 3 (c) 1) FQ () CD,,, C D 10 kn FQ, FQ, FQ ) M ( ), CD, C, C D 5 knm,,, 5 knm M, FQ, M (1 ),,,, ( ) ( 5 4 ),,,,,FQ,,,, F Q (5 3 ) 5 13, 5 3( b), EC x 0, C F Q,F Q CE d F Q d x,x 0 x 0 = F QC df Q d x = 5 10 = 0.5 m ( 3),,,, ( a), (1 ) MB = 0 MA = 0, A, B 5 4 (a) FA y = kn, FB y = 4 kn ( ), AC, CB BD (3 ) : 1),, (5 1 ) 10 AC :,, FQ A = kn, FQC = - = - kn

128 5 4 CB :,, FQ C = FQ B = 1-4 = - 3 kn DB :,, FQB = FQ D = 1 kn,, 5 4 ( b), AC E, ),, (5 4 ) AC :,, E, MA = 0 MC = - 1 = 0, ( 5 3), E A E (5 4 ), x0 = FA y q = = 1 m ME = = 1 knm 11

129 CB,, MC = = 0 MB = = - 3 knm DB :,, MB = 1 1 = 1 knm MD = 0,, 5 (4 ) : 4 (c) 1) FQ () AC,,, A C 4 kn, C 1 kn,, 1 kn ; B 4 kn,, 4 kn FQ, FQ, FQ ) M (), C 1 kn,,, ; B 4 kn knm,, 4 kn,, knm M, M, M 5 1 AB x = a x = b, (5 3 )(5 4 ) A, B b FQ ad = b qd x a b d M a = b a FQ d x FQB - FQA = A( q) A B ( 5 10) MB - MA = A( FQ ) A B ( 5 11), FQB, FQ A MB, MA A, B ; A( q) AB = b qd x a A, B ; A( FQ ) A B (5 10) ( 5 11 ), Fi, ( 5 3) ( 5 4) : = b FQ d x A, B a (1 ),, Fi 1 FQ - FQ = Fi ( 5 1) ( ),,

130 ),, M - M = Me i A( FQ ) i ( 5 13), Me i, Me i, ; A( FQ ) i,,,, (5 ( 5 1 ), 13),, ( 5 1 )(5 13) (( 5 1 )(5 13) ) ( ) 5 14, ( 5 13) E, C ME = MA + A( FQ ) A E = =.667 knm MC = ME + A( FQ ) EC = ( ) = knm,,,,,, ( a),, (AC), ( CE ) 5 5 ( b),,, ; ( ), 5 5, FC y, AC C (5 5 (c) ),, AC CE,, (1 ), 5 5( c), CE MC = 0 MD = 0, FC y = FD y = q a 5 5 (c) 13

131 5 5 AC (5 5 (c) ) Fy = 0 MA = 0, 5 5 (c) FA y = q a, Me A = 3 q a ( ) AC A B, BC, CE CD, DE (3 ) AC CE, (5 10) AB :,, 14

132 FQ A FQB = q a BC :,, FQB = FQ C = q a - q a = q a CD :,, FQ C = q a, FQ D = q a - q a = 0 DE :,, FQ D = q a, FQ E = 0, AC CE,, 5 5( d ), AC F, (4 ), (5 11) AB :,, MA = - 3 q a MB = - 3 q a + q a a = - q a BC :,, MB = MB = - q a MC = 0 CD :,, MD = MC = 0 1 q a a = q a DE :,, MD = MD = q a ME = q a, AC CE,,, 5 5( e) ( 1),,,5 ; 5 5(e) C 5 (d ) C ( ) (5 5 ( b) ),,,,,, (5 5( c) ),,, ( ),,, ;,,,,,,,,, 15

133 ,,,,,,,, 5 5,,, ( 5 3 )(5 4 ),,,,,,,,,, ( a) 5 6 (1 ), 5 6( b), ( c) 16

134 ) 5 6 ( b), ( c), 5 6 (e), ( d),, 5 6( f), 1., :,., 3. (1 ), FQ M, ( ) FQ :,, M :, (3 ), : FQ, ( ), FQ = Fyi ( ) M, ( ) ( ) C, M = Me Ci ( ) (4 ) : 1) ) ( ), x ( x ) 3) (5 3 ) ( 5 4) x, 4. (1 ) (5 3 ) ( 5 4) :,,, ;,,, ; 17

135 , ( ), d FQ d x = q dm d x = FQ d M d x = q (3 ) FQB - FQA = A( q)a B MB - MA = A( FQ ) A B 5., (1 ),,,,,,, ( ) 3 : ; q, FQ M ;,, q, FQ M,, : 1) ) ( ), 3) (,,, ), FQ, M 4) FQ max, M max, (3 ), () 18

136 A, B C, D C, C, D A, B , , 19

137 AB, CA, BD?? , F 130

138 , , ,

139 , Fa, q a, , ,

140

141

142

143 ,,,,,,,,, 6 1,,,,,,,,,,,,,, ;,,,,,, 1.,, cd ab, mm nn, 6 1( a),,, (6 1 ( b) ) : 136

144 6 1 (1 ), ( ),,,,,, : (1 ) :,,, ( ) :,,,,,,, (6 6 ),,,,,, ( ),,,,,, x (6 3( a) ), d x mm nn,,, y (), z,, z y (6 3 ( b) ) 137

145 6 3,, mm nn, d(6 3( c) ) O1 O,, O1 O, ab, = ab - ab ab,,, ( 6 = (+ y) d- d = y d y,, ( 6 y (6 1) 1), 1),,,, ( 6. 1),, ( ),, = E= E y (6 ), E/, ( 6 ), y,, 6 4 (a), ( b )

146 ( ),, z, 5, d A,,, xy M,,, Sz (6 ) ( 6 3),, A E y d A = A d A = 0 (6 3) z d A = 0 (6 4) A A yd A = M (6 5) E A yd A = E S z = 0 = A yd A, A z E/, z, Iy z (6 ) ( 6 4), A zd A = 6 5 Sz = 0 (6 6) E A y z d A = E I yz = 0 = A y z d A, A y, z E/, Iy z = 0 (6 7), y, z y,, z, y, z ( 6 6 ) (6 7),, : (1 ) ( ),,,, Iz, x, x (6 ) ( 6 5), yd A = A E y d A = E A I z = M =y d A, A z A 1 = M E I z (6 8) 1/, (6 8 ), EI z, 1/, EIz, 139

147 6 8 ) ( 6 ), = My I z, (6 (6 9) ),,,, ( 6 4( a), ( b) ), ( 6 8) (6 9),, y ( T ),, ( 6 8) (6 9),,,,,,,, ( l h l/ h 5 ), (,, l/ h 5, ( 6 9 ) 1 % ),,, (6 8) ( 6 9),,, ( 6 9 ), M y, ( 6 9 ), M, y,,, (a), ( b ) ) : ( 1) a, b, c, d; ( ) (1 ) C a, b, c, d : 1), 6 6 (c),, C, MC = 0 knm ), z, 6 6 ( b), z 140

148 6 6 I z = = mm 4 = m 4 3) C a, b, c, d 6 6 ( b ), a, b, c, d ya = 70 mm, yb = 50 mm, yc = 0, yd = 70 mm MC = 0 knm, ya = 70 mm, I z = m (6 9 ), a a = MC ya I z = = Pa = 93.6 M Pa MC = 0 knm, yb = 50 mm, I z = m (6 9 ), b b = MC yb Iz = = Pa = 66.8 MPa MC = 0 knm, yc = 0, I z = m ( 6 9 ), c c = MC yc I z = = 0 MC = 0 knm, yd = 70 mm, I z = m (6 9 ), d d = MC yd Iz MC = = Pa = 93.6 MPa,, C,, a, a 141

149 b d, b d ; c, c ( ) C ( 6 9 ), C 6 6( d) 6 6 7( a), ( b ) : (1 ) B Ca, b; ( ) B C; ( 3) 6 7 (1 ) B C a, b : 1) B C, 6 7( c),, C, ( ) MC = 10 knm B, MB = 8 knm ), ( ), y (6 7( b ) ), y,, 14

150 yc Ai y i Ai = , y, 6 = 66 mm 7( b ),, 6 7( b),,, I z = = mm 4 = m 4 3) C B a, b(6 7 (c) ) MC,, C, a, a ; b, b 6 7( b ), a, b ya = 66 mm, yb = 94 mm MC = 10 knm, ya = 66 mm, I z = m (6 9 ), C a C a = MC ya I z = = Pa = 33.9 M Pa ( ) MC = 10 knm, yb = 94 mm, I z = m (6 9 ), C b C b = MC yb Iz (6 = = Pa = 48.3 MPa () 7 (c) ) MB,, B, a, a ; b, b MB = 8 knm, ya = 66 mm, Iz = m ( 6 9 ), B a Ba = MB ya Iz = = Pa = 3.7 M Pa ( ) MB = 8 knm, yb = 94 mm, Iz = m ( 6 9 ), B b B b = MB yb I z = = Pa = 38.6 MPa () ( ) B C ( 6 9), C B 6 7( d), ( e) (3 ),, 143

151 B C), B, C, + max = Bb = 38.6 M Pa max - = C b = 48.3 MPa (1 ),,,,, I z y ( ),, 6, B C,B,,,C (B C),, ( 6 8) (6 9 ),,,, ( 6 8) (6 9),, ( h/ 0., h, ) 6 (6 9 ),, ( ) (), max = Mmax ymax I z ( 6 10) W z = I z/ ymax, ( 6 10 ), W z max = Mmax W z,, [ ] 3 h b ( 6 8( a) ), ( 6 11) d ( 6 I z Iz = bh3 1, ymax = h, W z = bh 6 8( b ) ), = d4 64, ymax = d, W z = d3 3 Dd (6 144 Iz 8 (c) ), = 64 ( D4 - d 4 ), ymax = D, W z = D ( d D ) 4

152 6 8,, max [ ], max = Mmax W z [ ] ( 6 1),,,, + max - max [ + ] [ - ], + max = M max y max + I z [ + ] ( 6 13) max - = Mmax y- max I z [ - ] ( 6 14), y + max y - max + max - max,,,,,, : (1 ),, (6 1) (6 13)( 6 14 ) ( ),, (6 1) (6 13)( 6 14 ) (3 ),, (6 1) (6 13)( 6 14 ), 145

153 3 6 9 (a) 0 a, [ ] = 170 MPa 6 9 (1 ), 6 B, Mmax = 4 knm 9( b), B, ( ) 6 9( a),,,, B (6 9 (c) ) ;,0 a W z = Iz ymax (6 max = Mmax ymax I z, = Mmax W z = 4. cm 3 = m 3 = 5 ), = Pa = M Pa < [ ] (1 ),, ( ) ( ), ( ),,, (a), [ ] = 160 M Pa (6 10( b ) ) ( 1), 6 (), B, () 146 Mmax = 8 knm 10( d),, B

154 6 10 ( ) 6 10 ( b),, B ( 6 10( e) ( 6 1 ), W z Mmax = [ ] = m 3 = mm 3, 10, W z = 49 cm 3 = mm 3, W z, ( a), [ + ] = 40 MPa, [ - ] = 80 MPa (1 ) 6, Mmax = 6 knm 11 (c), D ( ) 6 11( b ), y, y, y, y, yc = Ai y i Zi = , y, 6 = 70 mm 10 (a) z I z = = mm 4 = m 4 147

155 6 11 (3 ), [ + ] [ - ],, ( 6 13 )(6 14) 6 11 (c),,,, (6 11 ( d) ) 6 11( b) (6 13) ( 6 14 ) + max = Mmax y+ max Iz max - = Mmax y- max Iz y + max y - max = 70 mm = 130 mm = = Pa = M Pa < [ + ] , = = 7.69 MPa < [ - ] ( a) a = m; y1 = 10 mm, y = 80 mm; Iz = mm 4 ; [ + ] = 30 M Pa, [ - ] = 70 M Pa : ( 1) [ F] ; ( ) (6 ( 1) 6, D, ( g) ) [ F] 1 ( b),, A

156 6 1 ( ) : MA = Fa, MD = Fa 4 1) [ F],,, A D, (6 13) (6 14),, : A, (6 + max = MA y+ max Iz = MA y1 I z (6 - max = M C A ymax - Iz = M C A y = 1( c) ), F [ + ] = F Iz = N = 13 kn 1( c) ), F [ - ] =

157 F N = 45.5 kn D, (6 + max = MD y+ max Iz = MD y (6 - max = MD y- max Iz = Iz = F MD y1 Iz 1 ( d) ), F [ + ] = = F N = 39 kn 1( d) ), F N = 30.7 kn, [ F] = 13 kn ) (6 1( g ) ) [ F] T, A, (6 + max = M C A y + max Iz = M C A y Iz = F (6 - max = MCA y- max Iz = MC A y1 Iz = F ( e) ), F N = 19.5 kn 1( e) ), F N = 30.3 kn D, (6 + max = MD y+ max Iz = MD y1 (6 - max = MD y- max Iz = Iz = F MD y Iz 1 (f) ), F N = 6 kn 1( f) ), = F F N = 91 kn, [ F] = 19.5 kn (1 ),, 150

158 ,,,, ( ) ( y 1 / y ) > [ + ]/ [ - ],, D A,, ( D A ), (6 13 ),,,,,,, 6 3,,,,,,, (,, ), ( ),,,,,,,, ( 6 9 ),, , h, b, x y,,, FQ y ( 6 13 ( b) ) h b,, : (1 ) FQ (6 13( b) )

159 ), (6 13 ( b) ), h b d x 11 (6 13 (a) ), 6 13 ( b), 11,, FQ,, M M + d M(6 13( b ) ), 11,, ( y),, 1 (6 14 (a) ) y ( y), y mn, (6 m1 n A * 6 14 (c) ) F * 1 ( x ), F * 1 = * 1 d A = A * A 14 ( b) ), m1 1 d A( My * Iz d A = M y * I z * d A = M A I z, y * d A ( 6 14 (c) ), A * S * z =y * d A * A S * z ( 6 15) 6 14, n d A F * ( x ), F * = M + d M S z * ( 6 16) I z,,,, mn ( y) (6 14( c) ), d FQ = ( y) bd x ( 6 17) F * 1, F * d FQ x (6 14( d ) ), F x = 0, F * - F * 1 - d FQ = 0 ( 6 18) (6 15) ( 6 16 )(6 17) (6 18), ( 5 8 ), ( y) = FQ S* z I z b ( 6 19) (6 19), FQ ; b 15

160 , 6 Iz ; S * z y 15( a), S * z = A * y * C = b h - y 1 y h + y = b h 4 - y ( 6 0) (6 0) Iz = bh3 1 ( 6 19 ), ( y) = 3 FQ bh 1-4 y ( 6 1) h 6 15,,, 6 15 ( b), (c) ( y = h/ ),, ( y = 0),, max, A = b h ( = 3 FQ bh = 3 FQ A ( 6 ) ),, hb, (6 ), h = b, max, 3% ; h = b, 13% ; hb/, max, 40%, ( ),,,, ;,= 0( 6 16),,,,,,,

161 .,,,, FQ,,,,, FQ, ( 6 8), max = FQ S* z max Iz b ( 6 3), b ; Iz ; S * z max 6 17( a) d, ( 6 3), b = d, I z = d 4 / 64, S * z max 6 18 ( b), S * z max = ( d/ ) d 3 = d3 1 ( 6 4) max = 4 3 FQ A ( 6 5), A = d / 4, 1.33, max, 4% ( a), F, l, b, h,, (1 ),,, ( ) Mmax FQ max = ql = ql ( ) (6 11), max = M max W z = 3 ql bh 154

162 (6 ), max = 3 (3 ) 6 18 FQ max A max = l max h = 3 ql bh,l 5 h, max 10 max,,, 3. T, ( ),, ( ), 19( a), ( 6 19) y, Iz, b(),, S z * 6 19 (a), S * z = b h 4 - h 1 4 h y ( y) = FQ 8 Iz b( h - h 1 ) + ( h 1-4 y ) ( 6 6), ( 6 ( y = 0 ), 19 ( b) ) 155

163 max ( y = h/ ),, FQ 8 Iz [ bh - ( b - ) h 1 ] ( 6 7) min = FQ 8 I z ( b h - b h 1 ) ( 6 8) (6 7) (6 8),,,, 6 19( b ),, FQ, 6 19,, = FQ h1 ( 6 9),, y,,,,,,,,,,,,,,,, ( 6 19) (6 3 ),,,, (6 (6 9 ) 9), (a) Iz = m 4 : (1 ) a, b, c, d ; ( ) ( 1) 6 A DB, FQmax = 0 kn 0( b ),, () ( ) a, b, c, d a, d: 6 0( a), a, d, (6, ( 6 b : 6 3 ) (6 (6 156 a = d = 0 0 (a) ) 0( a),, = 40 mm; 0( b ) ) ( ) S * z = = mm 3 = m 3 3) b

164 6 0 = FQ S* z I z = = Pa = 3.44 MPa c : 6 (6 (6 0( a),, = 40 mm; 0( c) ) () S * z max = = mm 3 = m 3 3) c = FQ S* zmax Iz = = Pa = 3.63 M Pa (3 ) ( 6 3),,,, D 6 ( 6 0( c) 3),, ;,,, S * z ;, S z * FQ, (1 ), R0,,, 6 1,, y y, y, 157

165 ,,,, ( 6 19 ), max = FQ S * zmax Iz b, S * z z ; Iz ; b, b = ( ) S * z, Iz,, S * z = 3 Iz R0 = R R0 - R (3 ) S * z, Iz b, R 0 R max = FQ S* zmax Iz b, A = 0 FQ R0 = FQ A,,6 FQ max 9,,, max ( ) ( ), max = FQmax S* zmax Iz b ( 6 30), FQmax ; Iz z ; b ; S * zmax (, Iz/ S * z max ), max, max = FQ max S* z max Iz b [ ] ( 6 31) max [ ],,,, (, ), (, ), 158

166 6 10 6, F18 a, [ ] = 170 MPa, [ ] = 60 MPa (1 ) F, (5 1 ) ( 5 ),,, Mmax = 30 knm,,, FQmax = F = 30 kn 6 ( ) 18a W z = 185 cm 3, (6 5 ), max = Mmax W z = = Pa = 16. M Pa < [ ] (3 ) 18a ( Iz/ S * z max ) = 15.4 cm, d = 6.5 mm, (6 max = FQmax S* zmax Iz d = 31), = Pa = 30 MPa < [ ] , :,, (1 ),, ( ), max max, (3 ) max max, (6 1) ( 6 31 ),, max max ,,,,,,, 159

167 ( ),, ( ),,.,,,,, (),, (6 8 ) ( 6 9), (6, ( 6 9), 9 ),, ( 6 ( a) ),, ( 6 ( b ) ), 1.,, (, ),,,,,,,, (6 3 ), ( 6 ), (6, ; S * z 3 19), = FQ S z * I z ( 6 3), FQ S * z,

168 , ( 6 3),,,, (a) xy ( x, y, xy ) FQ,, 6 4 (1 ) (6 3),, S * z, S * z, s(6 4 ( b ) ), S z1 * = h s abcd, S * z1 bde f z, y( 6 4 ( b) ), S * z = bh + h 4 - y z I z, ( 6 1 = = FQ FQ h s I z =, 6 FQ hs Iz b h + h 4 - y Iz = 4( c) ( ) 3) FQ ( b h + h 4 - y ) Iz,,,, 6. 4( c),, 161

169 ,, ( 6 5( a) ),,, (6 5( b ) )6 5 ( ), ( a), C, z, y C z, z y y F, x y ( 6 5 (a) ), (6 3) ( 6 10 ), ( c),, d A FT FT,,, FT = b 0 d s = FQ b h 4 Iz ( 6 33), d A, FQ, 6 5 (c), A y FQ, A O ( 6 5 ( d) ) e = FT h F Q = b h 4 Iz ( 6 34) : F x y ( ), 6 5 ( b), FQ C, A, FFQ F FQ, xy F Fe( e A y ),, A, 6 4 ( b) F A y, 6 5 (a), F FQ, (6 5( a) ), A, ( ), A,

170 .,,, : (1 ) ; ( ),, ; (3 ),, ; (4 ),, ;, ;,,,,, (a), ( b) z, z, z,, 6 6 (a), ( b), 6 6 (a) ( b ), (6 6( a), ( b ) ) A,,, A, A 6 1,,,, ;,,,,,, 163

171 ,,,,,,,,, 6 1 e = 1 b 3 1 h 1 b b 3 e = b h 4 I z 6 5,,,,,, 1., 6 7 (a),,,

172 (, 6 8 ( b) ),,.,, 6 8( a) 6 8 ( b),, 6 8,,, 1.,,, 6 5,., W z/ A W z/ A, W z/ A 6 6 Wz/ A Wz A h 0.15 d 0.05 D ( ) h,,,,,,, 165

173 ,,,,,, T,,,,,,,,,,, ( 6 9 (a) ) (6 9( b ) ) ,,,.,,,,,,, 3.,,,,,, (1 ) : 166

174 , M I z = My I z z ; y, M, y,,,, ( ) :,,,,, max = Mmax ymax I z, W z max h b ( 6 = Mmax W z 8( a) ), d ( 6 I z = bh3 1, ymax = h, W z = bh 6 8( b ) ), Iz = d4 64, ymax = d, W z = d3 3 Dd (6 8 (c) ), Iz = 64 ( D4 - d 4 ), ymax = D, W z = D d D 4 6. (1 ) :, ( y) = FQ S* z I z b, FQ ; Iz z ; b; S * z y, FQ, S * z,, T ( ) :,, 167

175 ,,, S * z max max = FQ S zmax * Iz b, max, = 3 F Q A max = 4 3, FQ A max = FQ A 7. (1 ) :,,,, max = Mmax W z [ ],, ( ) : max = F Qmax S z * max Iz b [ ], : 1), Mmax, FQmax ; ), ; 3) max max, ( 6 1 )(6 31) 8., ; ; 6 1 d = 1 mm m,, E = 00 GPa 6 6, : ( 1) a, b, c, d ; ( ) a, b, c, d 168

176 6 3 T 6 ( a), ( b), : (1 ) ; ( ) (( c) ), , F, C = E = 00 G Pa, : ( 1) ; ( ) F , [ ] = 160 MPa: ( 1) ( ) ; ( ) W z/ A, ,, D1 = 40 mm, d/ D = 3/ 5, 169

177 , b = 100 mm, h = 00 mm, [ ] = 10 M Pa d = 40 mm ( ), [ + ] = 30 M Pa, [ - ] = 90 M Pa z I z = mm 4, y1 = 119 mm, y = 181 mm, [ + ] = 40 M Pa, [ - ] = 10 M Pa[ q] yc 6 10 T, 6 10 Iz = mm 4, = 35 mm,, [ + ] = 30 M Pa, [ - ] = 90 M Pa 170

178 , [ + ] [ - ] = , CD 10, B d = 10 mm BE [ ] = 160 MPa, [ q] 171

179 , a, b, c, d T 6 14, a, b, c, d, ,, 6 15 Iz = mm 4, yc = 130 mm : (1 ) ; ( ) [ ] = 10 M Pa, [ ] = 1 MPa, [ ] = 0.34 M Pa Me [ ] = 10 M Pa, [ ] = 1 MPah/ b = 3/, 17

180 a [ ] = 160 M Pa, [ ] = 80 M Pa T, 6 19 I z = mm 4, yc = 45 mm, a = 1 m, [ ] = 160 M Pa, [ ] = 80 M Pa [ q] h1/ h = 1/,, 173

181

182 ,,, 7 1, 7 1, x,, w, Ox w, w 7 1, xw,, xw,,, (6 8 ),,,,,,, 175

183 .,,,,,,, w 7 1, w x, x, w = w( x), 7 1,,. ( ),,, 7 1, x (7 1 ), rad, tan= w 7 1, x ( ),, ( ) ( ) ( ) 7 (a), ( b), (6 8),, 7,, ( ),,,,,, 176

184 , ( 6 1 = M E I z 8), (7 1),,, x,, Iz 1 ( x) = M( x) EI z, (7 ) 1/ ( x) M( x), EI,, w = w( x) 1 ( x) d w = d x 1 + ( d w d x ), 7 3/ (7 3) 1,, M( x),, d w ; d x, M( x),, d w (7 3) M( x) d w d x d x, (7 1 ) ( 7 3), d w d x 1 + ( d w d x ) 3/ = - M( x) EI (7 4) 7 3,, d w d x ( 7 4) d w = - d x M( x) EI d w rad, d x 1, (7 5) ( 7 5 ), M( x) 177

185 (7 5),,,, lh, l/ h > 5, 5%,,,,, ( 6 8 ),, 7 3,, ( 7 5) x, = d w d x = - M( x) d x + C EI (7 6) w = - M( x) d x d x + Cx + D (7 7) EI, C, D,, (7 4( a) ) ; (7 4 ( b) ) 7 4 ( ),,,,,,, 7 4,,,,, (7 6) (7 7 ),,,, 178

186 1 7 5 F, wmax (1 ), max EI, 7 3, M( x) = - F( l - x) ( 0 x < l) ( ) ( 7,, 1), d w = - d x M( x) EI = F( l - x) EI d w d x = - Fx EI + Fl x E I w = Fx3 6 EI (3 ) + Fl x EI = -, (c) ( a), ( d ) ( b ), (4 ) Fx E I + Fl EI C ( a) + Cx + D ( b) x = 0, w = 0 (c) x = 0, = 0 ( d) C = 0, D = 0 C, D ( a) ( b), = - w = - (5 ), F EI x + Fl E I x ( e) F 6 EI x 3 + Fl EI x ( f),, 7, max = B = Fl EI wmax = wb = Fl3 3 EI 5, B, w, ( 1) (7 6) (7 7 ) x w,,x 179

187 x ) 7 1, C, D F EI,, wmax (1 ), 7 7 FA y 6, = Fb, FB y = Fa l l 6, A, C, B, AC CB, AC : CB : M( x1 ) = FA y x1 = Fb x 1 ( 0 x1 a) l M( x ) = Fb x - F( x - a) ( a x l) l ( ) AC :,, CB :,, d d w = - d x w1 d x 1 = - M( x1 ) EI = - Fb le I x1 7 6 d w1 d x = - Fb le I x 1 + C1 ( a) w1 = - M( x ) EI Fb 6 le I x C1 x1 + D1 ( b) = - Fb le I x + F ( x - a) EI d w d x = - Fb le I x + F EI ( x - a) + C (c) w = - Fb 6 le I x3 + F 6 EI ( x - a) 3 + C x + D ( d), CB, ( x - a), ( x - a), (3 ) 180 x1 = 0, w1 = 0 ( e)

188 ( g), ( h ) ( a), ( b), (c), ( d), (e), ( f) ( b ), ( d), x = l, w = 0 ( f) x1 = x = a, w1 = w ( g) x1 = x = a, w1 = w ( h) C1 = C, D1 = D C1 = C = (4 ) Fb 6 lei ( l - b ) D1 = D = 0 (a), ( b ), (c), ( d) AC CB = 1 = Fb 6 le I ( l - b - 3 x 1 ) (i) w1 = Fbx1 6 lei ( l - b - x 1 ) (j) Fb 6 lei ( l - b - 3 x ) + F EI ( x - a) ( k) w = Fbx 6 le I ( l - b - x ) + F 6 EI ( x - a) 3 (l) (5 ),, 7 6, a > b, AC 1 = 0 1 = d w 1 d x1 = 0, x0 (j), wmax x0 = l - b 3 wmax = Fb( l - b ) 3/ 9 3 le I, w, (1 ) (j), w l = ( m) ( n) Fb 48 EI (3 l - 4b ) (o), F B, ( n) (o) w max = w l Fbl 9 3 EI Fb 16 EI = Fbl EI = Fbl EI,w max.65 %, F,, ( ),,(7 6) (7 7 ) ( ), 181

189 ,,, :, ( 5 3 ),,, ( x - a), ( x - a),, 7, x = a, 1 =, y 1 = y,c 1 = C D 1 = D, 7 3, l, EI, 7 W ( x) = 7 (a), ( ) (1 ), w( x) = qa 4 EI ( x3 - lx + l 3 ) ( a) (a), w ( x) = q 4 EI (4 x3-6 lx + l 3 ) ( b) (a), ( b ) ql 3 4 EI ; x = 0, w( 0) = 0; ( 0) = w ( 0) = x = l, w( l) = 0; ( l) = w ( l) = - qx 4 EI ( x3 - lx + l 3 ) ql 3 4 EI 7 7,, ( ), ( a), w ( x) = q 4 EI ( 1 x - 1 lx) = M( x) = EI w= - EI q EI ( x - lx ) = - q EI ( x - lx ) q ( x - lx ) M ( x) = FQ ( x), M ( x) = q( x), w= - M( x) EI, q( x) = M ( x) = - q, q (3 ), ( b )

190 ,,,,,, w = Fx 6 EI ( - x + 3 l) w B = Fl3 3 EI B = Fl EI w = Fx 6 EI ( - x + 3 a), ( 0 x a) w = Fa 6 EI ( - a + 3 x), ( a x l) w B = Fa (3 l - a) 6 EI B = Fa EI 3 w = qx 4 EI ( - 4 lx + 6 l + x ) w B = ql4 8 EI B = ql3 6 EI 4 w = M e x EI wb = Me l EI B = Me l EI 5 w = M e x EI w = Me a E I (0 x a) a - x ( a x l) wb = M e a E I B = Me a EI l - a 6 w = Fx 1 EI ( - x + 3l 4 ) ( 0 x l ) wc = - Fl 3 48 EI A = - B = Fl 16 EI 183

191 7 w = w = lx ) Fbx 6 le I ( - x + l - b ) Fa( l - x) 6 lei ( a x l) ( - x - a + f = Fb( l - a ) 3/ 9 3 le I ( x = l - b 3 A = Fb( l - b ) 6 lei B = - Fa( l - a ) 6 le I ) 8 w = qx 4 EI ( - lx + x 3 + l 3 ) f = 5ql EI A = - B = ql 3 4 EI f = - M e l 9 3 EI 9 w = - M e x 6 lei ( l - x ) ( x = l/ 3 ) A = - M e l 6 EI B = M e l 3 EI f 1 = - M e ( l - 3 b ) 3/ 9 3 lei 10 w = - ( 0 x a) w = - M e x 6 lei ( l - 3b - x ) lx + x ) M e ( l - x) 6 lei ( a x l) (3 a - ( x = l - 3 b / 3 ) f = M e ( l - 3 a ) 3/ 9 3 lei ( B x = l - 3 a / 3 ) A = - B = - C = - Me ( l - 3 b ) 6 lei M e ( l - 3 a ) 6 lei Me ( l - 3a - 3b ) 6 lei 184

192 4,,,,,,, (7 5),,, ( ), (7 1 ), ( a) EI, ( b ) 7 8( c) 7 1, wc1 = Fl3 3 EI ( ), wc = - 5 Fl 3 48 EI (), C wc = wc 1 - wc = Fl3 3 EI - 5 Fl3 48 EI = 11 Fl3 48 EI () 7 4,,,,,,,, ( a) q, EI 185

193 7 9 d F = qd x, 7 9( b ) 7 1, d F d wc = d Fx 48 EI ( 3 l - 4 x ) =, q, 7 wc = 1/ d wc 0 = 1/ 0 qx 48 EI ( 3 l - 4 x ) d x () qx 48 EI (3 l - 4 x ) d x = 5 ql4 768 EI () 1,,,, 7 1,,,, ( 7 5),,,,,,,,, ,, (7 10( b) ) (7 10( c) ) 7 10 (c),,,, 7, wc = 5 ql4 768 EI 1 ( ),, 7,, 7 7( b ) 1 1,,, 7,, 186 1

194 ( a) C EI, AB B BC,,, 7 11 ( b) 7 11 (c),, ( b), F,, Fa A B 1 B B = ( Fa) l 3 EI = Fal 3 EI () 8 ( b), AB B, BC, 7 11 ( b), C w1 = B a = Fa l 3 EI () 7 11 (c), 7 1 C w = Fa3 3 EI (), 7 11( b ) 7 11 (c) C, wc = w1 + w = Fa l 3 EI + Fa3 3 EI = Fa ( l + a) ( ) 3 EI ( a) ) C D 187

195 EI (7 7 1 ( AC ) ( CB ) 1( b ) ),,, 7 1 (c) 7 1( d), CB C AC C, (7 7 1 (c), 7 1 C C 7 wc = Fl3 6 EI () 1( c) ) 1( c), AC C, CB, C, 7, D 1 (c) wd1 = 1 WB = 1 Fl3 6 EI = Fl3 1 EI 7 1 ( d), 7 1 D ( ) 188

196 wd = Fl3 48 EI ( ), 7 1( c) 7 1( d) D, wd = wd1 + wd = Fl3 1 EI + Fl3 48 EI = 5 Fl3 48 EI D :,, ;,,,, () (a) C 7 13, ( AB ) (B BC),,, 7 13 ( b) 7 13 (c), BC B A B B, (7 13( b ) ) 7 13 ( b), 7 1 B 7 B = wb = F l E( I1 ) + F l 3 3 E( I1 ) + Fl l E( I1 ) = 3 Fl 16 EI 1 Fl l E( I1 ) = 5 Fl3 96 EI 1 () () 13( b), AB B, 189

197 BC 7 wc 1 l = B + wb = 3 Fl 16 EI1 13 ( b), C l (c), 7 1 C wc = F l 3 EI1 3 = Fl 3 4 EI1 5 Fl3 96 EI1 () = 7 Fl3 48 EI1, 7 13( b ) 7 13 (c) C, C wc = wc 1 + w C = 7 Fl3 48 EI 1 + Fl 3 4 EI1 = 3 Fl3 16 EI D CB E A, AB EI ( ) ( ) 7 14 AB, (CB ) ( AB),,, 7 14 ( b) 7 14( c) 7 14 (c), MA = 0, AB B FB y = ql (CB ) B (7 ( ( b ) )CB 14 ( b) ),

198 7, 7 FN CB, CB lcb = FN CB l EA ql ql l = EA = ql EA 14( b ), BC, AB 14( b ), AB D wd1 = lcb = ql 4 EA 7 14 (c), 7 1 AB D wd = ql 4 48 EI, 7 14( b ) 7 14 (c) AB D, D 5 wd = wd1 + wd = ql 4 48 EI + ql 4 EA 6,, ( ),,,, ;,, ( ),,, :,, 7 1, 7 5,,,,,,,, ;,, wmax [ w] (7 8) max [ ] (7 9), wmax, max ; [ w], [ ], [ w] = l 00 l ;, [ w] = rad l 500 l , [ ] =,, : ; ; 191

199 l = 4 m, F = 10 kn, E = 10 GPa, [ ] = 170 M Pa, [ w] = l/ 400 (1 ), Mmax = Fl, (a), W z Mmax max 7 15 = Mmax W z = Fl = = [ ] [ ] [ ] ( a) m 3 = 35 cm 3, No. 0a W z = 37 cm 4, Iz = 370 cm 4 7 ( ), wmax [ w] ( b) 1, ( ), (c) ( b ), Iz Fl3 3 E[ w] = wmax = Fl3 3 EIz / 400 = m 4 = cm 4, No. 3a W z = 69.0 cm 3, Iz = cm 4, No. 3a (1 ),,, ( ), 7 11,,,,, 1., M,,,, 19 (c)

200 wa max = Fl3 48 EI ; F q b = F l, Ma max 7 16 ( b) ), Ma max = Fl 4, (7 = Fl 5 ql4, wb max = EI 50%, 6. 5 % 16 ( b) ), = 0.65 wb max, (a) l, 0. 5 l( 7 17( b ) ), 50%, % EI E,, I, T 3.,, n,,, 7 18 (a), (7 18( b) ), 1 16 ; (7 18( c) ), 1 38, ( ),,,, 193

201 ,, ( ),, ,,,,,,,,,, 7 19( a),,, B,,,, FB y, F FB y, 7 194

202 9 ( b ), F FB y 7 19, B,, 7 wb = wb = 0 ( 7 10) FB y l3 3 EI - 5 Fl3 48 EI 1, B ( 7 11 ) ( 7 10 ),, FBy FB y FB y l 3 3 EI - FB y 5 Fl 3 48 EI = 0 = 5 F 16, ( 7 11),,,,,, 7 19( a), A,, MA, 7 19(c),, A = 0,,,,,,, : 195

203 1 ) ; ( ) ; (3 ),,,,,,,,,, ( a) F EI, k( ) (1 ) 1) : B,, ) : B,, FB y, ( 7 0 ( b) ) 3) : 7 0 B, B, 4) : (7 0( b ) ) B wb,, wb wb = ( a) = 5 Fl3 48 EI - FB y l 3 3 EI ( b) 5) : = FB y k ( b )(c) (a) 5 Fl 3 48 EI FB y =, FB y l 3 3 EI = FB y k 5 F EI kl 3 (c) ( d)

204 ) : MB = 0; MA = 0, 7 0 FA y = F EI k l 3 Me A = Fl EI kl 3 (1 ),,,, ( ),,, 7 7 1,, 13 B,, ( ), B, 7 13,, ( ) 7 1,(B), F By, F A y, M ea k =, F B y = 5 F 16, F A y = 11 F 16, M ea = 3 Fl, B (a) AB E I, CD EA AB C 7 1 (1 ) 197

205 ) : AB C CD,, ) : CD,, FN ( CD ), (7 1( b ) 7 1 (c) ) 3) : C, CD lcd, AB C w C, 4) : wc = lc D ( a) (7 1( b ) ) C w C, 7 1,,, CD (7 wc = 5 ql4 384 EI 1( c) ) lc D 5) : = FN lc D EA ( b ), (c) (a) - FN l 3 48 EI = FN a E A 5 ql EI - FN l 3 48 EI = FN a E A FN = 5 qa 4 48 l 3 1 +,, CD ( ) AB C (e) ( b) AB C wc = 5 ql4 384 EI - FN l 3 48 EI = 5 qa4 384 EI ( b) (c) ( d) 48 Ia A l 3 ( e) Ia A l 3,, 7 13, B,,, AB,,, (a), AB (1 ) AB AD, C C,,, 198

206 7 C,, FC y 7 ( b), w1 AB F FC y C ; w DC FC y 7 7 C, 1 1,, w = FC y ( b ) (c) (a), 7 ( ) w1 = w1 = w ( a) l 3 EI (5 F - FC y ) l 3 48 EI 3 = FC y l3 4 EI (5 F - FC y ) l3 48 EI FC y = = 5 F 4 wmax, wmax AB AB F, 1, AB F FC y, 7 1, wmax= wmax = Fl3 3 EI Fl3 3 EI - 5 FC y l 3 48 EI FC y l3 3 EI ( b) (c) ( d), B = 13 Fl3 64 EI 199 ( e)

207 e) ( d ), wmax wmax = = AB 60.9%,, AB (a) AB E IB A, 7 1 ( b) 7 3 B,, FB y ( b ) (a), 3 (c), wb = ( a) wb = FB y l 3 3 EI FB y FB y l3 3 EI ( b) = (c) = 3 EI l 3, (), 7 15,,,, 00

208 7,,,,, :,,,,,,,,,, y v ( 5),, v= E = M y ( 7 1) EI dv= vdv = M y EI d Ad x, dv ; d A, d x, M V= y M l A d Ad x EI = l EI ( A y d A) d x ( 7 13), A ; l ; y d A = I, A (7 13) M V= l EI d x ( 7 14),, (7 l EI V= M 14 ) ( 7 15) (7 14) (7 15),,, (7 14 )(7 15) 01

209 .,,., ( ) ( ), 3.,,,, 1 ( x) = d w = - d x M( x) EI M( x) EI, 4. (1 ) :,, = d w d x = - M( x) d x + C EI w = M( x) - d xd x + Cx + D EI, :, x, w ;,, n, n, ( ) ( ) :,, ( ) ( ), 7 1,,,,, : 1) ; ) ; 3),, 0

210 . (1 ) : wmax [ w] max [ ],,, ( ) : 7 1, : 1), ; ) ; 3),, T 4), E,,, 5. (1 ) : :,,,, ( ) :,, : 1) ; ) ; 3),,,, , EI,, B

211 7, EI, C , EI,,,, , EI,,, , 7 5, w( x) = qx 4 EI ( x - 4 lx + 6 l ) 04

212 EI, l, w( x) = qx 48 EI ( x3-3 lx + l 3 ) 7 6, : ( 1) ; ( ) ( ) ; (3 ) , EI

213 8 7 8, EI B C , EI , EI E , B, EI, kc

214 1 7 1 A EI , EI GI t A , q = 10 kn/ m, l = 3 m, E = 00 GPa, [ ] = 10 MPa, [ wmax/ l] = 1/ 50, h b, D = 80 mm, d = 40 mm, l = 400 mm, a = 00 mm; E = 00 GPa, F1 = kn, F = 1 kn, C [ w] = l, B [ ] = rad EI 07

215 EI , AB No. 18, BC, d = 0 mm, E = 00 G PaF = 30 kn,, C , F > 3 EI / l 3, k, 08

216 ,,,,, ;,,, 8 1 ( ),, 8 1,,, , 09

217 , 8 3, 3,, ;,,, 3,, x x, x x,,, x y x y 8 3,,, 6, 1,, 3 8 3, 1 > > 3, 3, (8 4 ),, ;,, 8 1, t D ( t < D 0 ), p, ( 8 5( a) ) (1 ), 8 F, ( b), F = p D 4 A = Dt, 10

218 8 5 pd = F A = 4 Dt = pd 4 t ( ) l, (8 5 (c) ), FN = tl ( a) l D d pl D d y pl D dsin (8 5 ( d) ) pl D 0 sind= pld, ld p, Fy = 0, tl - pl D = 0 = (a) ( b ), pd t,,,,,, ABCD, max = p,, ma x = p pd 4 t = 4 t D, 1 =, =, 3 0 ( b),, 11

219 8 6( a), x, y, x y y x, 6, 4,,, ( ) :,,, n x (8 6( b) ), :,, 8 6 : x n,, 8, y x, 6, ef, ae f, e f d A, ea, af d Acos, d Asin, 8 6 (c) Fn = 0, Ft = 0, d A + ( x y d Acos ) sin- ( x d Acos )cos+ ( y x d Asin ) cos- ( y d Asin ) sin= 0 d A - ( x y d Acos )cos- ( x d Acos ) sin+ ( x d Asin )cos+ ( y x d Asin ) sin= 0, x y yx, x y y x, 1 = x + y + x - y cos- x y sin (8 1)

220 x - y sin+ x y cos (8 ) (8 1 ) ( 8 ) (8 1) ( 8 ),,,,,,, (8 1) ( 8 ),,,,,,, (8 1 ) ( 8 ),,, (8 1) ( 8 ),( ), ( 8 1), d d = - [ x - y sin+ x y cos ],, = 0, x - y sin 0 + x y cos 0 = 0 (8 3) t an 0 = - x y x - y (8 4) 0, ,,, ( 8 3 ) ( 8 ),,, (8 (8 (8 sin 0 = cos 0 = 1 ), max min = x + y x y ( x - y ) + x y x - y ( x - y ) + x y ( x - y 4 ) ) + x y (8 5) :, x, x y, 4 ) 0, , max, (8 ), d d = ( x - y )cos- x y sin 13

221 d d 0,, 1, tan 1 = x - y x y (8 6) : 1, sin 1, cos 1 (8 ), max min (8 4 ) ( 8 6) 1 = = x - y tan 0 = -, 45 (8 1 )(8 ) - x 1 tan 1 + y = x - y cos- x y sin - 0 = x - y sin+ x y cos + x y (8 7), ( - x + y ) + = x - y + x y (8 8),,,, x + y, 0, x - y + x y, 8 7 ( b), ( Moh r, ), ( a),

222 1 ), OA = x, AD = x y, D D x ( ) OB = y, BD= y x, DDy (3 ) D, DC C, CD,.,, x, n(8 7 (a) ), D E, E n E, 8 7( b) OF = OC + CEcos ( 0 + ) = OC + CEcos 0 cos- CE sin 0 sin= x + y + x - y cos- x y sin=, E E F = E (8 1 )(8 ), 8 7 ( b), A1, B1,,, CA 1, CB1, ma x m in max = OA1 = OC + CA1 mi n = OB1 = OC - CB1 = x + y x - y + x y ( 8 5 ) ( 8 7 )G1 G,, max min = x - y max mi n = max - min + x y, A1 G1 /, / 4, : (1 ), ; ( ), 8 8 8( a),,, = T W P 15

223 8 8, 8 8 (a), xy 8 8 ( b), (8 5 ) max m in x = y = 0, x y = = x + y x - y, 1 =, = 0, 3 = - (8 4 ) tan 0 = - x y - x - y 0 = = x y = 8 8( d), D 90A1 ;, x 45 1 ( 8 8( b ) ), max 45, ( (c) ) (a), mn M Q, (8 8 9( b) ) C 8(c) C, 8 (8 5 ) 9 (c), x = 50 MPa, y = 0, x y = 40 MPa max m in = x + y x - y + x y = = 7.17 M Pa -.17 M Pa, 16

224 8 9 1 = 7.17 M Pa, = 0, 3 = -.17 M Pa (8 4 ), tan 0 = - x y = - 40 x - y 50 = = = - 961, 8 9 (c) ( 8 9( d) ),, x, 1, 8 9 (c) mn,,,, 45,, 8 9( b),,, ( 8 1 )( 8 ) (8 5) (8 6), 8, 9( a) ( A1 ),

225 A A,,,, 8 10 ( b ),,, ; 45 ;,,, , 3 11 (a), , 3, 8 11 ( b) 3, 3,, 3, 1, 1, 8 11( c), A1, C1,, 1, 3 (8 11( c) ), 1, 3 3,, D,,, 3,,,, 18 max = 1, m in = 3

226 max (8 9) 8 1 ( 8 9), ( 8 1 (a) ) (8 1 = 4 M Pa, = 0, 3 = - M Pa max = 1-3 = 4 - ( - ) 1( b ) ), = 3 M Pa 1 = 4 M Pa, = MPa, 3 = 0 max = 1-3 = 4-0 (8 = M Pa 1( a), ( b) ), :,,,(8 9) 8 4,, = E=, : E = - = - E,,, = G = G, E, G,, G = E (1 + ) 19

227 8 13,, 9,, 6,,, ;, : x, x, y, z x= x E, y= - x E, z= - x E y, x, y, z x= - y E, y= y E, z= - y E, z, x, y, z x= - z E, y= - z E, z= z E x, y, z, 8 13 x = 1 E [ x - ( y + z ) ] y = 1 E [ y - ( z + x ) ] ( 8 10) z = 1 E [ z - ( x + y ) ] x y x z y z = x y G = x z G = yz G ( 8 11) (8 10) (8 11), x = 1 E ( x - y ) y = 1 E ( y - x ) ( 8 1) z = - E ( x + y ) x y = x y G 6, 8 ( 8 13) 14,, 1,, 3,,

228 = 1 E [ 1 - ( + 3 ) ] = 1 E [ - ( ) ] ( 8 14) 3 = 1 E [ 3 - ( 1 + ) ] K, 45, 4 5= , F E = 10 GPa,= FA = 3 F, K FQ = 3 F, 6 3, = 3 FQ A = F K 8 bh (8 ), 15( b) 45= - = 3, 13 5= = 1, = 0 (8 45= 1), 1 E ( ) = - E ( 1 + ) = - F Ebh ( 1 + ) F = - Ebh = = kn,,, ,, v= 1 1

229 8 14 d x, d y d z 1, 3, 3 1 d x, d y, z d z,, dw = d v= 1 d yd z 1 d x + d zd x d y + 3 d yd x 3 d z, v= ( 8 15) (8 14), v= 1 E ( ) ( 8 16) 8 14, dv = d xd yd z dv1 = ( d x + 1 d x) ( d y + d y) ( d z + 3 d z) dv1 = (1 + 1 ) (1 + ) (1 + 3 ) d xd yd z, dv1 = ( ) d xd yd z = ( ) dv = dv1 - dv dv = ( 8 17), (8 14) = K = = 1 - ( ) ( 8 18) E 3 (1 - ) = E 3 3 (1 - ) av = av E K E 3 (1 - ), av = ( 8 19), K, E ; av 1, 3,, 3,,, v, v= vv + vd ( 8 0)

230 vv ; vd av ( ), vv vd, (8 6 ), i - av ( i = 1,, 3), 1, 3 (8 6( b ) ),, ( 8 16 ) vv = 3( 1 - ) av = 1 - E 6 E ( ) ( 8 1) ( 8 16 (c) ), av = 1 3 ( av ) = 0,,, ( 8 16 ) vd = v- vv = E [ ( 1 - ) + ( - 3 ) + ( 3-1 ) ] ( 8 ) 8 6,,,, u n = [ ], u,,, u s ;,, u b ; n,,, 3,,,,,,, :, 3

231 ,,,,,,,,,, :,, : 1. ( ),,, 1, b, b [ ], 1 = b ( 8 3) 1 [ ] ( 8 4), 1 ; [ ] :, ;,. ( ), 1 1 u,,, 1 = 1 u = b E ( 8 5) 1 = 1 E [ 1 - ( + 3 ) ] ( 8 6) u - ( + 3 ) = b ( 8 7) b [ ], 1 - ( + 3 ) [ ] ( 8 8) :,,, 3. ( ), s,, 4

232 max max s ( 8 9) = 1-3 s = s (8 9) ( 8 30 )(8 31), (8 1-3 = s 1-3 = s 3) ( T resca) ( 8 30) ( 8 31) ( 8 3) 1-3 [ ] ( 8 33),, 45 max, vd 4. ( ), vd s,,, s, ( 8 (8 35) (8 ) ( 8 34 ), vd s vd = vd s ( 8 34) = ) (1 + ) 3 E s ( 8 35) 1 [ ( 1 - ) + ( - 3 ) + ( 3-1 ) ] = s ( 8 36) (8 36) ( Mises), 1 [ ( 1 - ) + ( - 3 ) + ( 3-1 ) ] [ ] ( 8 37),,,, ( ),, ( Mohr),,,,,, 1u, 3u,, 5

233 8, 17, 1, 3,,,, [ + ] [ - ] (8 18 ), 1, 3,, (8 O1 O N P = O3 O1 O3 O O1 N = O1 L - O3 T = [ + ] O P = O M - O3 T = [ - ] O3 O1 = O3 O - O1 O = O3 O = O3 O - OO = ),, [ + ] [ - ] ( 8 38) [ + ] [ - ] 3 = [ + ] ( 8 39) 1, 3, 1 - [ + ] [ - ] 3 [ + ] ( 8 40), [ + ] = [ - ], 1-3 [ ],, 6

234 , r [ ] ( 8 41), r, 3 r 1 = 1 r = 1 - ( + 3 ) r 3 = 1-3 r 4 = 1 ( 1 - ) + ( - 3 ) + ( 3-1 ) ] r M = 1 - [ + ] [ - ] 3,, ;,,,, ; 8 6, 8 19, [ + ] = 35 MPa, = 0.5,,,,, 8 1 = 4 M Pa, = 0, 3 = - 36 MPa r 1 = 1 = 4 MPa < [ + ] = 35 M Pa 8 19 r = 1 - ( + 3 ) = (0-36) = 33 MPa < [ + ] ( 8 4) 7, [ ] [ ] 8,, 1 =, = 0, 3 = -,, 1-3 = - ( - ) = [ ] [ ] ( a) [ ] ( b) 7

235 a) ( b), [ ] [ ] = 0.5 [ ], [ ] = = [ 3 ] , (1 ), ( ), : 1) = x + y + x - y cos- x y sin = x ) 1 3 ma x m in - y sin+ x y cos = x + y x - y t an 0 = - x y x - y + x y (3 ),, (4 ),, max = 1-3 (5 ), x = 1 E [ x - ( y + z ) ] y = 1 E y - ( z + x ) z = 1 E z - ( x + y ) (6 ), ; 8

236 A, B, C, D, E, F, m, d l, A, B , MPa : 8 3 (1 ), ; ( ) ; (3 ) , ( M Pa) 8 4 9

237 5 8 5,, : 8 5 : (1 ) ; ( ) ; (3 ) , D = 1 m, t = 10 mm, p = 3 M Pa (1 ) 1, max ; ( ) ab , M = 10 knm, F = 10 kn, 1,,3,4, , AC,, x x y

238 9 8 9, AC 14 M Pa, x x y F = 0 kn, Me = 600 Nm, d = 5 cm,= mm : (1 ) A ; ( ) A ( ) (MPa) ,, A x = , y = Ax - x y - y E = 00 GPa, = 0.3, A? ,, 10 mm, 10 mm 10 mm 10 mm F = 6 kn, E = 70 GPa,= , d = cm, 30 30= E = 00 GPa,= 0.3, F , d = cm, 45 45= E = 00 GPa,= 0.3, Me 31

239 , : (1 ) x = 45 M Pa, y = 135 MPa, z = 0, x y = 0, [ + ] = 160 MPa ( ), x = 0 MPa, y = - 5 MPa, z = 30 M Pa, x y = 0, [ ] = 30 M Pa , 5b F = 00 kn, q = 10 kn/ m, L = m, a = 0. m, [ ] = 160 MPa d = 10 mm, Me = 1 Fd, 10 [ F], [ ] = 160 M Pa;, [ ] = 30 MPa , p = 3.4 M Pa, 600 kn, (1 ) ; ( ) s = 00 M Pa, n =, : Iy (1 ) ( > ) ; 3

240 ) , 8 1, 8 Q35, F Me, Me = 1/ 10 Fd k 8 30= d = 10 mm, E = 10 G Pa,= 0.3 F Me [ ] = 160 MPa, , D = 0 cm, p = 15 M Pa, [ ] = 160 MPat , d = 0 cm, t = cm, p = 4 MPa, F = 40 kn, [ + ] = 35 M Pa, [ - ] = 10 MPa 33

241

242 , 9 1 ( ), 9 1,,,, 9,, 9 1 9,,,,,,,,,,, 35

243 ,,,,, (9 3), ( 9, z Ox y z 9 F, 4 ),, F Fy = Fsin, Fz = Fcos 4 9 4, Fy x y ; Fz x z, F, Fy Fz wy = Fy l3 3 EI z = Fsinl3 3 EIz w z = Fz l3 3 EI y = Fcosl3 3 EI y, ( 9 5( a) ), w z, w = w y + w z (9 1) tan= wy w z = Iy I z tan (9 ), Iy Iz, F,,

244 9 5,, Iy, = Iz, =, F mn(9 4 ), Fy F z, M = F( l - x) Mz My = Fy ( l - x) = Fsin ( l - x) = Msin = Fz ( l - x) = Fcos ( l - x) = Mcos mn ( y, z) Mz M y, C = Mz y I z = My z I y = Msin y I z = Mcos z I y = + = M( sin y + cos z ) (9 3) I z I y,,, (9 3 ), y, z = 0, ( y0, z0 ),, (9 = M( sin y0 I z sin y0 I z + cos z0 ) = 0 I y + cos z0 = 0 (9 4) I y 4), y ( 9 6) tan= z0 y0 = - Iy I z tan (9 5)

245 , 9 4,, D1 D (9 6 ) D1, D max = M sin I z y max + cos zma x (9 6) I y 9 3 ( ),, (), ( ) EI,, ( ), 9 7 (a), ( ), q1, x q ( x) FN ( x), M( x)fn ( x) M( x), N = M = = N + M = FN ( x) A M( x) y I z FN ( x) A + M( x) y I z (9 7) ( d), DD, C C ( ) 38

246 max [ + ] max - [ - ] (9 8) , AC 16, l = m,= 30 F = 0 kn AC D, [ ] = 100 M Pa, AC AC 9 BC FC, M A FC sin = 0 FC = 0 kn 8 ( b) = 0, FC AC FC x AC FC y, AC FC x FC y = FC cos30= 17.3 kn = FC sin30= 10 kn AC 9 8( c), ( d), D,,, 16, W = 141 cm 3, A = cm, D, - max = FN A - + Mmax W = = = M Pa < [ ] AC ,,, (), 9 9, F, F K z, e F, F y Me = Fe,, FN = - F My = Fe P( y, z) 39

247 FN A = - F A,,, = + = - My z = I y F A Fez I y = Fez I y (9 9) , F y z,, ey, ez F, F y, z Me y, Me z,, FN = - F My = Me y = Fey Mz = Me z = Fez, P( y, z) = + + = - FN A - My z I y - Mz y I z = - F A - Fez z I y - Fey y I z ( 9 10),,, (9 ( z0, y0 ), 40 10), = 0,

248 F A Fez z0 I y + Fey y 0 I z = 0, ( 9 ay, az I y = Ai y, Iz = Ai z,, iy, iz,, 1 + ez z0 i y 11 ) + ey y 0 i z y, z, ay = - az = - (9 11) (9 1) : (1 ) ; i z ey i y ez = 0 ( 9 11) ( 9 1) ( ) ay ey, az ez,, ; (3 ),,,,,,,,, F 9 11 (a), 9 11 AB, ay = - h, az = ; i y = b 1, i z = h 1 ( 9 1), F a ey 1 = h 6, ez = 0b, c, d 1 A,,, A, ya z A (9 11), 41

249 ez i y z A - i y y A i ey z z A, iy, iz, ey, ez A 3,,, ( A ),, a, b, c, d 4, (9 11( b ) ) F, y, e = 60 mm, 9 1 F, mn C1 C max + = FN A + Mz W z C3 C4 FN = - 80 kn ( ) Mz = = 4.8 knm, = = 3. M Pa , ma - x = FN A - Mz W z = = 11. M Pa / = ( a), F1 F, A, B, C, D FN = - 5 kn ( ) Mz = = 3 knm My = = 0.65 knm FN, Mz, My A, B, C, D = FN A = = MPa 4 = Mz W z = / = 8 M Pa

250 9 13 (a) ; ( b ) M z ; (c) M y = My W y = =.5 M Pa 1/ A = = 8.83 M Pa, B = = 3.83 M Pa C = = MPa, D = = MPa,,, ( ) (a) AB, FB, AB 9 13 ( b) F, Me = Fa 9 13( c), ( d), A, M = Fl, T = Me = Fa A, 9 14( e), ( f),, C1 C, C1 9 14( g ), C1 = = M W T Wp 43 ( 9 13)

251 9 14, W = d3 3, W p = d3 16, ( 8 5), C1 C 1 3 = 0 = ( ) +,, (9 14), 1-3 [ ] ( 9 14) + 4 [ ] ( 9 17) ( 9 13 ), Wp = W,, 1 W M + T [ ] ( 9 16) (9 1 [ ( 1 - ) + ( - 3 ) + ( 3-1 ) ] [ ] 14), (9 + 3 [ ] ( 9 15) 13),, W 44 1 W M T [ ] ( 9 18)

252 My M z 9 15,,, M M = M ymax + M zmax T,, 9 15 (c) 9 15, 9 15 r3 = + 4 = 1 W M + T = 1 W M ymax + M z max + T [ ] ( 9 19) r4 = + 3 = 1 W M T = 1 W M ymax + M z max T [ ] ( 9 0) , C dc = 500 mm, D dd = 300 mm [ ] = 100 Mpa, AB, 9 16( b), (9 16( c) ), My M z (9 16( d), ( e) ),, (9 16( f) ), M = M y + M z C MC = = 1.01 knm B MB = = knm BCD, B ( ) (9 0) r4 = 1 W M B T B = 1 W = 1 38 W [ ] W = d3 3, 3 d = 5. 0 mm 45

253 ,,, (9 16) (9 18) ;, ( 9 19) (9 0 ),, (1 ) : 1) ), ( ), : 1), ),, 3), 46

254 ),, (3 ) ( ),, ( ), r 4 = max [ ] (4 ),, ( ) 1 r3 = 1-3 = + 4 = 1 W M + T [ ] ( 1 - ) + ( - 1 ) + ( 3-1 ) = + 3 = 1 W M T [ ], , F = 7 kn, C 1,,3,4? [ ] = 160 MN/ m,? A 9 ( : mm) 47

255 3 9 3 () F = 40 kn, No.18, Q35, [ ] = 10 M Pa , a, F, a/ mm ;? H T [ + ] = 30 M Pa, [ - ] = 80 M Pa 9 5 ( : cm) l = 4 m, 0. m0.1 m,, q = kn/ m, , 4 m, F = 137 kn, = 45.7, 3 kn/ m 3, 1 m, AB A B [ - ] 3.5 MPa, [ + ] 0.14 M Pa, , d = 50 mm A, , D = 60 mm, F = kn/ m, [ ] = 60 M Pa 48

256 , d = 30 mm, A3, [ ] = 80 M Pa, P N = 3 kw, n = r/ min, P1 = 101 N D = 50 mm, P = 75 N Fy : Fz = 3: 1, d = 50 mm,, [ ] = 60 MPa (1 ), ; ( ) 49

257 11 ( : mm) 9 1 ( : mm) , 60 cm, n = 100 r/ min N = 7.36 kw C, D F = 1.5 kn, F1 > F [ ] = 80 M Pa, , A 3 Fa = 650 N, Ft = 650 N, Fr = N, D = 50 mm, l = 100 mm [ ] = 90 M Pa , h,,,.5, (1 ) ; 50

258 ) , 9 16, a = 30 mm F = 1. kn[ ] = 165 MPa ( ) , F, (1 ) F, b, h, l, a ( ) a (1 ) = 5, a, b, c ( ) b, a, c , : e 1, : 51

259 19 ( : mm) 9 0 e = 1 - h d, F1, F M, 9 1, r

260 ,,,,, 10 1,,,,,,,,,, 10,,,,,,,,, 10 1, W =Fd ( 10 1) 53

261 Wc d F ( 10 ) F ,, 10 F,,, W = Wc = 1 F ( 10 3) 10 3 (a), ( b ), v= d ( 10 4), 10 V=vd V V = V ( Vc vc d ) dv ( 10 5) = d ( 10 6) vc = V dv = V ( 4, d ) dv ( 10 7) v= vc ( 10 8) V= Vc ( 10 9) 54

262 ,,, W = V (10 10) Wc = Vc (10 11) 10 3, : 1. FN FN, V= 1 FNl = F N l EA, F V= l N ( x) d x EA (10 1a) ( 10 1b) v= 1 (10 13). T, V= 1 T= T l GIP T, V= l T ( x) d x GIP (10 14a) ( 10 14b) 55

263 3.,, v V= 1 M= M l EI V= l 1 (10 15) M ( x) d x EI (10 16a) ( 10 16b) 1. (1 ),,, 10 5 (a) F1 F, EA, l, V= ( F1 + F ) l EA = F 1 l EA F1 F l + E A + F l EA 10 5( b ), (c) 10 5 (a), F1 F, V 1 = F 1 l EA V = F l EA VV 1 + V ( ) 10 5 (a), F1, l1, F1 W1 = 1 F1l1 = F 1 l EA 10 5 F1, F, l, F1 F, 56 W = W1 W 1 = F1l = F1 F l E A W = 1 F l = F l EA + W 1 + W = F 1 l EA F1 F l + E A + F l EA

264 F, F1, W= W = F 1 l EA F1 F l + E A + F l EA,,,. 10 6, F1, F,, Fn, 1,,, n,,,,,,,,, n V= Fi d i = 1 (10 17) n 1 V= i = 1 F i i (10 18) ,, 10 7, ( ) FN ( x)t( x) M( x) ( ), d(l), d d,, dv= dw = 1 FN ( x) d (l) + 1 T ( x) d ( ) + 1 M( x) d ( ) = It F N ( x) d x EA + T ( x) d x GIP V= F N ( x) d x EA + M ( x) d x EI + T ( x) d x GIP + M ( x) d x EI,, y z M y Mz, IP, 57

265 V F N ( x) d x EA + T ( x) d x GIt + M y ( x) d x EI y + M z ( x) d x EI z EA, A (1 ) A, B ( ) 4 V= i = 1 (3 ) FN1 = F, FN = F, FN3 = 0, FN4 = - F F N i d x EA = F l EA + F l EA + ( - F) l EA = F l(1 + ) EA W = 1 F A y = V A y = V F = Fl( 1 + ) EA A A y, A y F ,, EI ( ), (10 16 b), V= 0 M ( ) Rd EI M( ) = FR (1 - cos ) = EI 1 F 0 R (1 - cos ) Rd= 3F R 3 EI W = 1 F = 3FR 3 EI, 58

266 , F1, F,, Fn, 1,,, n, n V= Fi i = 1 d i, i Fi V= V( 1,,, n ) i d i, d i i dv= V, V i i Fi i,, dw = Fi d i Fi = V i (Castigliano), (10 19) 10 10, Vc Fi, i Fi V c n = i d Fi i = 1 V c = Vc ( F1, F,, Fn ) d Fi, dvc = Vc d Fi F i i = V c Fi (10 0 ) (Crotti Engesser), 59 (10 0)

267 Fk k V F k (10 1), k,, k = F F k N ( x) d x F N ( x) F N ( x) l EA = d x l EA F k (10 ) k = F F k N i ( x) li i = 1 Ei A i, n k = T F k ( x) d x l EIP, k = M F k ( x) d x l EI, k = FN ( x) l EA F N ( x) F k d x T ( x) + l EIP n = i = 1 FN i ( x) li E i Ai T ( x) = l EIP FN i ( x) F k T ( x) F k (10 3) d x (10 4) M ( x) M ( x) = l d x (10 5) EI F k T ( x) F k k, Fk,,, Fk, k d x M ( x) M ( x) + d x (10 6) l EI F k , AB AC 0 mm 4 mm, E = 00 G Pa, F = 5 kna : ( 1) A A B AC AB : FN1 = AC : FN = F F ( ) A A ( 10 3) A = AB AC A = F l E d FN1 l1 EA F 3 l E d 4 F N1 F + FN l EA A, A F 60 F N F = = 0.49 mm

268 Me ( a) ABC, EI,, A ( ) 10 1 (1 ) A 10 1 ( b), Me, AB BC (10 5 ) A A = EI 1 a 0 M( x1 ) 1 EI a [ M ( x1 ) Me M( x1 ) = - Me M( x ) = - Me d x1 ( - 0 Me ) ( - 1 ) d x1 + a 0 + a M( x ) 0 M ( x ) Me d x = Me a ( - Me ) ( - 1 ) d x ] = EI ( ) A A, A A F, F Me A, F = 0, Me A 10 1( b ), F Me AB BC M( x1 ) = - Me - Fx1 M( x ) = - Me - Fa M ( x1 ) F M ( x ) F = - x1 = - a (10 5 ), F = 0, Me A A = 1 EI a [ ( - M e ) ( - x1 ) d x1 0 + a 0 ( - M e ) ( - a) d x ] = 3 Me a EI , A B, F A/ B EI GIP 61

269 (1 ) : F, m - n (10 A/ B = M 0 E I 0 M = FR sin T = FR( 1 - cos ) T F M F = Rsin = R(1 - cos ) 6 ) A, B M F Rd+ T 0 E IP T F Rd= FRsin R sinrd+ E I FR (1 - cos ) R( 1 - cos ) Rd= FR FR3 0 EIP EI EIP ( a), Me 10 h 14( b ), = c 1/ b ( 1),, y = y y = c = c y x M = A yd A = h/ c 0 y3/ bd y = cbh5/ 5 ( a) ( b) ( b ) M = Me 6

270 = 5 Me cbh 5/ (c) (c) ( a) ( ) (10 6), ( d) (e) ( f), Vc vc = 5 Me y bh 5/ ( d) = 0 d= d= 3 ( e) 0 c 3 c vc = 50 M3 e y 3/ 3c b 3 h 15/ ( f) vc =dv = V 0 l h/ 0 Vc = 50 M3 e l 3c b h 5 (3 ) (10 0 ), vc bd yd x = Vc Me = 50 M e l c b h 5,,,,,,, (10 5 ),,, ( 10 ) (10 6 ), ;,,, ( 10 0 ) 10 5 (), 10 15,,, ( ),,,,,, ;,,,,, We ;, Wi, (),, 63

271 We = Wi (10 7) 10 15, F1, F, F3,, Fn,, F1, F, F3,, Fn 1 *, *, 3 *,, n *,, We = F1 1 * + F * + F3 * Fn * n = n i = 1 Fi i * (10 8),, (a),,, d(l) * 16 ( b ), (c), ( d ) ) dwi d * d * (10 = FN ( x) d * + T ( x) d * + M( x) d * (10 9) Wi = l [ FN ( x) d + T( x) d + M( x) d ] (10 30) (10 8 ) ( 10 30) ( 10 7) n Fi * i i = 1 = l [ FN ( x) d * + T ( x) d * + M( x) d * ] (10 31),,,,

272 0 17 (a),, K mm, K, mm 1,, FN ( x), T ( x), M( x) ( (a) ), d d d 10 17,,, () We = 1 () Wi = l [ FN ( x) d+ T( x) d+ M( x) d ] = l [ FN ( x) d+ T ( x) d+ M( x) d ] (10 3),, 1 ;, 1,,, (10,, (10 d= 3 ) = FN ( x) d x E A FN ( x) FN ( x) l EA, d= T ( x) d x, d= GIt M( x) d x EI T ( x) T ( x) M ( x) M( x) d x + d x l GI t + d x (10 33) l EI 33 ), ( 10 33) n FN i ( x) FN i ( x) li = i = 1 Ei A i 65 (10 34)

273 , ( 10 33) ( 10 33) M ( x) M( x) = l d x (10 35) EI T ( x) T( x) = l d x (10 36) GI t,, ; (10 33 ) ( 10 36), , A, B F, : = C 1, C B B ( 1) B BD 1 1 l1 1 = Fcos A sin 1 = 1 = C F cos C A sin l1 = 1 l1 = F lcos C A sin, BE, l = = = C l = 1 l = F A sin C C F A sin F l A sin cos ( ) B,, BD, BE FN1, B B = i = 1 FN il i = cos sin, FN = 1 sin = FN1 l1 + FN l = F l C A, E, = E, 66 1 = Fcos A sin 1 = E = Fcos E A sin l1 = l 1 = Flcos E Asin = F A sin 1 + cos 4 sin 3 cos

274 l =, B n = i = 1 FN i FN il i ( EA ) i = E = F E A sin l cos = = Fl E A Fl EA sin cos 1 sin cos + cos sin = Fl EA 1 + cos 3 sin cos ( a), q C EI C, C ( 10 M( x) M( x),, 10 : AB : M( x1 ) = - BC : x1 M( x1 ) = qa x1 - q x 1 M( x ) = - x 19(c) ) 19 ( b), (c), (10 C = EI 1 a ( - 0 M( x ) = qa 35 ), C x1 ) ( qa x1 - q x 1 ) d x1 + EI 1 a 0 ( - x ) qa d x = - qa 4 6 EI 67

275 C, (a), B F, Me = Fa 10 0,, A A B B 10 0 ( 1) A A A, 10, AB : M( x1 ) = - x1, M( x1 ) = - Fa 0( b ), BC : M( x ) = - a, M( x ) = - Fa - Fx, A = a 0 M( x1 ) M( x1 ) EI1 d x1 + a 0 1 EI1 a 1 ( - x1 ) ( - Fa) d x1 + 0 Fa 3 EI Fa3 3 EI M( x ) M( x ) d x = EI EI a 0 ( - a) ( - Fa - Fx ) d x = ( ) B B B, B, 10, AB : M( x1 ) = 0, M( x1 ) = - Fa BC : M( x ) = - 1, M( x ) = - Fa - Fx B = 1 EI a 0 3 Fa ( - 1) ( - Fa - Fx ) d x = EI 0( c) (a), R, A, B F B B H EI B, (10 1 ( b) ),,,,,, 68

276 10 1, B B H = 0 M( ) M( ) Rd= EI M( ) = - R(1 - cos ) M( ) = - FRsin EI 1 [ - R( 1 - cos ) ] ( - FRsin ) Rd= FR3 0 EI B H, B (a), F, EI, GIt A A 10 A, (10 ( b ) ), F, AB, BC M( x1 ) = - x1 M( x1 ) = - Fx 1 M( x ) = - x 69

277 T x ) = - a (10 33 ) A A T, T1 = a 0 a 0 M( x1 ) M( x1 ) EI d x1 ( - x1 ) ( - Fx 1 ) EI Fa 3 3 EI + Fl3 3 EI + Fa l GIt d x1 M( x ) = - Fx T ( x ) = - Fa + l 0 + l 0 M( x ) M( x ) EI d x ( - x ) ( - Fx ) EI + l 0 GIt d x + l 0 T( x ) T( x ) d xx = ( - a) ( - Fa) d x = GIt (a) AB, T1 C y > T,, 10 3, (10 3 (c) ), d x d= ( T1 - T ) d x h C, (10 ( a) 3( b) ), M( x) = x ( b) 1 y = l M ( x) d (a) ( b), C y = l/ x 0 ( T1 - T ) h d x = ( T1 - T ) l 8 h 70

278 ,,,(10 3),, 10 7;,, ( 10 33) ( 10 36),,,,, * 10 7 (10 33 ) ( ),, EI( GIP ),, M ( x) M( x) d x (10 37) l, M( x), M( x) x, 10 4 (a), ( b ) M( x) M( x), M( x),, x O O, M( x) (10 37 ) M( x) = xtan M ( x) M( x) d x = tanx M ( x) d x (10 38) l l 10 4, M( x) d x M ( x), xm ( x) d x M, M( x) M xc M( x) M, 71

279 , MC (10 35 ) x M x) d x = xc l l M ( x) M( x) d x = tanxc= MC M( x) M( x) C,,, 10 (10 M ( x) M( x) l d x = M C EI EI (10 39) 39 ),, 5 ( 10 ( a) = l h ; ( b ) = l h l h ; (c) = ; ( d ) n = 3 l h n ),,,,, ; M( x), M( x),,, 7

280 ( a) D EI (M( x) ) 10 6 ( b), D (10 6( c) ), (M( x) ) 10 6( d), M( x) 5, 10 1 = 3 aqa 3 = - a qa 5 = - 1 aqa 6( b ) = qa3 3, = 3 aqa = qa3, 4 = - 1 aqa = - qa3 4 1,, 3, 4 5 M( x) D (10 = M ( x) M( x) l d x = EI = qa3 3 = - qa3 4 MC1 = 5 8 l 4 = 5 l 3, MC = 5 8 l 4 = 5 l 3 MC3 = 1 l 4 = l 8, MC4 = 3 l 4 = l 6 MC5 = 1 3 l 4 = l 1 4 ),, 1 EI ( 1 M1 + M + 3 M3 + 4 M4 + 5 M5 ) = 1 EI ( 1 3 qa3 5 l qa3 5 l 3-1 qa3 l qa3 l qa3 l 1 ) = - qla 3 48 EI ( a), F EI C C F 10 7 ( b) C, C (10 7 (c) ), (M( x) ) 10 7 ( d) C C C = 1 MC 1 EI + MC EI = 1 EI 1 Fa a( - 3 ) + 1 EI 1 C C Fa a( - 1) = 5 Fa 6 EI,,,,,,,, 73

281 , 74

282 , :,,, 10 8,,,, ;,,,, 10 9 (a),,, 10 9( b ) FN FQ M;, 10 8, 10 30, ,, : ( ),, ;, ;, ( a),, B, 4, 3, 1 B, X1, ( b ) ( ) X1, B X 1 1,, 1 75

283 10 31( d ) ), B X 1 F (10 31 (c) ), X1 1 X ( 1 = 1 X + 1 F ( a),, 1 = 1 F + 1 X = 0 ( b) F 1 X X1 = 1 X1 11 (10 31 (e) ), (c) ( b ) ( 10 (X1 1 X = 11 X1 (c) 11 X1 + 1 F = 0 (10 40) 40) 11 1 F ), ( ) 11 = l F = l 1 0 EI xxd x = l 3 3 EI EI ( - qx ) xd x = - ql 4 8 EI X = 3 ql ( a), B, 10 3 (a), 3, 10 3 ( b), X1, X X3 B 1 F B ( ), X1, 11, X1, X X3,, B X 1 B ( )X1, X X3 76

284 B X 1 = 1 1 X1 + 1 X X3 + 1 F, 1 1 = 1 1 X1 + 1 X X3 + 1 F = 0, B X X3 11 X1 + 1 X + 13 X3 + 1 F = 0 1 X1 + X + 3 X3 + F = 0 31 X1 + 3 X + 33 X3 + 3 F = 0 (10 41 ), X1, X X3, (10 41) 10 3, n, 11 X1 + 1 X n X n + 1 F = 0 1 X1 + X + + n X n + F = 0 n1 X1 + n X + + nn X n + nf = 0 (10 4) ( 10 4) ij ( i = 1,,, n; j = 1,,, n), 1 F ( i = 1,,, n),,,, Mi ( i = 1,,, n) Xi i j if = M i M j l d x (10 43) E I = l M M i d x (10 44) E I = 1 ( i = 1,,, n) ; Mj ( j = 1,,, n) Xj = 1 ( j = 1,,, n) ; M ( 10 43) ij = ji (10 45) ( a),, 10 33( a), 4, 3, 1, C, X1, 10 33( b) X1, 10 33(c),, M1 ( x1 ) = - x1 M1 ( x ) = - x 77

285 1 F = EI 1 a 0 ( - x1 ) ( qa M x1 ) = qa x1 M( x ) = qa x - x1 ) d x1 + EI 1 a q x 1 1 = EI 1 a ( - 0 x1 ) ( - x1 ) d x1 + EI 1 a 0, X1 X1 ( - 0 x ) ( qax - q x ) d x = - 3 qa4 8 EI = - 1 F = 9 qa a3 ( - x ) ( - x ) d x = 3 EI X1,, ( d) ( a), EA F FA y, FA x, FB y, 1 AC,, X1,, 10 34( b ),, F F N i, X1 = 1 FN i

286 i F Ni FN i l i FN i FNi l i FNi FNi li F F N i a 0 a - F 1 a - Fa a F 1 a - Fa a a 0 a a 0-6 F - a - Fa a F F F F F F - Fa( 1 + ) 4 a(1 + ) 1 F = 6 i = 1 FN i F N i l i E A = - ( 1 + ) Fa E A 79

287 1 = 6 i = 1 FN i FN i l i E A X1 X1 = - 1 F = F 11, = 4 (1 + ) a E A F F N i F FN i X 1 FN i X F F N i = FN i + FN i X (a),, C F, C EI, EA, I = AR / (1 ) A B FA y = FB y = F, 1,, X1,, ( b) F (10 M( ) = - 35( c) ) FN = 0 F R( 1 - cos ) X1 = 1 ( 10 35( d) ) 80 FN = 1

288 1 F = EI [ - 0 F 11 = M ) = Rsin - FR3 R(1 - cos ) ] RsinRd= 1 1 R E A X1 + EI 0 = - 1 F 11 = EI 0 (1 - cos ) sind= - Rsin RsinRd= R E A + R3 EI FR 4 I A + R = F 1 + FR 3 EI ( ) C,,,,, () M F F F N = FN + X1 FN = = M( ) + X1 M( ) = -, C ( 10 C C = FF N F F N l E A M F = - + EI 0 F F N = 0 1 F 1 + F R( 1 - cos) + F 1 + Rsin R(1 - cos ) 35( c) F = 1 ), M( ) M( ) Rd= EI (1 + ), :, ; ( ) ; ;, ;,,,, (a),, ( b ),,, (c) :,, ( ) ;,, ( ) 81

289 10 36,, 10 37( a), 3, A, 3, FN, FQ M, (10 37 ( b) ),, A FQ, FN M, ( (c) ),, A FN M, FQ (10 38( a) ), (10 38 ( b) ( c) ),

290 (a),, EI , AC BD B D, FN M(10 39( b ) ), FNB = FN D = qa M, M X 1, 10 (10 39 ( d) ) M( x1 ) = 0 M( x ) = qax - 1 qx X1 = 1 ( 10 39( e) ) M( x1 ) = 1 M( x ) = 1 1 F = 1 EI a [ M( 0 x1 ) M( x1 ) d x1 + a 0 1 EI a [ 1( qax qx ) d x ] = qa3 3 EI 39(c) M( x ) M( x ) d x ] = 83

291 11 = 1 EI a ( M( x1 ) M( x1 ) d x1 0 + a 0 1 EI a ( 1 1d x a X1 1 1d x ) = a 0 E I = - 1 F = - qa 11 6, (f), M max = qa 3 M( x ) M( x ) d x ) = (a), C, Me, C EI ( 1) 3, C, Me/,, C,, X1, ( b), ( Me/ ) ( 10 X1 = 1 ( 10 40( d) ), 84 1 F = EI 1 / 0 11 = EI 1 / 0 M() = Me M( ) = 1 Rsin M() M( ) Rd= EI 1 / 0 Me RsinRd= Me R EI M() M( ) Rd= EI 1 / R sin Rd= R3 0 4 EI 40 (c) )

292 X = - 1 F 11 = - Me R ( ) C, (10 M( ) = Me, C C = EI 1 / 0 - Me sin 40 (e) ), M( ) = 1 M( ) M( ) Rd= EI 1 / ( Me 0 - Me sin Me R ) Rd= 4EI ( - 4),,,,,,,, (1 ) :, ; ( ) :,, n V= Fi i = 1 d i n 1 V= i = 1 Fi i (3 ) :, ;,, Fi = V i i = Vc Fi k = V F k (4 ) :, 85

293 n i 1 Fi * i =( FN ( x) d * + T ( x) d * + M( x) d * ) l (5 ) :,, = l [ FN ( x) d+ T ( x) d+ M( x) d ], FN ( x) FN ( x) = l EA T ( x) T ( x) M ( x) M( x) d x + l d x + GIt l d x EI (6 ) :,,,,, , EI , Me A, C G , F A, = c, c

294 , B F B EA , F A EI A A A EI , A, B F A , F B , EAA F A 87

295 , EI B , EI,, , q A A, EI E It , AB E I, 1 EAA F A A , F B EI 88

296 A, Me,, d, E, G B , EI, GIt A B F , h, T1 T,, T1 > T A x y

297 , EI, , AB134 5 EI, EA, I = Aa / 3C, D F, () , F A C C D EI , EI,

298 , ( ),,,,,,,, ; ; ( a), FP FR, A,,,, A 11 1( b),,,, 11 1( c), A,,,,, 11 1 ( b) (c), , ( F < Fc r ),, ( ),, ( 11 ( a) ), ; ( F = Fcr ),, 91

299 ,,, ( 11 ( b) ) ; ( F Fcr ),,,,,,, (11 ( c) ),, ;,,, Fcr,, 11,,,,,,, 1907, 548 m,,,,,,, 11 w 11 3, x, x F w, w, M ; w, M, M w,, 9 M = Fw ( 11 1) d w = - d x d w = - d x M E I ( 11 ) F w ( 11 3) E I

300 k = F E I, (11 d w + k w = 0 (11 4 ) d x 4), w = Asin kx + Bcos kx (11 5 ), A, B k, : x = 0, w = 0; x = l, w = 0 B = 0 (11 6 ) Asin kl = 0 (11 7 ) (11 7) : A = 0, (11 5 ), w 0,, ( ) ; kl = n, n = 1,, 3, Fcr = n EI l 11 3,, n = 1, Fcr Fcr = EI ( 11 8) l (11 8) Fcr, Fcr EI, ( l ),, ( ), (11 k = ( 11 l ( 11 wmax 11 5 ) w = Asin x l 8) I ( 11 9) 9),, x = l/, = A, A 1,, l = 800 mm, d = 0 mm, Q35, E = 00 GPa, Fcr = Ed 4 l 64 = 3 Ed 4 = = N 64 l Q35 s = 35 MPa,, Fs = d s = = N > Fc r, 93

301 Fcr (11 Fwmax 11, d d x = 1 ( x) = 8), 4 OA A M( x) EI, F wmax 11 4 OAC, F wmax : F < Fcr, ( OA ), OA, ; F > Fcr,, AA,, AB A C, ( AB), ( AC),, AB A C A, A,, 11 4, AC, AA,,,, F = Fcr,,,,,,,,,,,,,,,, 11 4 ODEG,, ( ), F < Fmax, ODE,,,, ( ), ( ), EG,, Fmax 94

302 Fc r, ( ) Fcr Fcr,,,,,, ;,,,,, 1., 11 Fcr, Fcr 5 (a), FR, 11 x M( x) = Fcr w + FR ( l - x) d w = - d x d w d x M E I = 1 [ - Fc r w - FR ( l - x) ] EI + Fcr EI w = - FR EI ( l - x) 5 ( b), k = Fcr EI (11 (11 10) d w + k w = - k FR ( l - x) (11 11) d x Fcr 11 ), 11 5 w = Asin kx + Bcos kx - FR Fcr ( l - x) (11 1) w= Akcos kx - Bksin kx + FR 11 5 (a), x = 0, w = 0, w= 0 x = l, w = 0 Fcr (11 13) B - FR Fc r l = 0 (11 14) Ak + FR Fcr = 0 (11 15) Asin kl + Bcos kl = 0 (11 16) (11 14 ) ( 11 15) 95

303 B FR Fcr l, A = - FR kfcr (11 17) (11 17 ) ( 11 16) FR Fc r ( 1 sin kl - lcos kl) = 0 k, FR (11 (11, 18 ),, 10 ) tan kl = kl (11 18) kl = 4.49 Fcr = k EI = 4.49 EI l EI (11 19) ( 0.7 l) 11 6., l, 11 6( a), F = Fcr, l,,, Fcr = EI (11 0) ( l) l, Fc r 11 6( b), l/ 4 CD,, l/ CD l/, Fc r = EI (11 1) ( 0.5 l) ( 11 8 )(11 19) ( 11 0) (11 1 ), 96 Fc r = EI (11 ) ( l)

304 l,, ;, Fcr EI EI EI EI ( l) ( l) (0.7 l) (0.5 l) ,,, ;,,,,,,, 0.5 1, 1, Fcr, 11 7 x w, EI,, x M( x) = - Fcr (- w) EI d w = - F(- w) d x d w + k w = k ( a) d x, k = Fcr EI 97

305 w = Asin kx + Bcos kx + ( b) w= Akcos kx - Bksin kx (c) x = 0, w = 0, w= 0 ( d) x = l, ( d) ( b), (c), ( g) kl = n w = A = 0 ( e) B = - ( f) cos kl = 0 ( g) ( n = 1, 3, 5, ) ( h) kl = Fcr, EI l =, Fcr 11 7 = EI = EI (i) 4 l ( l) 11 3,, cr, cr = Fcr A = EI ( l) A, i, [ ] ( 11 i = I A = l i c r 3), (11 3) (11 4) (11 5) = E (11 6),,, ( l) ( ) ( i) cr, I, A ( ),,,,

306 ,, p,, cr = E p E p p, (11 p = E p 7 ), p,, p Q35, E = 10 GPa, p = 00 MPa, (11 7) p = E = = 10 p p,,,, < p,,, 1. c r = a - b (11 8), a, b, MPaa b a, b a/ MPa b/ MPa p s Q35 s = 35 MPa b 37 MPa s = 306 MPa b 471 MPa s = 353 MPa b 510 MPa

307 11 8 ) cr cr, cr,, s, cr s, ( 11 8 ) - s = s (11 9) b,, (1 ) p,,, ( ) s < p, (3 )< s,,, cr, 11 8, , a1 b1 cr = a1 - b1 ( p ) (11 30),, cr = s 1 - p (11 31), cr, 11 9 Q35 16Mn cr = ( ) MPa ( 13) (11 3) c r = ( ) MPa ( 109) (11 33) , E = 00 GPa, p = 65 MPa, : A ; B x z,, x y, l = 3 m,, b = 10 cm, h = 15 cm 300

308 (1 ) ; ( ) b h? (1 ) :, x, x x z y y ( z ),,, =, z = ( l) z I z A = x h l 1 1 = = z ( y ),,, = 0.7, y = ( l) y I y A = 0.7 l 1 b 1, x (11 7 ) = y = 7.7 < z 11 10, Fcr = A E = ( ) b h : p = E = = 86.3 < p z = N = kn 138.6, z = y, z = h l 1 1 = y = 0.7 l 1 b 1 h b = 0.7 =.86,( ),,, 11 4,, 301

309 n Fc r F nst (11 34), F ; Fcr ; nst ; n (11 34 ) F Fcr nst = [ Fst ] (11 35) cr = [ st ] (11 36) nst, [ Fst ] [ st ] nst,, nst,,,,,,,,,, An = FN An [ ] (11 37) ,, l =.4 m, 15 mm 15 mm 1 mm, 3 mm F = 800 kn, Q35, nst = 1.48, [ ] = 160 M Pa

310 (1 ) :,,= 1;,,, ( z ), Iz = Iz1, A = A1 iz = Iz A = I z1 A1, Iz1, iz1 A1 z, = Iz1 A1 = iz1 15 mm 15 mm 1 mm iz1 = 3.83 cm = 38.3 mm A1 = 8.9 cm = mm iz = iz1 = 38.3 mm = l = 6.66 i z Q35, s = 35 M Pa, E = 10 GPa, p = 13, < p, cr = ( ) 10 6 = Pa = 08.3 MPa Fcr = cr A = = N = 1 04 kn ( ) : n = Fcr F = = 1.51 > nst = 1.48 An = = m = mm = F A n = = Pa = MPa < [ ] , AB No.14, CD, d = 0 mm, Q35, A, C, D F = 5 kn, l1 = 1.5 m, l = 0.45 m, E = 10 G Pa, p = 00 MPa, s = 35 M Pa ns = 1.45, nst = 1.8? (1 ) AB :, AB,,, C,, Mma x = ( Fsin30 ) l1 = = Nm = knm 303

311 FN x Fcos30 = = N = 1.65 kn No.14 max = Mmax W z + FN x A Q35 max [ ], W z = 10 cm 3 = mm 3 A = 1.5 cm = mm = = Pa = 163. M Pa [ ] = s = 16 M Pa ns = max - [ ] 100 % = 0.7 % < 5 % [ ] 11 1 ( ) CD : CD, FNC D i =,= 1 Q35, = Fsin30= F = 5 kn = l = i s = a - s = b s < < p, ( 11 CD =, 304 I A = d 4 = 5 mm = = ) c r = = 03. M Pa FN CD A = = Pa = 79.6 M Pa ( )

312 , n cr =.55 > ns t = 1.8, (11 4),,, :, ;, (11 34 ), [ st ], [ st ] = c r = nst c r nst [ ] [ ] = [ ] (11 38) = FN A [ ] (11 39), FN ; A ; [ ] ;,, = c r ns t [ ] = c r n = cr n nst u u nst, u, (11 14), cr < u, n < nst, 1,, (GB ),, l/ 1 000, 96, a, b, c, d, a, b, c, d, a, b, c, d, ( GB ), < 1 TC13, TC11, TB17, TB15 TB11, 91, = (11 40) 65 > 91, = 800 (11 41) TC17, TC15 TB0, 75, = (11 4) 80 > 75, = (11 43), ( MPa)T C11 ; 305

313 TC 3 ; TC15 ; T C17 ; TB15 ; TB17 ; TB a s

314 1 4 b s

315 1 5 c s

316 1 6 d s : s , AB, d = 00 mm,, TC15, [ ] = 11 M Pa q = 50 kn/ m 309

317 (11 = AB = l = i cos30 = d 4 ) AB 1 80 = AB = [ st ] = [ ] = = 7.43 M Pa AB FN = AB = FN A = FN d AB 4 q = 13.3 kn.4 sin = = Pa = 6.79 MPa < [ 0. st ] , Q35, 6 m, b ( ) 30 mm 80 kn, [ ] = 160 M Pa,,, = 1.3, b a (1 ), = l/ i, = 0.5, [ st ] = [ ] = = 80 M Pa A = F = [ st ] = , 14a, A = cm, iz m , iz i z, 11 = l = i = = 141 = = 0.5,, = = 5.5 cm

318 A F = [ st ] = a, A = 1.95 cm, iz 11 = l = i = 14 4 = 0.416, = 0.4, = = ( ) b [ st ] = [ ] = = M Pa F A = = M Pa < [ st ] m = 6.8 cm, z iz, xy, xz, xz, 11 14, b, y iy, iy = iz, iy = iz, b Iy = I y 0 = A( b - z0 ) i y = I y A = i y 0 + ( b - z0 ) 16a, iy 0 = 1.83 cm, z0 = 1.8 cm, iz = 6.8 cmiy = iz, (3 ) a b = = 7.81 cm b = 7.81 = 15.6 cm = 156. mm ( ),,,, ( 11, 1 0,, 0 = 14, 1 = 0 1 = l = a i1 i1 15( b ) ),, i1 i1 = 1.83 cm, = 1.0, 1 a =

319 a.7 m (4 ) 11 15,,, An = A - 4d = = m = F A n = = Pa = M Pa < [ ] ,,,,,,,,, ;,,,,,, 11 5,,, = l, i,,,,,,,,, 31

320 ,,, 4 Imin,,,, ( (a) ) (11 16 ( b) ),,, ( ),,,,, ( (c), ( d) ) a, Iz = Iy,, l1,, ( ),, 11 16,,,,, 11 a, 17,, E E,,, s p,,,,,,,,,,,, 11 18,, 313

321 1 18( a) 11 18( b), AB, (1 ), Fc r ( ),= l i c r = EI ( l) = E p,, p = E p (3 ) : 1) ) (4 ) : 1) c r = a - b c r = a1 - b1 ) n = Fc r F n st (5 ) : 1) ; 314 = F N A [ ]

322 ) ; 3) ; 4) 11 1, Fcr = EI, ( l) ( ) ( A)>.0 ( B) 0.7 < <.0 ( C)< 0.5 ( D) 0.5 < < ,,,,, ( ) ( A) y ; ( B) C ; ( C) z ; (D) y z 11 3,, ( ) ( A) ( B) ( C) D) , ( ) ( A),, ; ( B), ; ( C), ; (D) 11 5, l Fcr , E = 00 GPa (1 ), a = 40 mm, l = 1. m; ( ), h = b = 50 mm, l = 1. m; (3 ) No.0, l =.0 m AB BC, EI, : (1 ) x, ; ( ) B, , EI,, B F F?F, F? 315

323 No.0a t1 = 0,, l = 6 m, Q35, E = 00 GPa, = /, ABC,, ABC, F ( 0 < < ) , l = 400 mm, h = 15 mm, b = 10 mm, E = 10 G Pa, p = 100, s = 60,, a = 577 M Pa, b = 3.74 MPa ,, A = mm E = 80 GPa, p = 53, s = 0, a = 385 M Pa, b =.14 MPa 316

324 , bh,, h/ b x z = 1 z, y = 0.7 ; x y, , AB, d = 80 mm; BC, a = 70 mm, Q35, E = 00 GPa, p = 10, s = 6,, a = 304 M Pa, b = 1.1 MPa 317

325 [ F] A B, C, l = 3 m, nst = AB AC, d = 80 mm, BC = 4 mq35, nst =.0 : (1 ) F, [ F] ; ( ) F CA,, F AB d = 40 mm, l = 800 mm,, Q35 :? (1 ) ; ( ) F = 70 kn, AB nst =.0, (3 ) No.18, [ ] = 160 MPa 11 17, T C15, d = 100 mm, l = 4 m, [ ] = 10 M Pa , 80 mm 80 mm6 mm, b l = 6 m, F = 450 kn Q35, [ ] = 160 MPa, a 318

326 , AC d = 5 mm, Q75, [ ] = 180 MPa, BC d = 50 mm, TC13, [ ] = 8 MPa, , l = 3.5 m, F = 400 kn, d = 0 mm, b [ ] = 180 M Pa AD A, B d1 = 50 mm, Q35, E1, E = 00 GPa, [ ] 1 = 160 M Pa; C d = 100 mm = 10 GPa, p = 55, nst = , AC CD Q35, AC, CD, C, D d = 0 mm, b = 100 mm, h = 180 mm; E = 00 GPa, s = 35 MPa, p = 00 M Pa; n =.0, nst = 3.0, 319

327 1 30

328 , ;, 1 1,,,,,,,,,,,,,, : (1 ) ; ( ), 1,,,,,, 31

329 1 1 1, a P, A, P d P, (), P g a,, FNd, FN d - P - P g a = 0 FNd = P + P g a = P 1 + a g d = FNd A = P A 1 + a g = st 1 + a g = kd st 1 1 st = P A st Kd = 1 + a g, Kd, d = Kd st [ ] 1 1 D,, A, 1 3

330 , qd, D, qd an = D, = 1 A an = AD g g FNd FNd, qd d FNd = qd 0 d = FNd A sin D FNd = AD 4 g d= qd D = D 4 g = v g v = D v d, d A,, A 1 d = v g [ ] 3 d = 100 mm, P = 0.6 kn D = 400 mm, n = r/ min ( 1 3 (a) ) ( Med ) t = 0.01 s, 1 3,,, Med = - I0 ( a), I0, N ms ;, rad/ s 33

331 , = - (a) Med Med n, = t 60 = - n 30 t = I0, n 30 t rad/ s,,, Med (1 Td (4, 1 14) dmax = Td W P = I0n d t = Td = Med = I0n 30 t N/ m = 65. M Pa = ( b) 3 ( b) ), 1 4 l = 1 m 16, A = 108 mm 4( a), a = 10 m/ s,, dmax (c) 1 4, qd = Aa g,, A, qst 16 qst = 01.1 N/ m, qd = qs t a g = = 05 N/ m,, qs t qd,, 34

332 q qs t + qd = = N/ m, FN d (1 4 ( b) ), Fy = 0 FNd - ql = 0 FNd = 1 ql = = N, d d = FNd A = = Pa =.6 M Pa dmax ( 1, Md max 4 (c) ), Md max, Md max = Md C = 6 q = = N m 16 Wz = m 3,, d max d max = Md max W z = = N/ m = MPa,,,, 1 3 (), ( ),,,,,,,,,,,,,, : (1 ) ; ( ) ; (3 ) ( ),, ; (4 ) ; (5 ),, 35

333 5, P h,,,, Fd d, (1 5) (1 5 ), 1 5 P h,,,, d d , V = P( h + d ) ( 1 1),, T = 0 ( 1 ) V d,, Fd d, 1 Fd d,, V d = 1 Fd d ( 1 3),, (1 1) ( 1 )(1 3) (1 4), T + V = V d ( 1 4) P( h + d ) = 1 Fd d ( 1 5) Fd P ( ), st st, d d,, Fd P = d = d st st

334 Fd (1 5),, Fd d P, d = d st st st P( h + d ) = d - s t d 1 P d st - h st = 0 ( 1 6) d = st ( h ) st d,, d = st ( h ) ( 1 7) st Fd = K d = P( h ) ( 1 8) st Kd Kd, : = d = h s t st d = Kd st Fd = Kd P d = Kd st ( 1 9) (1 10) (1 ) Kd P st st, Fd, d d ( ) ( 1 9), h = 0,, Kd =,, (3 ) ( 1 8), Fd P, st k, st, Fd (4 ), st P 1 6, A, E, P v d, Fd, 0, T = 1 P g v, V = 0 37

335 V d = 1 Fd d,, T + V = V d, 1 P g v = 1 F d d, Fd = P, st d st P,, 1 P g v = 1 P d st 1 6 d = st v g st Kd = v g s t = v g st (1 11) Kd,, , l = 1 m, d = 5 mm, h = 40 mm, P = 400 N, E = 500 GPa (1 ) (1 7( a) ), ; ( ) (1 7( b) ), C = 1 MN/ m, 1 7 (1 ), 38 st = Pl E A = Kd = h s t = m

336 Kd s t = P A = = 141 = M Pa d = Kd st = = M Pa ( ), st, st, st, st = s t + st = Pl E A + P C = = Kd = h = = 15.1 st d = Kd st = = 1.3 M Pa , EI, W P, h, B, C dc dmax m 1 8 (1 ) st = Pl3, (1 9) 3 EI Kd = h P l 3 / 3 EI = 1 + ( ) C (1 8( b ), (c) ) stc = MC EI EI h P l 3 = 1 EI ( 1 l l ) ( 3 Pl + Pl ) = 5 Pl3 48 EI 39

337 d C Kd stc = ( EI h P l 3 (3 ) A, d max stmax = Pl W = Kd s tmax = ( EI h P l AB B,, A ( A ), G = 80 G Pa, d = 100 mm, l = 1. m, Ix n = 90 r/ min = 0.6 knms, A, B AB,, ) 5 Pl3 48 EI ) Pl W 1 9 0, T V d T = 1 Ix T = V d, V d = T d l GIP 1 I x = T d l GIP Td = I x GIP l, IP W t dmax = Td W t = d4 3 ( 16 d 3 ) = = I x GIP lw t d 4 = A dmax = GI x A l, 330

338 dmax ( ) = Pa = 951. M Pa, [ ] = MPa dmax,,,,, ((1 9) ( 1 11 ) ), K d, K d P, Kd, d max dmax = Kd st max [ ], st,, st,, (1 ) st (1 5), ( ),, s t = Pl E A ; st = P A d = Kd st = v g st, A, l, d,,, ( 1 10( a) ) (1 10 ( b) ) st = EPv ga l (3 ) ( 1 18 ) (4 ), ( 1 19) ,,, (1 11 ), W A W, k = W A (1 1) 331

339 k []/ ( J/ mm ), k,, 1 11 k, k ( 1 1 (a) ),, U, 4,, V, 1 1( b) 1 1, k 1 13,, k 1 13,,, k,, k,, V, V,,, %, FATT, 33

340 k, 1 13 (1 ), ( ),, ( ),, ( ) Kd = h s t st, Kd d = Kd st [ ] P = 60 kn, 1 s.5 mfnd () 1 1 l A a, P1 = 5 kn, l = 4 m 0a, P = 50 kn 3 s 10 m [ ] = 170 MPa, ( ) P = 10 kn, d = 40 mm, [ ] = 10 MPa 1 5 l, A, P1 P

341 v = 5 m/ s, = 7.6 kn/ m 3, AB CD 10 mm, D P = 10 N = 78 kn/ m 3 AB n = 300 r/ min, AB n = 300 r/ min, AB, h = 56 mm, b = 8 mm, l = m, r = 50 mm = 76 kn/ m 3 AB 334

342 P l A B, A y, : (1 ) ; ( ) A x ; (3 ) d = 100 mm, I0 = 0.5 kgm, 300 r/ min, s, ( ) 1 11 P = 5 kn h = 10 mm, 0 b B, 1 11 E = 10 GPa ( ) ( : mm) 335

343 1 1 P = 40 N, h = 60 mm, E, 1 AC, BD, AB k = 5.3 N/ mm, E = 10 GPa, 40 mm8 mm, 1 13 P 1 13, EI, W, , P v H, Kd = H + v / g st l = 400 mm, d = 1 mm, B, 1 15 AB E = 10 G Pa, 000 Nmm, , P = kn, v = 1 m/ s l = 3 m, d = 00 mm, E = 11 GPa , P = 5 kn, v = 100 cm/ s l = 0 m, Fd A = 4.14 cm, E = 170 G Pa,

344 ? d 5 l, H, Kd = H = st H st d = 300 mm, l = 6 m,, P = kn E1 = 10 GPa, ( ) : (1 ) ; ( ) 0.5 m ; (3 ) 150 mm, 40 mm, E = 8 M Pa, 0.5 m d = 6 mm, D = 10 mm, n = 18, G = 80 GPa 5 mm, 100 mm,? 337

345 ;,, ; 13 1,,, 13 1, A, 1,, 3, 4 A 1,, 3, 4,,,,, 80%,,,, (1 ), b, ( ) (3 ),,, (4 ),,, 13 ( ),,, m,,,,,,, 10-4 m,,,,,,,,,, 338

346 ,,,,,,,, , ( 13 3 ), ( 13 4) (13 5) :, ( ), r r = Smin Smax, Sm, ( 13 1) Sm = Smax + Smi n, Sa, ( 13 ) Sa = Smax - Smin ( 13 3) Smax = Sm + Sa ( 13 4) Smax = Sm - Sa ( 13 5) 339

347 , Smax = - Smin ( 13 5 ) r = - 1, Sm = 0, Sa = Smax (13,, 6), r = 0,, r = 1, Smax = Sm in = Sm, Sa = 0 r 1,,, S,, S ;, S, 13,,, ( s, b ),, (13 10, 13 7 (a) ), d = 7 10 mm, 7( b ) 13 7, ( 13 7 ( b) ),,,, 340

348 N1, 1 max, N1 1 max max, N,, N,, S (13 8),, S N,, r, r - 1 N , : S N ( ), 10 7, ; S N ( ), ( 10 7 ), S N, S N 13 9 r = - 1, r = 0, r > 0 S N, r r = , ; ( ),,,,,,, KK,,, K= K= ( 13 6)

349 , - 1 > - 1, - 1 > - 1, KK1,, KK

350

351 : R, ; b,,,,,,, :, ;,, ; 13 1,,,,, 344

352 = ( - 1 ) d - 1 = ( - 1 ) d - 1, ( 13 7) ( 13 8), - 1, ( - 1 ) d 1, ( - 1 ) d :,, d/ mm > 0 30 > > > > d/ mm > > > > > ,,,, = 1,,,,,,, = ( - 1 ) - 1 = ( - 1 ) - 1 ( 13 9) (13 10), - 1, ( - 1 ) 1, ( - 1 ) 13,

353 3 b/ MPa xb / MPa K 1.5 K :, ;,< 1 ;,,,,,,,,,,,,, 1, ( - 1 ), ( - 1 ) ( - 1 ) = - 1 (13 11) K ( - 1 ) = - 1 (13 1) K,,,,, 346

354 , ( - 1 ) ( - 1 ) (13 11) ( - 1 ) n, [ - 1 ] = ( - 1 ) n (13 13), max (13 max [ - 1 ] = ( - 1 ) n 14 ), ( - 1 ) max n (13 14), ( - 1 )/ max,,, n, n= ( - 1 ) max n n n (13 n 11 ), n=,, n= - 1 n (13 15) K max - 1 n (13 16) K max Smax ( 13 5 ), () Sm Sa,,,, n= n= - 1 nf (13 17) K a + m - 1 nf (13 18) K a + m 347

355 ,, = =,, (13 19) (13 0) b / MPa ( ) ( ) m = 0, m = 0,,, a m, max min,, ns n= n= s ns (13 1) max s max ns,,, max + 3 max s, max max s, s = s/ 3, 1 s max + ns 1 1 s n s max s s, nn, max max 1 n+ 1 1 n n 348 nn n + n n

356 , n = nn n + n n (13 ), n ; n ; n, n (13 15 )(13 16 )(13 17 ) ( 13 18) , b = 900 M Pa, s = 500 MPa, - 1 = 410 M Pa M = 700 Nm n = 1.6,, max = M W = 700 = 57 M Pa 3 ( ) 3, R d = 5 50 = 0.1, D d = , 13 1 = 0.73, 13 = 1 (13 15 ) n= - 1 = K max , b = 600 M Pa, - 1 = 50 MPa, s = 80 MPa Mmax = 500 Nm, Mmin = 100 Nm n =, ns = 1.6, (1 ) W = 3 d3 = 3 43 = 6.5 cm 3 max = 1., K=, = 3.39 > n = Mmax W = = Pa = 79.6 MPa min = Mmin W = 1 5 max = 15.9 M Pa m = 1 ( max a = 1 ( max r = mi n = 1 max 5 = 0. + min ) = 47.8 MPa - m in ) = 31.6 M Pa 349

357 ) K,,, d0 d = MPa, K=.00; 13 1,= 0.88 ; 13,= 1 (3 ) (13 17 ) n= K a a m = (4 ) (13 1 ) n = = ( f), b =, 50 = 3.37 > n s ma x = = 3.5 > ns knm, T 0 1. kn m, b = MPa, - 1 = 450 MPa, - 1 = 50 M Pa n =, (1 ),,, r = - 1, r = 0 max = Mmax W = = 81.5 MPa 3 ( ) 3 max = Tmax W t min = Mmin W = = M Pa ( min = 0 a = m = 4.5 MPa ) 3 = 48.9 MPa ( ) r d = 5 50 = 0.1, D d = K= 1.56, = 0.73,= 0.78, = 1., ( b) 10 (e) K= mm,= 1, = 0.1 (3 ) nn, ( 13 15), n=, ( n= = K max = K a + m 18), = =

358 4 ) n (13 n = nn n + n = =.36 > n ), 13 5,,,, 1., (),,,,, ( (a) ) (13 16 ( b ) ) ,, 3.,,,,,, 13 6,,,,,,,,,, s, 351

359 ,,,,,,,,, : ( (a) ) ; (13 17 ( b) ) ; (13 17(c) ),,, , a,, 13 18, ( a) A x a cos sin sin y a 3 cos 1 + sin sin (13 3) x y a 3 cos sin cos 35

360 A,,, a, a,,, K, K = a (13 4) M Pam 1, KI, KIC,, KIC KIC KIC, KI KIC,, KI = KIC (13 5),,,, (1 ) ( ), r = m in, r = - 1, max r = 0, r m a (3 ), r, - 1 r r, - 1 < 0 < b (4 ) : 1) ),, 3),, ( - 1 ) = - 1, K, 1;, 1;, 1 1 (5 ) K 353

361 ,, M = 750 Nm, b = 600 M Pa, - 1 = 50 M Pa, n =, ,, b = 500 M Pa, - 1 = 0 MPa, M = 50 Nm, n = 3, , P = 110 kn,, b = 500 M Pa, - 1 = 40 M Pa n = ,, b = 1 00 M Pa, b= 700 MPa, nf =, [ - 1 ], , F, Fmax = 100 kn Fm in = 10 kn, nf =, : D = 50 mm, d = 40 mm, R = 5 mm, b = 600 M Pa, - 1 = 170 MPa, 0.05, = 354

362 , Mmax = 5 Mmin = 51 Nm, b = 950 M Pa, s = 540 M Pa, - 1 = 430 M Pa,= 0. n = 1.7, ns = 1.5, 13 8, D = 50 mm d = 40 mm, R = mm,, Mmax = 00 Nm, Mmin = - 00 Nm, Tmax = 500 Nm, Tmin = 50 Nm, b = 500 M Pa, - 1 = 00 MPa, - 1 = 115 M Pa, n = KIC 13 9 b = 450 M Pa, = 3 MNm - 3/, a = m, u ( ) ,,,,

363 A) ; ( B) ; ( C) ; (D) 13 11, ( A), ; ( B), ; ( C), ; (D),,, 13 1 b - 1 4, ( A) - 1 < b < 0 ; ( B) - 1 < < b ; ( C) 0 < - 1 < b ; ( D) 0 < b < , 13 13,,, 4 ( A) a b ; ( B) bc ; ( C) c d ; (D) d e

364 ,,,, 14 1,,, (, s ), (),,,,,,,,,,,,,,,,,,,,,, (, ), (,, Fu qu Meu ) 357

365 , ( ),, 14 1( a) a, b, c p e s 14 1, p e s,,,,,,, 14 1( a), : s,,, s ;,,, 14, 1 ( b) Fu n,,,, Fmax [ F] = Fu n (14 Fmax [ F] ( 14 1) 1),,,,,,,,,,, 358

366 ,,, 14,,,, 14 ( a) 14 A, < 14 (a), s,, 1, 1 >,, F 1 1 s, ( ),, (14 1 (a) ), 1,, s,,, 1,, ( 14 ( b) ),, (), FN s, FNu ( ),, FN s = FN u = A s ( 14 ),,, ( ), () (14 1 ( b) ),,,, (, ),,,, ( ),,,, n, n + 1,, Fu,,, 359

367 14 ( b ),, ( ) 4 (3 + 1 = 4), 4,,,,,, (14 1) (a), AB, 1,, s = 40 MPa, l = 500 mm, AF = 100 kn, n =.0, A 14 3 (1 ) :, 1,, 14 3( b ), s A, ( ) : 14 3 ( b), MA = 0, Fu 3 a - s A a - s Aa = 0 Fu = s A (3 ) : : F [ Fu ] = Fu n A nf = 3 s = = 3 a A n, m = 78 mm ( 1),, 1, FN = 6 5 F = 1. F,,,Fs, F s = 5 6 s A,,, 0% ( ),, 360

368 4 14 4( a) Fu 1,, 3, s, A 14 4 (1 ) :,,,,, 14 4( b)14 4(c) 14 4 ( d) 14 4( c),,, 14 4( a)14 4 (c) FN is ( ) : 14 4( b), X = 0, FN3 sin60- s Asin30= 0 Y = 0, ( Fu ) 1 - s A - s Acos30- FN3 cos60= 0 FN3 = s A 3 ( Fu ) 1 = (1 + 3 ) s A 14 4 ( d), X = 0, FN1 sin30- s Asin60= 0 Y = 0, Fu1 - s Acos60- s Acos30= 0 FN1 = 3 s A Fu = 4.5 s A 361

369 14 4( c), F Fu1,,,, 14 4( d), 1,,, 14 4( c) Fu = ( ) s A n,, n + 1??, 14,,,,,, n n + 1,,,,, (a) Fu AB,1,,3, s, A 14 5 (1 ) :,,,,,, 14 5( b) 14 5( c) 14 5 ( d), FN is 36

370 ) : 14 5( b), MD = 0, Fu1 = 3 FN1 s + FN s = 5 A s, MB = 0 MA = (c) 14 5( d), Fu = FN1 s + FN3 s = 3 A s Fu3 = ( FN s + 3 FN3 s ) 1 = A s, 14 F Fu3 5( d), A s,,, 14 5( d) Fu = A s 14 3,,,, max = T W P = 16 T d 3, max s (14, Ts, 7 (a) ),, Ts = W P s W P = d3 16, 14 6 Ts = d3 16 s ( 14 ),, max,,, ( 14 6 ),,, s,,,,,, ( ),, 14 (14 7 ( b) 7(c) ),,,, Tu, 363

371 Tu = A s d A 14 7 d A = d, (14 u = d3 1 s ( 14 3) 3),, (14 3) (14 ), Tu Ts = 4 3 = 1.33,, 33% ( a) d = 30 mm s = 10 MPa, n =, [ Me ],, Tmax Tu,,,, Tmax [ T ] = Tu n, Tmax = Me, Tu = d3 1, [ Me ] d3 1 n s = = 44 Nm 364

372 4 4,,,,,,,,,, 14 9 (a), 14 9,, max = M W max = Mymax I z, max s (14 9 ( b) ),, Ms,,, Ms Ms = = W s ( 14 4) Iz y max s ( 14 5),,,,, ( ),,, s,,,,, ( ), (14 9( d) ) 365

373 14 9 (e) ),,,,,,, Mu, 14 10, Mu,, 14 11,,, (a), A1 A, 14 11( b ), Fx = 0, A1 s = A s A1 = A,,,,, 14 11,,, ;, ( 14 11),,,,, (14 1 ),,, 366

374 Mu =y s d A A 1 +( - A y) ( - s ) d A = s ( y1 A1 + y A ) Mu = A s ( y1 + y ) ( 14 6), A ; y1 y A1 A ( ) 14 1 (14 5), Mu, 14 1, 14 1 M s bh s 6 D 3 s 3 s D d 4 D 4 Mu bh s 4 D 3 s 6 D 3 s D = D - d Mu M s

375 Mu Mu s = 40 MPa (1 ) :,, z 14 13,,,, z, ( ) Mu :, z z y1 y (14 = 10 mm = 50 mm A = = mm 6), Mu = A s ( y1 + y ) = ( ) Nm = 8.8 knm = 14 13, 14 14( a), C ( ), C s,,,, C : s s,, C,, (a) C C Mu, C,, C Mu,, C, C (14 14( b ) ),,,,,,,,,, 368

376 ( a), C,,,, ( 14 14( b) ),,,,,,,, ;,, n, n + 1,,,, (a) Mu (1 ) :,,,, 369

377 , 14 ( ) :,, FA y = qu l 15 ( b) 14 15( b ), AC, MC = 0, FA y l - qu l 1 l - Mu = 0 Mu = qu l 8 qu = 8 Mu l (1 ),,, M max M u, q u = 8 M u l = ql 8, M max = q u l 8 ( ),,,, 14 AC, CB C A, B,14 15 ( b), 15 ( b),, C M u - M u = - M u, q u,, l/ qu xd x = qu l 0 4 qu l - Mu= 0 q u = 8 M u l qs qu, a = 1 m, 40 M Pa Ms (1 ) : 1) : Wz = Iz ymax = ( ) = mm 3 = Wz s = = Nm = 51.9 knm ) : 14 16( b ), C, Mmax = qa,,, qs 370 Mmax = Ms = qs a =

378 qs Ms a = = 51.9 knm ( ) : 1) : A = = 7 10 mm y1 = y = = 41 mm Mu = A s ( y1 + y ) = Nm = knm ) :,, 14 16( c) 3) :,, qu = Mu a = (3 ) : qu qs Mmax = Mu = qu a = Mu Ms = kn/ m = = 1.38, 38% (a) Mu (1 ) :,,, B C, = 371

379 B C, 14 17( b ) ( ) : 14 17( b ), AB, MC = 0, Fu a - FA y a - Mu = 0 ( a), AC, MD = 0, Mu - FA y a = 0, ( b ) (a), FA y = Mu a ( b) Fu = 3 M u a (a) Mu (1 ) :,,, A, C D,, 14 18( b )14 18( c) 14 18( d ), Mu ( ) : ( b), Fu a - Fu a - Mu (+ ) - Mu = 0 Fu1 = 4 Mu a 37

380 4 18( c), Fu a - Fu a - Mu ( + ) - Mu = 0 14 Fu = 5 Mu a 18( d), Fu a - Mu - Mu = 0 Fu3 = 3 Mu a, ( d),, 14 18( d ), Fu = 3 Mu a ( a),, Mu (1 ) :,,,,,, A, C D, 373

381 14 19 ( b) 14 19(c) 14 19( d ), Mu ( ) : ( b), Fu a - Mu - Mu = 0 14 Fu1 = 6 Mu a 19( c), Fu a + Fu a - Mu - Mu = 0 14 Fu = 6 Mu 5 a 19( d), Fu a - Mu - Mu = 0 Fu3 = Mu a, ( d),, 14 19( d ), Fu = Mu a 1., ; s, ;,,.,,, 3.,, Fu qu Meu 4., 374

382 .,,,, 6., Fmax [ F], [ F] Fu n; Fmax 7.() (1 ) : FN s = FN u = A s ( ) () : n ( ), n + 1, n ( ),, : 1) n + 1, ; ),, (1 ) : u = d3 1 s 1), ) Mu = A s ( y1 + y ), y1 y h b ( 6 8( a) ), d ( 6 Mu 8( b ) ), = bh 4 s Mu = d3 6 s Dd (6,= D - d Mu ( ) : = D3 6 8 (c) ), [1 - ( 1 - D ) 3 ] s 375

383 ,, n, n + 1,, : 1) n + 1, ),, AC, B F A, s Fu , C F,, s, AFu 14 3 D, d, s Tu Ts Meu d = 30 mm, s = 100 M Pa , Me, Meu d = 40 mm, s = 100 MPa , s = 40 M Pa 376

384 4 6 ( : mm) 14 7 T 14 7, s = 40 M Pa, n = ( : mm) , s = 40 MPa, n = 1.5 h = b Fu Mu Meu, Mu 377

385 Fu, Mu Fu Mu Fu Mu

386 1 ( a) Fmax = F; ( b) Fmax = F; (c) Fmax = 3 kn ; ( d) Fmax = 1 kn ( a) FN1 = F, FN = F; ( b ) FN1 = F, FN = 0; ( c) FN1 = F, FN = F; ( d ) FN1 = F, FN = - F 3 FN1 = - 0 kn, 1 = 50 M Pa ; FN = - 10 kn, = - 5 MPa ; FN3 = 10 kn, 3 = 5 MPa 4 FN1 = - 0 kn, 1 = 5 M Pa ; FN = - 10 kn, = 33.3 MPa ; 5 FN3 = 10 kn, 3 = 50 MPa / MPa / MPa = E = 70 G Pa,= [ F] = 57.6 kn 9 [ F] = 1.5 kn 10 d 6 mm, b 100 mm 11 [ F] = A[ ] 1 = AC 80 7, CD [ F] = 41 kn 15 D = Fl 3 EA 379

387 16 (1 ) A C = -.5 M Pa, C D = M Pa ; 17 l = 18 l = ( ) AC = , C D = ; (3 ) l = mm Fl 4 EA Fl b ln E ( b - b1 ) b1 19 (1 ) [ F] = kn, ( ) B = m 0 x = 0.05 mm (), y = 0.50 mm () 1 A C = ( + ) Fa EA (1 ) x = 0.6 m; ( ) F = 00 kn 3 (a) Fmax = 3 F; ( b) Fmax = 5 3 F 4 A = m 5 [ F] = kn 6 (1 ) FA = 00 kn, FC = 0 ; ( ) FA = kn, FC = 4.5 kn 7 (1 ) = - 35 MPa, = 70 MPa ( ) = 17.5 M Pa, = - 35 MPa 8 = 7 M Pa 9 T = Dhd = l 00 mm, a 0 mm 3 L 100 mm, 10 mm mm 34 = 99.5 M Pa, b s = 15 M Pa,= 15 MPa,= 15 M Pa 3 1 ( a) yc = zc = 4 R 3 ; ( b ) yc = h 3, zc = b 3 3 ( a) S z = bh 8 ; 380 ( b ) Sz = B 8 ( H - h ) + bh 8 ; ( c) Sz = 5 40 mm 3

388 3 ( a) yc = - (4 b - a) h 3( a + b) ; ( b ) yc = , z c = a 3 4 ( a) I y = hb3 1 - d 4 ; ( b ) I y = cm Iz Iz = ( a) I y = mm 4, Iz = mm 4 ( b ) Iy = m 4, I z = m Iz = m a = 111. mm 3 9 ( a) I y = Iz = d4 64 ; ( b ) Iy = 5d4 3, Iz = d4 3 ( c) Iy = 11d4 64, I z = 105d4 19 ( d) I y = Iz = 33d =.14, Imax = mm 4, Imi n = mm 4 ; 4 1 ( a) Tmax = Me ; ( b ) Tmax = Me ; ( c) Tmax = 40 knm; ( d) Tmax = 4 knm 4 ( 1) Tmax = knm ; ( ) Tmax= knm 4 3 Tmax = 38 knm, Tmax = knm d 39.3 mm, d1 0 mm, D 40 mm 4 7 max 4 8 max = 81.5 MPa, max = 438 M Pa 4 9 G = 79.6 GPa 4 10 d 70 mm = 1.17 / m 4 13 (a) MA = 3 Me B, MB = 1 3 Me ; 381

389 b) MA = ml, MB = ml 4 14 [ Me ] = 37.7 N m, Tmax = 5 3 Me 4 15 V= m l max IP IP 6 GIP = 0.8 M Pa = Me =.0 knm,= rad 4 0 W1 W W3 = max 4 5 W t1 W t = max1 max = 4.5 M Pa,= 1.75 / m = 1 - e r 5 1 ( a) FQ A = - qa, MA = 0, FQB = - 3 qa, MB = - 7 qa, FQ C = qa, MC = - 3qa, FQ D = - 3qa, MD = - 4 qa ; ( b ) FQ A = qa, MA = 0, FQB = - qa, MB = 0, FQ C = qa, MC = qa, FQ D = 0, MD = 3 qa 5 ( a) FQ A = 3 qa, MA = 0, FQ B = 0, MB = 0, 4 FQ C = 3 qa 4 FQ D = - qa 4, FQC = qa 4, MC = - 3 qa 4, FQ D = qa, MD = MD = qa ; ( b ) FQ A = 0, MA = - Fa, FQ B = 0, MB = 0, FQ C = F, FQC = F, MC = MC = Fa, FQ D = F, FQ D = 0, MD = MD = qa ; 5 3 ( a) FQmax = 0, Mmax = Me ;, MC = - qa 4 ; 38 ( b ) FQ max = Me l, Mmax = Me ;

390 c) FQmax = q0 l 6, MQmax = q0 l 6 ; ( d) FQmax = q0 l q0 l, Mmax = ( a) FQmax = F, Mmax = Fb; ( b ) FQ max = Me l, Mmax = ame l ( c) FQmax = qa, Mmax = qa ; ( d) FQmax = qa, Mmax = qa ; ( e) FQmax = qa, Mmax = qa ( f) FQmax = F, Mma x = Fa; ( g) FQmax = 3 qa, Mmax = 6 qa ; ( h ) FQmax = qa, Mmax = qa ; 5 5,, 5 6 ( a) Mmax = Fl, FQ max = Fl 4 6 ; ( b ) Mmax = Fl 6, FQmax = F ; ( c) Mmax = Fl 6, FQmax = F 5 7 ( a) FQmax = qa 4 ( b ) FQ max = qa 4, Mmax = qa ;, Mmax = qa ( a) FQ max = 5 qa qa, M max = 4 ; ( b ) FQ max = 3 ql 10, M max = ql ( a) FQ max = 3 qa, M max = 7 qa ; ( b ) FQ nax = qa, Mmax = 3 qa 5 10 (a) FQmax = qa, Mmax = 3 4 qa ; 5 11 a = 0. l 5 1 a = ( b) FQmax = qa, Mma x = qa - 1 l = 0.07 l 5 13 (a) FQmax = qa, Mmax = qa ; ( b) FQmax = qa, Mmax = qa ; (c) FQmax ; ( d) Mmax = Fl 8, FQ max = F = 3 qa 9 qa, Mmax = 8 ; 383

391 d) FQmax = qa, Mmax = qa 5 14 (a) FQmax = 5 kn m, Mmax = 6 kn ; ( b) FQmax = kn, Mmax =.5 knm; (c) FQ max = 0 kn, Mmax = 17.5 knm; ( d) FQmax = 10 kn, Mmax = 10 knm 5 15 (a) FQmax = qa qa, Mmax = ; ( b) FQmax = qa, Mma x = aq ; (c) FQ max = 3 qa ( d) FQmax = qa, Mmax = qa, Mmax = 5qa 5 16 ( a) FQmax = F, Mmax = Fa; ( b) FQmax = 3 ql 9 ql, Mmax = ( a) FNmax = F, FQ max = F, M max = Fa ( b) FN max = qa, FQmax = qa, M max = qa (c) FN max = qa ( d) FNmax = Me a qa qa, FQmax =, M max =, FQ max = Me a, M max 5 0 FN max = F, FQ max = F, M max = FR = Me 6 1 max = 100 M Pa 6 ( 1) a = MPa, b = 0.95 M Pa, c = 0, d = 41.9 M Pa ( ) a = M Pa, b = MPa, c = 0, d = 6.55 M Pa 6 3 ( 1) max + = 30.3 M Pa, max - = 69 M Pa 6 4 max ( ) + max = 69 M Pa, - max = 30.3 M Pa = 80 MPa, F = 604 N 6 5 d = 11 cm; h = b = 1 cm 6 6 max = MPa, max = 187. M Pa; 41. % 6 7 max = 10 MPa = [ ], max = 6. MPa < [ + ], max - = 5.4 MPa < [ - ], 6 9 [ q] = 7.69 knm max = MPa < [ + ], - max = 55.8 MPa < [ - ], 6 11 a = l 3 384

392 1 [ q] = 4.48 kn/ m 6 13 a = 0, b = 0.48 M Pa, c = 0.67 MPa, d = a = 0, b = 1.9 MPa, c =.04 M Pa, d = (1 ) ma x = M Pa ; ( ) = 17. MPa 6 16 [ Me ] = 11.5 M Pa 6 17 b = 130 cm, h = 190 cm 6 18 max = M Pa < [ ], max = MPa < [ ], 6 19 [ q] = 14.8 kn/ m 6 0 ( max ) 1/ ( max ) = 1/ 7 1 ( a) wmax = ql4 8 EI, ql3 max = 6 EI ; ( b ) wmax = 5 ql4 384 EI, max = ql 3 4 EI 7 ( a) C = Me a E I, wc ( b ) C = Me a = EI Me 6 le I ( l - 3b - 3 a ), wc = Me a 6 le I ( l - 3b - a ) ( c) C = Me Me a, wc = 3 EI 6 EI ( l + 3 a) ( d) C = Fa Fa ( l + 3 a), wc = 6 EI 3 EI ( l + a) 7 6 ( 1) x = 0, w = 0; x = l, w = 0 ; ( ) ; ( 3) FQmax = ql 7 7 ( a) wmax = ql4 8 EI, Mmax = ql 8 + Me l EI, ql3 ma x = 9 EI + Me l E I ( b ) wmax = 5 ql4 384 EI + Me l 16 EI, max = ql 3 4 EI + Me l 3 EI 7 8 ( a) wc = qal3 4 EI, B = ql 3 4 EI ( b ) wc = qa3 (4 l + 3 a), 4 EI B = qa l 6 EI 7 9 ( a) w = Fb4 6 EI ( 3 l - b) - Me l EI Fb,= EI - Me l EI 385

393 b ) wmax = 41 ql4, max = 7 ql3 384 EI 48 EI 7 10 (a) C = ( b) C = 0 57 qa4 4 EI 7 11 (a) wmax = 5 ql4 768 EI + ql 16 k ( b) wc = F( l + a) [ a 3 EI + l + a kl ] 7 1 A y = Fa ( a + 3 h) 3 EI 7 13 A y = Fl3 3 EI + Fa l GIt + Fa3 3 EI 7 14 b 90 mm, h 180 mm 7 15 [ w] = l = = 0.04 mm [ ] = = rad wc = mm < [ v] = 0.04 mm B = rad < [ ] = rad 7 16 (a) FA y = 7 qa 64 ( b) FA y = 7qa (a) FA y = F, FB y = F 7 18 max 7 19 Mmax = ( b) FA y = - FC y = 3 Me l, FB y = 57 qa, MB = 9 qa qa qa, FB y =, FC y = 8 16, MB = Fl 8, MA = MC = Me 4 = MPa, BC = 31 MPa, wc = 8.03 mm 3 le I ( F + k ) ( kl EI ) 8 3 ( a) 1 = 57 M Pa, 3 = - 7 M Pa, 0 = , max = 3 M Pa; ( b ) 1 = 57 MPa, 3 = - 7 M Pa, 0 = , ma x = 3 MPa ; ( c) 1 = 5 MPa, 3 = - 5 M Pa, 0 = - 45, max = 5 M Pa; ( d) 1 = 11. M Pa, 3 = MPa, 0 = , max = 41. MPa ; ( e) 1 = 4.7 MPa, 3 = M Pa, 0 = , max ( f) 1 = 37 MPa, 3 = - 7 M Pa, 0 = , max 8 4 ( a) 1 = MPa, = M Pa; 386 ( b ) 1 = 5.3 MPa, = M Pa; ( c) 1 = - 10 M Pa, = - 30 MPa = 44.7 M Pa; = 3 M Pa

394 5 8 6 ( 1) 1 = 150 MPa, = 75 MPa, max = 75 MPa ; ( ) = 131 MPa, = M Pa 8 7 1: 1 = = 0, 3 = - 10 MPa : 1 = 36 M Pa, = 0, 3 = - 36 M Pa 3: 1 = 70.3 M Pa, = 0, 3 = M Pa 4: 1 = 10 MPa, = 3 = x = M Pa, x y = MPa 8 9 x = 37.9 M Pa, x y = 74. M Pa 8 10 (1 ) - 6 0= M Pa, - 6 0= 9 M Pa; ( ) 1 = MPa, 3 = MPa, = (a) 1 = = 50 MPa, 3 = - 50 M Pa, max = 50 M Pa; ( b) 1 = = 3 = 50MPa, max = 0 ; (c) 1 = 130 MPa, = 30 M Pa, 3 = - 30 M Pa, max = 80 M Pa 8 1 x = 80 MPa, y = = 0, = M Pa, 3 = - 60 M Pa; l1 = mm, l = 0, l3 = mm 8 14 F = 38. kn 8 15 Mn = Nm 8 16 (1 ) r 3 = 135 M Pa < [ ] ; ( ) r 1 = 30 M Pa = [ ] 8 17 r4 = 15.4 MPa < [ ] = 100 MPa, = MPa, max = 100 M Pa 8 F = kn, Me = knm, r4 = 6.9 MPa 8 3 t = 4.68 mm 8 4 r M = 9.1 MPa < [ + ] 9 1 max = M Pa < [ ] 9 + max = 79.6 MPa, - max = 117 M Pa, A = M Pa 9 3 max = 11 M Pa max = 6.9 MPa < [ + ], max - = 3. MPa < [ - ], max = 5.09 MPa, - max = 5.9 MPa 9 7 A = M Pa, B = MPa

395 9 1 = 33.5 MPa, 3 = M Pa, max = 1.7 M Pa 9 10 t = m 9 11 F = 788 N 9 1 (1 ) 1 = 3.11 MPa, = 0, 3 = - 0. MPa ; max = 1.67 MPa 9 13 d = 6 cm ( ) r3 = 3.33 MPa < [ ], 9 14 d = 3 mm B r3 = MPa < [ ], C r3 = MPa > [ ] 9 17 (1 ) a = 6 Plcos / ( bh ) - 6 Plsin / ( bh ) ; ( ) t an= b/ h, 9 18 (1 ) a = 7.10 M Pa, b = M Pa, c = M Pa; ( ) = 4.76, a = 7.48 MPa, c = M Pa 10 1 (a) V= 3 F l 4 EA ; ( b) V= M e l 18 EI 10 (a) V= F l = 96 EI, C = Fa3 6 EI ; ( b) V= M e l 18 EI, C = 5 Me a 3 EI 1 55 Me l 81 Gd W = F3 l 3 C A B = 10 7 A = 4 Fl3 3 EI ( + 1) Fl E A 10 8 (a) A = Fl3 3 EI - Me l EI, A = Fl EI 10 9 A = 388 ( b) A = - 3 qa4 8 EI, A = 5 qa3 6 EI 3 Fl3 1 EI

396 0 10 x = FR 3 EI, y = F R 3 4 EI ( a) A = Fa E A ; ( b ) A = Fa E A 10 1 ( a) B = - 5 qa4 8 EI, B = qa3 3 EI ; ( b ) B = 5 Fa3 3 EI, A = - Fa 6 EI B = - 3qa3 8 EI A = qa4 8 EI + qal3 3 EI + qa3 l GI t A = 5 Fa EA + Fa3 3 EI B = - FR3 EI, B = FR EI B = = 5 Fa3 6 EI 16 RMe d 4 ( 1 E + 1 G ) + 3 Fa3 GI P x = l( T1 + T ) h FC = 15 qa 3, y = l( T1 - T ) h 10 4 FN1 = FN5 = F, FN = FN3 = FN4 = F 10 5 = FR3 EI 10 6 MA = - ( 8-1 ) 6 7 Fa

397 1 6 (1 ) Fc r = kn ; ( ) Fc r = kn ; (3 ) Fc r = kn 11 7 (1 ) x = 0.41 l, Fcr = ( ) Fcr = EI (0.7 l) EI (0.41 l) ; 11 8 (1 ) F = EI ; a ( ) F = EI a 11 9 T = = arctan (cot ) ( a) Fcr = 4.05 kn ; ( b ) Fcr = kn ; ( c) Fc r = 3.13 kn 11 1 ( a) Fcr = kn ; ( b ) Fcr = 33.9 kn ; ( c) Fc r = kn ; ( d) Fcr = kn hb = [ F] = 160 kn ( 1) [ F] = kn ; ( ) = ( 1) F 119. kn ; ( ) n = 1.69; (3 ) F 73.6 kn [ ] s t =.39 MPa a = 0.79 cm [ F] = kn [ F] = kn 1 1 FNd = 90.6 kn 1 dmax = l 1 + a g 1 3 dmax = 140 MPa 1 4 d = 5.6 M Pa 1 5 l = l (3 P + P1 ) 3 EA g 1 6 dmax 390 = 4.63 M Pa

398 7 dmax = 68.3 M Pa 1 8 dmax = 107 MPa 1 9 = cos g P, M( x) = ( l - x) x 1 - l 4 l 3 g l, Mmax = Pl g l 1 10 dmax = 10 MPa 1 11 dmax = 160 M Pa 1 1 dmax = 166 M Pa 1 13 Pa W he I Pa d = M Pa 1 16 dmax = 16.9 MPa 1 17 Fd = 10 k N 1 18 da = 8 HP E 3 d ld 5 D + 5, db = 8 HP E ld 1 19 ( 1) st = M Pa; ( ) d = 6.9 M Pa; ( 3) d = 1. M Pa 1 0 F = 10.4 kn, dmax = 63 MPa, d = 100 mm 13 1 (a) m = 15 MPa, a = 45 M Pa, r = - ( b) m = - 15 M Pa, a = 45 MPa, r = - 13 n= n= : n= 1.6 > n, : n=.31 > n, 13 5 [ - 1 ] = 34 M Pa, [ - 1 ] = 36 MPa 13 6 n= n= n = u = 571 MPa

399 14 1 Fu = A s 14 Fu = A s 14 3 Tu Ts = 4( 1-3 ) 3( 1-4 ), = d D 14 4 Mu = 0.35 knm 14 5 Mu = 3.35 knm 14 6 Fu = 30 kn 14 7 Fu = 90 k N 14 8 b = 40 mm, h = 80 mm 14 9 (a) Fu = 6 Mu l ( b) Fu = 6 Mu l ( a) Meu = 3 Mu ; ( b ) Meu = Mu ( a) Fu = 3 Mu a ; ( b ) Fu = 3 Mu a 14 1 ( a) Fu = 6 M u l ; ( b ) Fu = 4 Mu 3 a ( a) Fu = Mu a ; ( b ) Fu = 1.5 Mu a 39

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