:,,,, ( CIP ) /,. :, ISBN CIP ( 2001) : : 127, : : : ht t p: / / www. nwpup. com : :

Transcription

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2 :,,,, ( CIP ) /,. :, ISBN CIP ( 2001) : : 127, : : : ht t p: / / www. nwpup. com : : 787mm1 092mm : : 480 : : :

3 ( ) 21,,,,,,,,, *,, ;,,,,,,

4 *

5 * * * *

6 * *

7 * ( ) ( )

8 1 1,, : (1 ) : (2 ) :,, ;, (3 ) :, ; ; : (1 ) (2 ), (3 ) 1 2,, (1 ) :, (2 ) :,, 1

9 (1 ) :,, (2 ) :,,, (1 ) :, (2 ) :, (1 ) :,, (2 ) :,,, 1 3,,,,,,,,,,,, : (1 ), (2 ),,,, ;,, ;, : (1 ); (2 ); (3 ) 1.,,,, 2

10 ,, 2.,,, (1 ):,,,,, ( 1 1 ) (2 ):,,, ( 1 2) 3., (1 ) :, ( 1 3 ) (2 ):, ( 1 4 ) (3 ) :, 3

11 , ( 1 5, 1 6) (4 ) : ( 1 7 ) 1 7, 1 8 ( a),,,,,,,,,,, 1 8 ( b) ( a) ( 1 9 ( b) ), ( 1 9( a) ),,,,, ( ( b) )

12 1 9( b ),,, ; ; ;, 1 9 ( c) 1 9,,,,,,,,, 1 4,,, : (1 ):,, 1 10 (2 ):, 1 11 (3 ) :, 1 12 (4 ) :, 1 13, (5 ) :,, 1 14, 5

13 (1 ) :,, 1 15 (2 ) :, 1 16, 6

14 (1 ) :, 1 10 (a), ( b ) (2 ):, 1 10 (c), ( d)

15 2 1,,,,,,, (, ), : (1 ) : 2 1 ( a),,, (2 ) : 2 1 ( b ),,, ( c), ( ),, 2 1( d),,, 8

16 ,,,,, 2 2, 1.,, x y ( 2 2 ( a) ), 2 2.,, A x, y AB ( 2 2( b) ), 3 2 2,, 1. ( 2 3 (a) ) A, A,,, ( 2 3 ( b) )( 2 3 (c) ), 2 3, 2 3, 2 4 (a), E F 6,, 5; 3,,, 9

17 ( b )A, 6,, 4; 3, A,, 2,, 2 4 (c), A 3 9,, A x, y, 3 1, 2, 3, 5, 4,, n ( n - 1 ),, A, 2, 3 2,,, 2 5( a), AB 3,,,, 2 ) 5 ( b),, ( 2, 3, 4, 2 3, m, h, r,, 10

18 2 5 3 m, ( 2 h + r), =- W = 3 m - ( 2 h + r) (2 1),,, W W,, W ( 2 1) h,, 2 6( a), ( b), (c) ( a), 2 7 m = 8, h = 10, r = 4 W = 3 m - (2 h + r) = ( ) = 0 7( b ), m = 9, h = 12, r = 3 W = 3 m - (2 h + r) = ( ) = 0 7( b ), j 11

19 , b, r, 2 j,, ( b+ r). W = 2 j - ( b + r) (2 2) 2 7( b )( 2 2) W = ( 9 + 3) = 0 : (1 ) W > 0, (2 ) W = 0 (3 ) W < 0, ( ) 3, W3 W 0 (W 3 ),, 2 8, W = - 1,, 2 8, 2 4, : ( ), 2 9( a), AB CD,, A, C ;, B D A B CD, AB CD O,, O O,,,,, EF( 2 9 ( b ) ) O,,,,, ( 2 9( c), ( d) ) 12

20 2 9 ( ) 3 3, 2 10( a),,, A, B, C 3, A, C AC C BC, C, C,,,, 2 10( b ), (c) 2 10 (),, 2 11 A BC A, AB, AC, A,,, 2 12, (1, 2, 3 ), ( 2, 4, 3, ),,, 13

21 (7,10, 9),,,, ( ) ( ), ,, ; 2 13 (a), O, O,, 2 13 ( b),,,,,, 2 13( c),,,,, , 3, C A C BC,, C, 3,,,?,

22 2 15 (a)c ( 2 15( b) ), X = 0, N1 = N2 = N Y = 0, 2 Nsin- P = 0 N = P 2sin = 0,, P0, N,,,, , W,,,, (1 ), ;, (2 ), (3 ), (4 ), W = 3m - ( 2 h + r) = 33 - ( ) = 0 :,, FE,, BCE, A D, A B DC,,, AB CD EF,,

23 W = 3 m - ( 2 h + r) = 33 - ( ) = 0, AC,, A C CE, CE, EF,, E FG, CED, ABC, W = 2 j - b - r = = 0,,, ( b), 9, 3 3, 6 3, AB, DC, FE,, BC, DA O1, FB, A E O2, DF, EC O3,,, W = 2 j - b - r = = 0, BG, DB F CH,, CE, :, BG, A D, B, A E, C H, C 2 19, ED, H F,, O B C,, 16

24 , A,,,, * 2 6,,, 2 20 (a), O12, O13 O23,, ;, 2 ;, 2 20 ( b ) 20 (c), O13 O2 3, 1 2, (a), O12, O13 O23,, ;,, 2 21( b ) ; 2 21( c),,,,, 2 22 ( a), 3, 3,,, 3,, 3,, A, B, C 17

25 D, E, F ( ( b ) ), AB 1, DE 2, 2 22 (c), 2 22 ( d ) A BC DEF, A D BE CF O, 2 22,,,,, 3, 2 7,,,,,, 18

26 ,, 2 23 ( a),,,, X1 X2 ( 2 23 ( b) ),,, X1 X2, 3 H A X = 0, 4,, ( 2 24), 3, 3 3,,, ;,,,, , 19

27

28 , 2 4, 2 5, 2 6, 2 7,2 8,2 9, 2 11, 2 12, 2 14, 2 15, , 2 3, 2 10, 2 13, , 21

29 , 8 22

30 3 1,,,, ( 3 1) 3 1, 3,, 3, 3 : N Q M N:, ( 3 2 (a) ) 3 2 Q:, ( 3 2 ( b) ) 23

31 ( 3 M:, 2 (c) ),,,, 3 : N = ; Q = ; M =,,, :,, (),,,, (, ),,,, 3 3( a) :, x, d x ( 3 dq d x = - q( x) d M d x = Q d N d x = - p( x) ( 3 1) :,,,, 3 1, 3 ( b ) ),

32 3 1 ( = ) ( q ) ( ) * ( = ),, ( a) 3 4 (1 ) :, M A = V B 8 = 0 Y = 0 VB = 6 kn() V A - 5 = 0 V A = 10 kn() (2 ) :, QA = QC = V A = 10 kn 25

33 ( 3 QC = QD = V A - 8 = 2 kn QE = QB = V B = - 6 kn 4 ( b) ) (3 ) :, ( 3 MA = 0 MC MD ME MB = 0 = 10 1 = 10 knm = = 12 knm = = 4 knm MH = = - 2 knm MH = 6 1 = 6 knm 4 (c) ) DE,, 3 MD M E, D E, DE F, DE Mmax, : DE M F MF = = 12 knm Q M, a = = 1 m Mmax = = 13 knm 3 2,,,,,, 3 5 ( a) A B, A B M A M B q, A B : MA M B, 3 5 ( b ) q, 3 5( c),, A B ( 3 5 ( d) ), 3 5 ( b ) 3 5 ( c), 3 5 ( d ) :, 3 5 ( d), q,,, 3 5( d) 3 M, M0 M M( x) = M( x) + M0 ( x) 26

34 , 3 5 ( d ) M0 M, M, A B, ( a) 3 6 B, D MD = 0 27

35 3 6( c) MB = = - 2 knm ( ) BD, AB A B P M A, MB ( 3 6 ( b ) ), A B, MA, MB ( ), 3 MC = ( d) A B C = 3 knm ( ) 3 3, ( 3 7 (a) ), 3 7 ( b) 3 7, 3 8, AC, ; CE, ;, EF,,,,,, ( 3 9 ), 3 8, :,,,,,, 28

36 ,,,, (a)

37 3 10 ( b), CE C CDE, A BC, C V C, A BC C ( 3 10 (c) ), A C (1 ) : 3 10 (c),, CE, VC = V E = 20 kn() A C, V A = 60 kn(), V B = 140 kn( ) (2 ) :,, 3 10 ( d)( e),,, (a)q,, C, D,

38 CD, B, E, C, D B, E x, CD Mmax = 1 8 q( 2-2 x) 2 = 1 2 q( - x) ( b) B, E, Mmin = - q( - x) x q( - x) 2 = qx2 = - x = 1 2 ( 2-2 ) 1 2 qx (2 - x) q( 2 - x) x Mmax = Mmi n = 1 2 q[ (2-2 ) ] 2 = 1 4 q (c) 3, 11 ( d),,,,,,,,,, (a),,,,,, A C, CF F H F H, GE,, GF E, EF, ME = qa2, CE CB EF,, A B,, 3 12 ( b),, (), EG QEG = 1 2 qa qa2 2 a = 1 2 qa, : ( 90 ),,,, QEG BD 31

39 QBD = qa qa2 2 a = qa 3 12, AB, A B (A B ) 3 12 (c), MB = 0 Y = 0 32

40 , 3 QA = q2 aa qa2 2 a QB = - 2 qa qa = qa 12( d) = 11 8 qa, Y = 0, B E, ( 3 V B = - 12 (e) ), 1 8 qa( ), V E = 5 4 qa(), 3 12( a) 3 4,,,,, ( 3 13 ( a) ) ( 3 13( b ))( 3 13 (c) ) 3 13,,,,, 3 1, : (1 ), 33

41 ,,, (2 ),,,, MAB A B A (3 ) 3 14 ( a) (a) : X = 0 H A = P( ) MA = 0 VC = 2 p( ) Y = 0 V A = 2 P() ( b ): AB, 3 14 ( b), BC, 3 QBA N BA MB A = P = 2 P ( ) = 2 P( ) 14 (c), QBC N BC MBC = - 2 P = O = 2 P ( )

42 (c) :, N, Q M 3 14( d ) ( e) (f) ( d) : B ( 3 14( g ) ) X = P - P = 0 Y = 2 P - 2 P = 0 M = 2 P - 2 P = (a) (1 ) : 3 15 X = 0 HB = 8 kn() MA = 0 V B = 6 = 29 kn() Y = 0 V A = = 21 kn () (2 ): A C : MAC = 0, MCA = = - 32 knm ( ) MEA = 0 CD : 35

43 MCD = = - 32 knm ( ) MF = = 31 knm ( ) MDC = = - 56 knm ( ) BD : MB D = 0 MDB = = - 48 knm ( ), 3 15( b ) (3 ) A C, A E QAE = QE A = 0 QEC = QCE = - 8 kn N AC = - 21 kn ( ) BD, B QB D = QD B = H B = 8 kn N BD = - 29 kn ( ) CD, A E QCD = 21 kn, QDC = - 29 kn NC D = - 8 kn ( ), ( 3 15 (c), ( d) ) (4 ): C D, 3 15 (e), (a) (1 ) : MA = 0, VB = 12 = 6 kn() Y = 0, V A = = 18 kn( ) X = 0, H A = HB = H C, MC = 0 C, 6.5H - 66 = 0 H = 5.54 kn (2 )M : DC :, MDC = = knm ( ) MCD = 0 DC = 5.54 knm ( ) 3 16 ( b) (3 )Q, N : DC,, 36

44 QDC = V A cos- HA sin= = kn QCD = - V B cos- HB sin= = kn NDC = - V A sin- H A cos= = kn N CD = V B sin- HB cos= = kn 3 16 (c), ( d) (a) G ; G,, ( 3 17 ( b) ),, G, ( 3 17 (c) ),, ( 3 17( d) ) 3 5,,,, 37

45 3 17, ( a) M H D = q() A B M, BD M, BC, B, MBC = 3 2 q2 ( ) M, 3 18 ( b ) ( a) M A, C, 3 18, CE A F, CE AF,, Y B = 0B F, DE,, M ( ) E, MEF = m( ) F 38

46 , MFE = ( b) ( a)m A B, BD, M MDC = 3 knm, MC = 0 M BC = 3 knm ; B M BA = = 13 knm MAB = 5 knm, M, 3 20 ( b) ( a)m 3 21 (a)( A B), DE, C DE DE M, C, MDC = MEC = MC 0 = 1 8 q( 2 a) 2 = 1 2 qa2 ( ) D, E, MDA = 1 2 qa2 ( ) MEB = 1 2 qa2 ( ) A, B, MAD = 0, MBE = ( b ) 39

47 3 6, ;,, ;,,,, 3 21,,, 3 22 (a), t1 t2 ( t2 > t1 ), ( ),, 3 22 ( b), A,,, 3 22,,, 3 23 (a), AB, 3 23 ( b ),, A BC ( ), 40

48 3 23,,,, 3 24 ( a), P, 3 24 (a), 3 24 ( b ), M 3 24 ( b ), A C DB M, CD ( 3 24( c) ),,,

49 M, Q, N

50 3 4, M, Q , M

51

52 3 7 M

53 3 8 M

54 3 9 M,

55 ( a) MA = 20 knm ( ) ( b) MC = 40 3 knm ( ) ( c) MC = 15 knm( ) ( d ) MC= 19 knm( ) 3 2 ( a) M = 0 ( b) MC = 1 4 P ( c) MC= - 2 knm ( ) ( d ) ME = 5 knm ( e) MC = 7 knm ( f) MC= ( a) Mmax = 1 8 q2 ( b) Mmax = q2 8cos ( c) Mmax = 1 8 q2 3 4 ( a) MB = knm ( ) 3 5 ( b) MC = 3 2 qa2 ( c) MC = - 1 knm ( ) ( d ) MB = knm( ) 3 6 ( a) MBC = 90 knm ( ), QBC = 20 kn, NBC = - 5 kn 48 ( b) MCA = 2 knm ( ), QCA = 3 kn

56 ( c) MCA = 80 knm( ) ( d ) MCD = 16 knm ( ) ( f) H = 2 kn ( g ) MA = 12 knm ( h) MCD = 16 knm ( ) 3 7 ( a) MDC = 16 knm ( ) ( b) MCA = 20 knm ( e) MCD = 640 knm( ) ( f) MEC = 0 ( g ) MDC = Pa( ) ( h) MCE = 0 ( i) H B = 4 P() ( j) ME D = 1 2 qa2 ( ), MGC = 2 qa 2 ( ) : 49

57 4 1,,, ( 4 1( a), ( b ), ( c) ), 4 1,, 4 1( e),,,,,,, ( ),, 4 1( d )

58 , f /, ( a),, ( 1) : MB = 0 MA = 0 V A = P ibi V B = P ia i X = 0 H A = H B = H, M C ( 4 1) ( 4 2) = 0 V A 1 - P 1( 1 - a 1) - H f = 0 H = V A 1 - P 1( 1 - a 1) f ( 4 3) ( 4 1) ( 4 2), ( 4 3( b ) ) 4 3 V 0 A V 0 B, ( 4 3) C M 0 C, V A = V B H = V 0 A = V 0 B M 0 C f ( 4 4), ( ), C M 0 C f,, C, f,, ; f,, f 0,,, ( 2) :, K x, y ( 4 4 4( b) K M = [ V A x - P 1( x - a1) ] - H y VA = V 0 A, ( ( a ) ), 4( d) ) K M 0 K,

59 M = M 0 - H y M K M 0 K H y,,, K Q K, 4 4( b) Q = V Acos - P 1cos - H sin = ( VA - P 1) cos - H sin = Q 0 cos - H sin Q 0 = V A - P 1, K, K,, K, 4 4( b ) N = ( V A - P 1) sin + H cos= Q 0 sin + H cos, ( 4 M = M 0 - H y Q = Q 0 cos - H sin N = Q 0 sin+ H cos 4 4 ( 4 5) 5),, ( a), y= 4f 2 x ( - x ) V A = V 0 A = V B = V 0 B = H = M C f = = 75 kn = 105 kn = 90 kn, 8,,,, = 24 m f = 6 m, 51

60 y = 4f 2 x ( - x ) = ( 24x - x 2 ) = x - t an = y = 1 - x 12 x m 2, : x 2 = 6 m y 2 = x - t an 2 = 1 - x 2 24 = = 4. 5 m x 12 = 1-6 = 0. 5, 12 2 =

61 2, 2 sin 2 = , cos 2 = M 0 2 = = kn m Q 0 2= 7. 5 k N, Q 0 2= 1. 5 kn M 2= M 0 2- H y 2= = 45 kn m Q 2 = Q 0 2 cos 2- H sin 2= = kn Q 2 = Q 0 2 cos 2- H sin 2= = kn N 2= Q 0 2sin 2+ H cos 2= = k N N 2= Q 0 2sin 2+ H cos 2= = kn, ( ) M/ ( knm) x y t an 0 sin cos M 0 - Hy M Q/ ( kn) N / ( kn) Q 0 Q 0 cos - H sin Q Q 0 sin H cos N ,, N, Q, M 4 5( c), ( d), ( e) 53

62 , MC = 0,,, : VZ ( 4 6), V A = V 0 A, VB = V 0 B, Z = M 0 C h h C Z, H = Zcos = M0 C f V A = V 0 A + H tan V B = V 0 B + H tan ( 4 6) 4 6 f C,,, 4 3,, 4 7( b ), K, M N N, M= N e e= M N ( 4 7( c) ), N Q, S ( 4 7 ( d) ), S,,,, A, B C,, 4 7( a),,

63 4 4,,,,,, ( 4 5), M = M 0 - H y = 0 y =,, y,, H, ( a) q 4 8( b) M 0 = q 2 x - qx 2 2 = 1 2 qx ( - x ) H = ( 4 0 MC f y = = q 2 8f 7) M0 H - 4f x ( - x ) 2, q= qc+ y, q C,, ( 4 M= 0, M = M 0 - H ( f - y ) f - y = M 0 5) q y H M0 H ( 4 7)

64 , y, M 0,, x - y = 1 H q, d 2 M 0 = - q, dx 2 d 2 M 0 dx 2 y = q H ( 4 8),, q= qc+ y ( 4 5), y - H y =,, qc H y = Ach H x + Bsh H x - qc A, B x = 0, y= 0, A= qc x = 0, y = 0, B= 0 y = q C ch H x - 1, H,,, m = qk qc ( 4 9) qk = qc+ f, m = q C + f qc qc = f m - 1 = x / 2, K = y = f m - H 2, 1 ( chk - 1) ( 4 10) K m : = 1, y = f, ( 4 10) chk = m ( 4 11) K = n( m + m 2-1) ( 4 12) 56

65 , m= q K, m= 1, ( 4 10), qk = qc,, y = f 2 4 qc 4 4 ( ) ( 10( a) ),, ( 4, N N + dn M 0 = 0 dn = 0 N = S - S 2N sin d 2 - q d = 0 d, sin d 2 = d 2, N - q= 0 N, q, N - ( N + dn ) = 0 10( b) ), 4 10 = N q = y= 4f 2 x ( - x ), K / 4 D 57

66 K H = 50, MK = kn m, Q K = kn, Q K = kn, N K = kn, N K = kn 4 2 M D = 1. 07q kn, M K = 44 k Nm, QK = kn, N K = kn ( )

67 5 1,,,,,,,,,,,,,, : ( 1) ( 2), ( 3) ( ), 5 1( a), ( 5 1( b) ), 5 1,,,,,,,,,,,,,, d h ( 59

68 5 2) 5 2, : 1. ( 1) :, ( 5 3( a ), ( e), ( f) ) ( 2) : ( 5 3 ( b), ( d) ) ( 3) : ( 5 3( c) ) ( 1) ( 5 3( a) ) ( 2) ( 5 3( b), ( f) ) ( 3) ( 5 3( e) ) 3. ( 1) ( 5 3( a) ) ( 2) ( 5 3( d) ) 60

69 5 2,,,,,,,,,, N N x N y 5 4, x y, N = N x x = N y y ( 5 1),, ( a ) 5 4, A E, E, ( 5 X = 0 N EC= 0 Y = 0 N E F = P ( ) F, D, C, B A,,, A,,, 5 5,, ( 5 5( b ) ) 5( a) ),,, : 1. L ( ),,,, ( 5 2. T ( ) 6( a) ), ( ), ( ) ;,, ( 5 6( b) ) 61

70 3. X ( ), ( 5 6( c) ) 4. K (, ), ( ) ( 5 6( d) ) 5 6,, 5 7( a ), ( b) ( ),,,,,, ( ), M = 0, ( a ) 1, 2, 3 ( 1) 62

71 ( 2) 1, 2, 3, ( 5 8( b) ) 5 8 F, 1, 2, 3 F, M F = 0, N a Pa = 0 N 1 = 3P ( ) 2 N 2, 2, A,, N 2, 1,,, N 2 C, N 2x A, N 2y 2a ( 5 8( b ) ) MA = 0, Pa + N 2y2a = 0 N 2y = P N 2 = N 2y 2 2y N 2 = N 2y 2 2y 3 N 3, 2 = P a 2 + ( 1 2 a ) 2 = a 5 2 P ( ) MC = P 2a - Pa + N 3 xa = 0 N 3 x = - 2P N 3 = N 3x 3 3 x = ( - 2P ) 5 2 a a = - 5 P ( ), ( ), X = 63 0

72 Y = 0, ( a ) a, b ( 1), 5 9 ( 2) a N a, -, ( 5 9( b) ) Y = 0, N a + 15 k N= 0 N a = - 15 kn ( ) ( 3) b N b, - ( 5 9( c) ) Y = N by= 0 N by = 5 kn N b = N by b by = = k N ( ),,,,,,,,,, ( 5 10( a), ( b ) ) 5 10,, 2 ; 3,,, 64

73 ( 5 11( a), ( b) ) ,,,, , 2, ( 1), X A = 0, YA = 12 k N( ), YB= 4 k N( ) ( 2) 1, 2, 3 : 65

74 a ) m- m,, ( ), C, M C = 0, N 14-48= 0 N 1 = 8 k N( ) b) n- n, ( 5 12( b) ), F, N 2 G X 2 Y2, MF = 0, ( 12-2) Y22. 5= 0 Y2 = 6. 4 kn N 2 = Y2 2 2y = = 8 kn ( ) 2 c) D, 5 12( c), N 3 D X 3 Y3, Y = 0, Y3 + Y2 = 0 Y 3 = - Y2 = kn N 3 = Y3 3 3y = ( ) = kn ( ) ( a) a, 5 13 a, ( 5 13( b ) ),, B N b = 0, Y1 = 0 N a P 1 2 = 0 N a = 2 3 P ( ) ( a) a, b 66

75 , a, ( 5 Y = 0 14( b) ) N a y + N cy = 0 N a y - N cy + 3 = 0 ( 1) 5 14 K K, K ( 1) ( 2), N a = N a y a a y N a = - N c, N a y = - N cy ( 2) 2N a y + 3 = 0, N a y = - = ( ) ( ) 3 = kn 5 2 kn ( ) N a, M D = 0 N b, b ( 5 14( c) ) MC = N b6 = 0 N b = - 6 kn ( ) ( a) a, H A = 0,, N K E = N K F ( 1) K K N K E = - N K F ( 2) ( 1), ( 2), N K E = N K F = 0, N E C= N CH = N F D = N D G= 0 a G H ( 5 15( b) ), Y = 0, N by+ P = 0 N by = - P 67

76 N bx = N by bx by = ( - P ) ( a ) 1 2 a = P X = 0, N a = P ( ) : 5 16( a), ( b), ( c) (,, P = 10), N = M 0 r, M 0, r,,,, r,,,,,, ( ),, M 0,,,,,,,,,, 68

77 5 16, : ( 1),,,,,,,,,,, ( 2),, ;, ;,, ( 3),,, ( 1830 m) ( m),, 5 6,,,,,, ; 3,,,,,, 69

78 ( a) ( 1) ( 2),, M C = N EG2 = 0 N E G = 6 kn ( ) E G, ( 5 17( a ) ) 5 17 ( 3), AC ( 5 17( b ) ) H C = 6 kn ( ) V C = 2 kn ( ) ( 5 17( c), ( d), ( e) ) 5 18( a),,, 70

79 ,, 5 18( b) ( a),,,,, ( 1) : A B, T A T B, AA BB, X = 0 H A = H B = H MA = 0 V B + VB = Y = 0 4P1. 2d + 2P2d 4d V A + V A = 6P P = 3. 8P 5 19( b), C MC = 0 = 2. 2P H B ( 0. 8d d ) - ( V B + V B )2d = 0 H = H B = V B= H B y x V A = 3. 52P = 2. 2P2d d 4. 4P0. 8d d = 4. 4P V A = 3. 8P P = 0. 28P VB = 2. 2P P = P = 3. 52P ( 2) : X = 0,, 4. 4P T B E = T E C = H B 2 + V B 2 = ( 4. 4P ) 2 + ( 3. 52P ) 2 = 5. 63P H = cos P d ( 0. 2d ) 2 + d = 4. 49P 2 71

80 , C ( 5 19( c) ), Y = 0 N C C = 2T C E sin 1 = P 0. 2d = 1. 76P ( 0. 2d ) d

81 N E E = 2. 64P, T B E = T A D, T C D = T C E,, N D D = N EE = 2. 64P ( 3) : ACB ( 5 19( d) ), ( 5 19( e), ( f) ) * 5 7,,, ( 5 3( c) ),,,,,,, ( 5 20 ( a) ),,,,,, ( 5 20( b ) ),,, ( a ) 5 21 W = 0,,, A, B, C, G 5 5 VA = VB = 0, H A = 0 N A C = N A J = N BG = N BH = 0 N CD = N C I = N GF = N GI = 0 21( b) E I N E I= 0 N D H = X, 21( b) X,, 73

82 , ( a ) W = 0,,, N G E, N GF, N H A, N H I 5 22( b), 5 22,, AB N A B = X,, ( 5 22( b) ), A, A 5 22( c) X, ,

83

84

85 *

86 ( a ) N 1= - ( b ) N b= - 45 kn ( ) 8 3 P ( ), N 2= 5 6 P ( ), N 3= 2P ( ), N 4= P ( ) ( c) N 1= 125 kn ( ), N 2= 150 kn ( ) ( d) N 2= 1 3 P ( ) 5 4 ( a ) N a = 5 kn ( ), N b= 15 kn ( ) ( b ) N c= P ( ) ( c) N b= P ( ), N b= 0 ( d) N b= - 20 kn ( ) ( e) N a = 0, N b= 0 ( f) N a = 0, N b= 5 13 kn ( ) ( g) N a = 20 2 kn ( ) ( h ) N a = 5 3 P kn ( ) ( i) N a = 0, N b= 5 2 k N( ) 5 5 ( a ) N a = 0, N b= 30 kn ( ) ( b ) N a = kn ( ), N b= 1. 3 kn ( ), N c = k N ( ), N d= - 59 kn ( ) 5 6 ( a ) N D F = 60 kn ( ), M G= 45 kn m( ) ( b ) H = 25 kn ( c) H = 60 k N, VA = 30 kn ( ) 78

87 5 7 ( a ) ; ( b) 5 8 ( a ) N 2= 0; ( b) N a = 2 P ( ) 79

88 6 1,,,,, ( ),, A B A B ( 6 1 ( a), ( b ) ), A B ( 6 1 (c) ), RA, RB,,,, 6 1,,, P = 1,, 80

89 6 2( a) A B, P = 1, RB A, x P = 1 x, P = 1 y P = 1 x,, RB, MA = 0, 1 x - RB = 0 RB = x, 0 x RB x, RB 6 2, 6 2 ( b) 6 2( b ) RB P = 1 : P = 1 A, B, RB, RB, 1 RB : (), (,, ), = 1,, = 1,, ( 6 3 ( ) ),,, = 1 = 1 0,, - ( - ) = 0 = - = - = 0 (0 )

90 ,, 6 3 ( ), = 1,,,, = 1, = 1,,, ( ) = 1,, = 1,, ( 6 = 0 = - 4( ) ) + = 0, = - (0 < ) = 1, ( 6 4 ( ) ) = 0 - = 0 = = - ( < ),, ;,,, ( ), 4( ),,, = 1,, = 1, = 1, = - ; = 1, =, = 1,, 1, = 1, 82 = 1, ( ) = 1

91 ,, (6, = 0 - = 0 4 ( ) ), = = (0 ) = 1, ( 6 4( ) ), = = - ( < ),, 6 5 ( ),,, = 1, ( 6 6 ( ) ), = 1, = 0, = - = 0, = ( ), = 1 ( ) ( = 1, ),, 6 6( ), ( ) ( ) = 1,, = - = - 1 < - 1 = 1,, = = <

92 , 6 6( )( ),, = 1,, = 1, = 1, = - ( 0 < ) 6 6 ( ), ( )

93 6 3,, :,, 6 7 ( ),,,,, = 1 ( 6 = 1, 7( ) ), - = 0 (6 1 ) = (6 2 ) 6 7 = 1, = 1, ;,, (6 2 ) ( ) = ( ), = 1 (6 3) ( ) = ( ) (6 4) ( ) = 1, ; ( ),, ( ), ( 6,, : (1 ), 7( ) ) (2 ) ; ( ) (3 ), ;, 6 8( ), ( 6 8 ( ) ) (+ ) - = 0 (6 5) = + 85 (6 6)

94 += 1 = ( 6 8 ( ) ), ( ),,,, = 1 8 ( ) ( ) - = 0 =, 6 8 ( ),,,, 1 2, 6 4,,,,, 6 9( ), 6 9 ( ) = 1, ;, 86

95 = 1,, = 1, ( 6 9 ( ) ) = -,, = 1, ; = 1, = ( ) 6 9, : (1 ) = 1, (2 ) = 1, (3 ) = 1,,, 6 9( ) ( ), 87

96 ,,,,, ;,,,, ( ),,,,,, ;, ; = 1,,,,,, ( ),,,,,,,, 1, ( ),,,,,,,, 6 10 ( ),, ( ),,, (),,, = 1, ( 6,, 11 ( ) ),, = 1,,, - ( 6 11 ( ) ) = 1,,, 88

97 6 10 = = - +,, = 0, = ; =, =,, ( 6 11 ( ) ),, : (1 ); 89

98 6 11 (2 ), 6 12, 6 12, = 1,,,

99 91

100 6 13 * 6 6,, 6 14 ( ), (4-1) = 0 = 0 = 0, ;,, 6, ( 4 2) = 0-14( ) : 0 ;,,,, 6 6 (4 5 ) 14 ( ) = 0 - = ( ), 0 ;,, 6 14( ),, 6 14 ( ), 6 14 ( ), ( ) 92

101 ,,,,, 93

102 ,,, 6 15 ( ),, =

103 ,, = 0,, 3 + = 0 = 0 = - 3 (6 7),, = 0, 3 + = 0 = - 3 (6 8) (6 7 ), 3,,, ; (6 8 ), 3,,,, 6 15( ) (6 7 )( 6 8), 0, = - 0 (6 9), -,, = 0, = + 0 ( 6 10),, 6 15( ), = 0,,,,,,, 6 0, = 0, = - ( 6 11) = 0, = + ( 6 12) 15 ( ) 95

104 6 = + 0 ( 6 13) 15 ( ) 0 = 1, -, = 0 0, = 0, = - 0 ( 6 14),,, 6 15 ( ),,, 6 = 1, ( 6 15 ( ), ( )( ), = ( )) 0,, 6 15 ( ) = 1,, = 0 = 1,,,, 6 15 ( ) = 1, : = 1, = - 1 ; = 1, = 0, 6 15( ),,, ( ) ( ) 6 8,,, 1, 2, 3, 6 16 ( ) ; 6 16 ( ) 1, 2, 3, 1, 2, 3, = 1, 1 1 1, 2 2 2, 3 3 3, 1, 2, 3 =

105 , 1, 2,,, 1, 2,,, (6 = = = 1 ( 6 15) 15), , 6 17,,,,, = = ( )= = 1,,, = = 1 = = ( 6 16) ( ) ( ), ( ), ( ) 18 ( ) ;, ( ), ( ) ; = ( ) ( ), ( ) = = 97

106 ,, ( ) = ( ) ( 6 17) = ( 6 18) ( ),, 6 19 ( ) 1, 2, 1 = = 1.8 (6 18) 2 = ( ) = = ( ) = 10 ( ) = 10 * 6 9,,,,,,,, , 6 20 ;,, 6 20,,,, :

107 ,

108 ,,, (, ),, ( ),, ( ) 6 8, ; ( 6 21) (,, ), ( 6 18 ) 100

109 =,, ;,, ( 6 22 ), ( ),,,, 6 23 ( ), 1, 2,,,, 6 23 ( ), 1, 2,,, 1 = ( 6 19) 6 23,, :,, 6 24( ) 6 24 ( ), ( 6 20), 2 2 = 1 ( ) + 2 ( ) + + ( + ) = ) = 101

110 = 2-1 = = = 1 (, ), ;,, = = = 1, ( 6 (6 21) :,, 20 ), 0 ( 6 21) = 1 > 0, 0 = 1 < 0, 0 = 1, : 0 = 1 0 = 1 (6 ( 6 22 ) (6 22 ) 22) :,,,?,,,, ( ),,,, ( 6 22 ),,,,,,,,, ( ),,, ( ),,, 102

111 ,, ( ), =,,, = = 0 ( 6 25 ) ( ), 20, 6 25 (1 ) :, 3 1 2, 6 26 ( ) 6 26 (6 1 = 1 16, 2 = - 22 ), 1 16, 3 = 3 16, 4 = ( ) 1 16 < , > 0 =

112 = , > 0 + ( ) > 0, 3 1 2, 5,, = ( 2 ) : 3, 6 26( ), < > 0,,, = ( = ),,,,, : ( + )- 0 - ( + ) 0 = =

113 + + ( 6 23) :, ( 6 = = 1 - = 0 = 28), = = 0 = 1 ( 6 24) ( ), ( 1 = 2 = 3 = 4 = 82 ), 3.5, 1.5 ( 1 ) 6 29 ( ) (2 ) 2 3, ( ), (6 23) > < ( ), (6 23), > > (3 ) 2, 6 29 = 82( ) = ( )15,, 6 30( ) (1 ), 130, 6 30( ) (6 23) 105

114 > < , 130, = = (2 ), 130, 6 (6 23) > < ( ), = = 2 720, 6 = ( ), 6 11,, ( ),,,,,,,, =, 6 15 = = = / ,,, 106

115 , 2 = : 2 = 1, 2 = 1 2 = 2 2 = 1 1 = 1 1 = : (1 ), (2 ) ( ), 6 32, 1, (3 ), ( ), (4 ) ( 6 32), 00.5, / ( / ) () 1/ 8 1/ 4 3/ 8 1/ 8 1/ 4 3/

116

117 / ( / ) () 1/ 8 1/ 4 3/ 8 1/ 8 1/ 4 3/ / ( / ) () 1/ 8 1/ 4 3/ 8 1/ 8 1/ 4 3/

118 ( )15,, ( ), ( ) (1 ) : = 6,= 0, = 5.11 /, = = ( - 1 ) 6 = (2 ) : = 12,= 0,, = 10,= 0, = 13,= 0, = 0, = 12, ( 6 = = 3.44 / = 2.95 / 34) ( ) = 3.11 / = = = (3 ): = 18, = 1 3,, ( / ) / = 16,= 1 3 = 0.333, = ( ) = 2.33 /

119 = 20,= 1 3 = 0.333, = ( = 18,= = ) = 2.20 / (20-18) = 2.27 / = = = ,,,,, : (1 )? (2 ),,,,,,,,, ( 6 34),,,,,,,,,,, ,,,, = ( - - ) 111

120 = - = ( - - ) -,, = ( ) = 0 = 2-2,,,, ( 6 ( 6 25) = ( 2-2 ) 2 - ( 6 26) 26 ),,,,,,,,,,,,, ( )15, 6 35 (1 ) : 6 35 ( ), 2, = 2, = 350, 2 (6 112,, = 1 ( ) = ),,

121 = = 2-2 = = (10 - ) = (2 ) : 6 35( ), 2 = 130, = = 1 035, 1 062, %, 6 13,,,,, 6 36 ( ), ( 6 36( ) ) (),,, ( ), 6 36 ( )( ),,, ( 6 36 ( ) ), 6, 6 37 ( )( ), 37( ), ( )( ),,, + - ( ), ( ),, = + ( 1 + ) + = + (1 + ) - ( 6 10) 113

122 , 1 : = /, 10, = 1.82, = ,,, 6 38 ( ),,, ( 6 38 ( ) )

123 , 6 6 6, = ( 1 + ) 2 = + = 2 /

124 , = (1 + ) 2 + / ( ), ( ),, ,,, ,,, 6 4,,, ,,,, 6 6 :,,, = 1 6 7, = 1 6 8,, = 1 6 9,,,,

125 (,,,, ) 6 11 (,,, ) 6 12 (,,, ) 117

126 6 13 (,, ) 6 14 (,,,, ) 6 15 (,,,,,, ) = 4 ( - ),,,, , , , 6 24,,, 118

127 (, ) 6 23 (,, ) ,,, ,, = 20, = 12 /, 10, 119

128 ( ) = 7.5 = = = = - 29 = = = 237, = 149, = =

129 7 1,,, ; 7 1( a), A A A, A AA, A Ax A y, 7 A, A, 7 1( b ), A, 2,, A A, B B, A Ax ( ), B Bx ( ), A, B AB, AB = A + B, 7 2, C, D C ( ) D ( ),, C, D CD, CD = C + D, , ( ), 7 3, 118

130 ,, 7 3,,, : (1 ),,,,,,, (, 1/ 700, 1/ 900) (2 ),,,, (3 ),,,,,,,, : (1 ), ; (2 ), ; (3 ), ( ),,,,,,, 7 2, 119

131 : 7 4( a) P1,, P1, P1, ( b) P1 W = 1 2 P ( b ) OAB P1 1 P1 7 4, ( ) 7 4( a), P1 t P1 W = P1 t t 7 4( b )A BCD P1 t,,,,, ( 7 5( b ) ) 7 7 5( a) ), ( 7 5 (a),, M Q N,, 5( b ),,, 120

132 d s 7 5( a) d s 7 5 (c) 7 5( b) d s CD C D:,,, d s, 7 5( d ) ( a) ; ( b ) 7 5( c) 7 5 ( d) dw = Nd+ Qd+ Md 5( c),, CD,,, dw = - ( Nd+ Qd+ Md ) W = - 0 Nd+ 0 Qd+, W = - 0 Md (7 1) Nd+ 0 Qd+ 0 Md (7 2) 0, :,, W + W = 0 : ( ) 121

133 7 5( a) () 7 5( b ) W = Pi i + Ri Ci Pi i = Nd+ 0 Qd+ 0 Md- Ri Ci 0 (7 3) :,,,, :,,,, 1.,,,,, 2.,,,, 7 6( a), A C A, C Cy 7 6 ( a) ; ( b ) 7 6( a),, C, C, C P, A R A P ( 7 6 ( b ) ), 7 6( b )7 6( a), PC y + RA C A = 0 Cy = - CA R A P 122

134 RA = - P 0 (7 4) (7 4 ) (7 Cy = CA 0 (7 5) 5 ), Cy P, P = 1, Cy P, ( a), K k - k K 7 7 ( a) ; ( b ), ;,,, K P = 1, ( 7 7( b ) ) P = 1 Ri ( N, Q, M) ( 7 3), K = ( Nd+ Qd+ MRd ) - Ri Ci (7 6) : K, d, d, dci P = 1 P = 1 Ri (7 N, Q, M 6 ) K, K ;,,,, 123

135 ,,, 7 8( a) A,, 7 1 A = A, 8( b),,,,, 7 8 (c),,, 7 8( d ) 7 8,,,,, 7 8( e), ( 7, 8 (f) ), AB = A + B d 1 d A + 1 d B = A + B = AB d,,,,, 124

136 7 4,,,, ( 7 6 ) R i Ci, (7 6 ), K P = MRd P + Qd P + Nd P (7 7) M, Q, N d s ; d P, d P, d P d s N P, QP, M P, MP, QP N P d P = MP E I d s d P = KQP GA d s (7 8) d P = N P E A d s E, G ; A, I; K, K = 1.2; K = 10 9 (7 8 )( 7 7) KP = MR M P E I ; K = 2; KA A f d s + K QQP GA d s + NN P E A, ( 7, A f d s (7 9) 9 ),,,, (7 9 ),,,,,,, 125

137 1.,,,, (7 9) 2. KP = MM P E I ds ( 7 10), N, N P E A, ( 7 9 ) 3. K P = NN P E I d s = N N P E A ( 7 11),,, ( 7 10 ) ;, 4. KP = MM P E I ds + NN P E A,, (7 KP = MM P E I ds ( 7 12) 9 ) d s + NN P E A ( 7 13) ( a) A, I, A 7 9 ( a) ; ( b ) (1 ) A P = 1, 7 x 7 9 ( b), A B : M = - x, N = 0, Q = 1 BC : M = -, N = - 1, Q = 0 (2 ) ( 7 9( a) ), 9( b ) A B : M P = qx2, N P = 0, QP = qx BC : M P = q2, N P = - q, QP = 0 126

138 (3 ) ( M ) A y = MM P EI 0 ( - x) ( - d s = 1 2 qx 2 ) EI d x + 0 ( ) ( Q) A y = K QQP GA, A y ( Ay N) = ( M ) A y = NN P + ( Q) A y ( - ) ( - EI d s = qx 0 GA 1 2 q2 ) E A d s = ( - 1 ) ( - q) d x = 0 EA + ( N ) A y = 5 q4 8 EI 1 + d x = 5 q4 8 EI d x = 3 q2 5 GA q2 EA () () 24 EI + 8 I () 25GA 2 5 A 2 ( 4) :, b, h, A = bh, I = 1 12 bh3, = 1 3, () E G = 2( 1 + ) = 8 3 A y = 5 q4 8 EI ( ( h ) ( h ) 2, h, h = 1 10, A y = 5 q4 8 EI ,, ( a), C E = kn/ cm 2, A = 12 cm ( a) ; ( b ) 127

139 (1 ) C P = 1, 7 10 ( b ) (2 )NP NP, 7 10 (a) (3 )N P = 1 N, 7 10( b ) (4 ) Cy, 7 1,, 2, DE, ( ) N/ k N NP/ k N / cm A/ cm 2 E/ ( kn/ cm 2 ) NN P E A / cm AC A D - DE - DC = cm Cy = = cm () ( a) A B,, A B 90 RB By 7 11 ( a) ; ( b ), ( 7 11( a) ), M P = - PR sin ( 7 11( b ) ), M = - Rsin (7 10) 128

140 By = MR M P ds = E I EI 2 PR 3 0 sin2 d= 7 EI PR3 EI ( - Rsin ) ( - PR sin ) Rd= sin = PR3 4 EI (),,, KP = MR M P E I,, : ; E I = ; MM P,, ds 7 12 AB, M, MP x, M x, = MR M P d s E I MM, M = y = xtan = EI 1 MR M P d s = tan xmp d x = tan E I EI xd P d P M P, xd P y, xd P MP y, MP C y x C, P xd= x C = t an EI xc = yc E I yc M P C M,,

141 = MR M P d s = E I y C E I (7 14) : (1 ) ; (2 )yc ; (3 ): yc,, 7 13,, ( ) 7 13,, 1. (1 ),, 7 14 (a), 1 EI MR M P d x = 1 EI ( 1 y1 + 2 y2 + (2 ) E I, E I, 7 14 ( b ), y3 )

142 2. MR M P E I 7 14 d x = 1 y1 EI y2 EI 2,, (1 ) ( 7 15 ), ( ),, 1 = 1 2 a 2 = 1, 2 b y1 1 EI MR M P d x = = 2 3 c d y2 = 1 3 c d 1 EI MM P d x = 1 EI ( 1 y1 + 2 y2 ) ( 2 ac + 2 bd + ad + bc) 6 EI, :, (2 )( 7 16 (a ) ), ( 7 16 ( b ), ( c) ), 7 16( a) M P 7 16 ( b ) 7 16 ( c), :,,, MA, M B (a)c EI (1 )MP 7 17 ( b) (2 ) C P = 1, M7 17( c) ( 3) C y M P, MP, M,, 131

143 Cy = yc E I = 2 1 EI q = 5 q4 384 EI () (a)d Dy E I 7 18 MP M7 18 ( b), ( c), CB M 1, A B M 2, 132

144 1 = = y1 = 5 6 P( 1 ) D y = y C E I = 1 EI 2 = 1 2 = y2 = P( 2 ) P P = 29 P3 48 EI () (a) C, D EI 7 19 MP M7 19 ( b), ( c) 7 19 ( b) 7 19( c) CD = - 1 EI ( qa2 2 aa) = - 2 qa4 3 EI ( ), C, D ( a) C C E I = MP M 7 20 ( b ), ( c)m P A B BC, C = 6 E I 21 4 q2 1-1 EI ( q2 1 2 ) + 1 EI ( q2 2 1) + 1 EI ( q2 2 1) = 133

145 3 q 3 32 EI () 134

146 (a), CD, CB () E A, AB EI, C C y 7 21,, N P, N, M P, M R, 7 21( b), (c) ( 7 13 ) Cy = N N P E A + yc E I = 3 1 ( ) EI EA ( - 20) ( ) 5 = 96 EI EA () 7 6, ;, 7 22 (a), t1, t2 t2 > t1,, K Kt ( 7 Kt 6 ) = Nd t + Qd t + MRd t ( 7 15) d s t1 d s t2 ds,,,, d t d t,, d t = 0 d t d t : 135

147 ( h1 = h2 ), t0 = t1 + t ( a) ; ( b ) ( h1 h2 ), h; t0 = t = t2 t1 h2 + t2 h1 h h1, h2 ; - t1 t1, t2 ds 7 22 ( b),, d t = t2 d s - t1 d s h (7 16), ( 7 17 )d t = 0 ( 7, Kt = N =Nd s N ; d t = t0 d s ( 7 16) = ( t2 - t1 ) d s h 15 ) Kt = N t0 d s + MRt h d s = t0 Nd s + t MR t0 Nd s + t h MRd s = = td s h h t0 N ( 7 17) d s ( 7 18 a) + t M R (7 18 b) h M R =Md s M 136

148 , N, t0 M t ( M t ),,,,,, Kt = t0 N ( 7 19),,, K = N ( 7 20) ( a) 20,, - 10, 0 A A y = 4 m, = 10-5,, h = 40 cm 7 23 ( a) ; ( b) ( c) t1 = = - 30, t2 = 0-20= - 20, t0 = t1 + t2 2 = = - 25 t = t2 - t1 = ( - 30) = 10 M, N( 7 22 ( b), ( c) )( 7 18 b),, Ay = t0 N + t h M R = ( - 25) ( 2 ) + 10 h h 2 = cm () ( 2 ) 2 = = 137

149 * ( a), CD, 2 cm, E = N, E, E P = 1, 7 24 ( b) P = 1 CD ( 7 24( b) ) K y NCD = = kn K y = = 5 6 cm() 7 24 : N,, N CD, CD 2 cm, 7 7,,, (7 4 ) KC = - Ri Ci ( 7 21) Ri ; Ci (7 21), Ri Ci, :, ( a), A a, B B 7 25 ( b), (c),, 7 25 ( b) V A = h (), 7 25(c) V A = 1 ()(7 21) 138

150 B x = - Ri Ci = - ( h a) = ha ( ) B = - R i Ci = - ( 1 a) = - a (), (7 7 C y A 21), 26 B, : Cy = 2 A = () = 2 ( ) 7 25 ( a) ; ( b) ( c) ,,, P1 P2, 7 27 (a)( b), WW, W+ W= 0, P1 M1 M2 1 2 = EI d s + N1 N2 EA d s + Q1 Q2 K GA d s ( 7 22), 1 2 : 1 ; 2 139

151 12 P2 P1, W W, W+ W= 0, P2 M2 M1 2 1 = EI d s + N2 N1 EA d s + Q2 Q1 K (7 22), ( 7 23 ),, GA d s ( 7 23) P1 12 = P2 21 ( 7 24), :, (a) ; 7 27 ( b) 7, P1 = P2 = 1, (7 24) 1 12 = = , (a) ; ( b) ( a) ; ( b ) 12 21,, , = 2 1 ( 7 25)

152 , :, P1 P2, , = 2 = 1 k12 1 = k2 1 2 k12 = k2 1 ( 7 26), : 1 2, , (a) 2 P2 = 1, 1 k12, ; 7 30( b) 1 k12 1 = 1, 2 P2 = 1 21,, k = 0 k12 = ( 7 27), :,, * (a), P = 1, K KP K P x,, K P K P 141

153 P = 1 K, 7 31 (a), KP = PK,, P = 1 K K P, K P K = 1 P = 1, 7 PK, PK P K 7 31( b ) P = 1, = 1 K, 31 ( b), KP K P K = 1,,, 7 = PA, MA (a), A AP, AP = 1 P A ( 7 32 ( b) ) P A,, AP, MP, 7 32( c), ( d), M A

154 x, 7 AP = PA = 1 EI 1 2 x( - x) (2 - x) 6 EI ( - x) x = ( 2 - x) 3 x( - x) ( + x) 6 EI 32 ( b) AP = 7 1 (1 )( a), B y? (2 )( b), A, Cy? (3 )( c), Cx? (4 )( d), E I =, Q, N, B x? (1 )( a), E A =, Dx CD? (2 )( b), E A =, G y? 143

155 ,?? 7 4, B y? 7 5, Cy, C? 144

156 , B? 7 7, B y? 7 8, Ax, Ay? 7 9, A (A )? 145

157 , Cx, D? 7 11, C C, D? D ( E I = knm 2, E A = kn) 7 13 D, h = 1, , CD DE t, E 7 15 C 146

158 A 0.01 rad, B 0.01 a, D C 7 17 CD 0.5 cm, F ( 1) By = 7 q4 24 E I () ( 2) A = M 3 E I ( ) C y = M2 16 E I ( ) 147

159 ( 3) C x = q4 24 EI () ( 4) Bx = qr4 2 EI () 7 2 ( 1) D x = 3.83 E A ( 2) Gy = 123 E A () 7 4 B y = q4 8 E I () P a() CD = P E A ( ) 7 5 Cy = 2 () 3 EI C = 1 3 E I ( ) 7 6 B = 19 8 E I ( ) 11 q4 7 7 B y = 120 E I () 7 8 A x = 7 q4 () 24 E I Ay = 5 q4 8 E I ( ) 7 9 A = 0.45 E I ( ) 7 10 C x = () D = EI EI ( ) Pa 2 6 E I ( ) 2 P a 3 24 E I ( ) 7 12 D x = 0.52 mm () 7 13 D x = 165 () 7 14 Ey = 10 t() 7 15 C x = 2 cm() C = rad ( ) 7 16 D y = 0.01 a() C = 0.01 rad ( ) 7 17 Fx = cm () 148

160 8 1,,,, 8 1 ( a),, 8 2 (a),,, ,, 8 3 (a), B, 8 3( b ),,, 8 1( a), B C, 8 1 ( b), ( c), 8 2 (a),, 8 2( b),,, 149

161 8 1, 8 1( b), (c) X1, 8 2 ( b) X1, X2, X3 X4 8 3,, : ;, :,,,,, : (1 ) : (2 ) ( ) : (3 ) : () 8 2,,, ;,,,,,, : (1), ( 8 4(a), ( b), (c), ( d) )

162 (2 ), ( 8 5 ( a), ( b ), (c), ( d) ) 8 5 (3 ), ( 8 6 (a), ( b ), (c) ) 8 6 (4 ) ( ), ( 8 7 (a), ( b ) ) 8 7, 8 8 ( a), 151

163 , ( b ), 8 8,,,, 8 8 ( c),, 8, : (1 ) 8 1 ( a), (2 ) 8 9 (a), ( 8 9 ( b ) ), ( 8 9 (c) ),, (a), ( 8 6 )n, 3 n8 10 ( a) 34 = 12,, 8 10 ( b), 3 4,,, h, h, 3 n - h8 10( c)34-4 = 8, W,, = - W 8 4( c), ( 2-1 ) W = 3 m - ( 2 h + r) = =

164 , (a) 11 (a),, B, X1, 8 11 ( b ), X1, P X 1,, 8 11 ( b) X1,,, ( ), 8 11 ( b) 8 11 ( a), X1?, X1, X1,, X1 ( ), X1, 8 11 (a), B Y B, B ( b ), X1, B B 1 P ( 8 11( c) )X1 11 ( 8 11 ( d) ) 11 1 P, B, X1 Y B,, : X1 1,, 1 = P = 0 (8 1) 1 X1 X1 ; 153

165 ( d) ) ; 11 X1 X1 ( P X1 ( 8 11 (c) ) 1, 11, 1 P X1, 8 11 ( a) ; ( b) ; (e) M P ( f ) M 1 ; ( g) M ; ( h ) Q, 1 1 X1, 1 1 = 11 X1 (8 2) 11 X1 = 1 X1 (8 2 )( 8 1) 11 X1 + 1 P = 0 (8 3), 1 1, 1 P,, ( a), 11 1 P,

166 M P ( 8 11 (e) ) X1 = 1 M1 ( 8 11 = 0 2 MR1 EI 1 P = 0 (8 3 ) MR1 E I 11( f) ),, ds = y C EI M P d s = y C E I = 1 EI ( ) = 3 = - 3 X1-5 P3 3 EI 48 EI = 0 X1 = 5 16 P() 3 EI 1 EI ( P 5 6 X1, 8 11 ( g)( h) M1 X1 ) = - 5 P3 48 EI M = MR1 X1 + MP (8 4) = 1 ; MP 8 4, 8 12 (a) B X 1 X2, 8 12( b ) 8 12 (a) ; ( b ) X2 X1 X2,, B X 1,, 1 = 0 2 = 0 (8 5) 1 X1, X2 X1 ; 2 X1, X2 X2 155

167 , ( 8 5) = P = 0 2 = P = 0 (8 6),, 1 1 = 11 X1, 12 = 12 X2, 21 = 2 1 X1, 22 = 2 2 X2, ( 8 6) 1 1 X X2 + 1 P = X X2 + 2 P = 0 11, 21 X1 = 1 X1 X2 ; 12, 22 X2 = 1 X1 X2 ; 1 P, 2 P X1 X2 (8 7) (8 7 )X1 X2,,,, : M = MR1 X1 + MR1 X2 + MP (8 8) M1, M2 M P X 1 = 1, X2 = 1, 8 12 ( a), 8 12( b ), 8 13( a)( b ), ( 8 3), X1 X2,,, 8 13 (c),, 8 13 n, n,,, n, n, n 156

168 11 X X i X i n X n + 1 P = 0 21 X X i X i n X n + 2 P = 0 n1 X1 + n2 X2 + + ni X i n + + nn X n + n P = 0 (8 9) :,,, 11, 2 2,, nn, i j ( ij),,,, ij j i, ij = ji ( i j), i P,,,,, ii = MRi 2 EI i j = MR i M R j EI ip = MRi M P E I d s + K Qi 2 GA ds + Ni d s + K Q i GA Q j 2 EA ds d s + Ni N j E A d s K Qi QP d s + GA d s + Ni N P E A d s,, X1, X2 ( 8 10),, X n,,, M = MR1 X1 + MR2 X2 + + MRn X n + Mp Q = Q1 X1 + Q2 X2 + + Qn X n + Qp ( 8 11) N = N1 X1 + N2 X2 + + Nn X n + N p Mi, Qi, Ni Xi = 1 ; MP, QP, N P (8 11),, Q, N,,,, ;, ; (a),, B, X1 X2,, 8 14( b)b, 11 X X2 + 1 P = 0 21 X X2 + 2 P = ( 8 12)

169 ,, X1 = 1, X2 = 1, 8 14 ( c), ( d), ( e), 11 = MR1 2 EI 22 = MR = EI d s = 1 EI ( ) EI ( 2 ) = EI d s = MR 1 M2 21 = EI 1 P = MR1 M P d s = EI EI ( ) = 3 6 EI d s = EI ( ) = EI 1 EI ( q2 3 4 ) EI ( 1 2 q2 ) = - 3 q4 8 EI 2 P = MR2 M P d s = EI 1 2 EI ( q2 ) = q4 8 EI 8 14 ( a) ; ( b) ; ( c) M 1 ; ( d) M 2 ; ( e) M P ; ( f ) M,, 158

170 5 6 X1-1 4 X2-3 8 q = X X q = 0 X1 = 9 22 q, X2 = q(),, : M = MR1 X1 + MR2 X2 + MP M AC = 9 22 q - ( q) q2 = 1 22 q2 ( ) 8 14 (f),,, : (1 ) (2 ),, (3 ) (4 ) (5 ), (6 ), (a)ei = (1 ), (2 ) A, B B,, 8 15 ( b ) (3 ) A, B B, 11 X X X3 + 1 P = 0 21 X X X3 + 3 P = 0 31 X X X3 + 3 P = 0 (4 ) ( ) X1 = 1, X2 = 1 X3 = 1, M1, M2 M3 ( 8 15 (c), ( d), (e) ),, MP ( 8 15( f) ), 11 = 1 EI ( ) = 3 EI 22 = 1 EI ( ) = 3 EI 33 = MR2 3 EI d s + N2 3 EA d s = 0 + E A = E A 159

171 8 15 ( a) ; ( b ) ; ( c) M R 1 ; ( d ) M R 2 ; (e) M R 3 ; ( f ) M P ; ( g) M ; ( h) Q ( M3 = 0, ) 12 = 21 = - 13 = 31 = 0 23 = 32 = 0 1 EI ( ) = - 1 P = 1 EI ( q2 ) = q 3 24 EI 2 P = - 3 P = 0 6 EI 1 EI ( q2 ) = - q 3 24 EI (5 ),, 2 X1 - X q2 = 0, 160 X1 = - - X1 + 2 X2 - E A X 3 = q2 = q2, X2 = 1 12 q2, X3 = 0

172 , E I,,, E I, E I (6 ) M = M R1 X1 + M R2 X2 + M R3 X3 + MP, 8 15 ( g),, 8 15( h ) (a), E I = (1 ) (2 ), B, C, 8 16 ( b) (3 ) B, C, 11 X X2 + 1 P = 0 21 X X2 + 2 P = 0 (4 ) ( ) X1 = 1, X2 = 1, M1, M R2 M P ( 8 16( c), ( d), ( e) ), E I = 1, 11 = 22 = = = 21 = = P = q = 1 12 q3 2 P = q q = q3 (5 ) 2 3 X X q3 = X X q3 = 0 X1 = q2, X2 = q2 ( 6) M = MR1 X1 + MR2 X2 + MP 8 16 ( f), 8 16( g) (a) E A (1 ) (2 ) CD, X1, 8 17 ( b) (3 ) CD, 11 X1 + 1 P = 0 (4 ) X1 = 1 161

173 8 16 N1 NP, 8 17( c), ( d ): 11 = N1 2 EA ds = N1 2 EA = 1 EA 1 1 a4 - ( 2 ) 2 2 a2 = 4 (1 + 2 ) a EA 162

174 8 17 ( a) ; ( b) ; (c) N 1 ; ( d ) N P ; ( e) N N1 NP 1 P = 2 (1 + 2 ) EA E A = 1 EA 1 Pa2 + ( - 2 ) ( - 2 P) 2 a = P a (5 ),, X1 = - 1 P = P ( ) (6 ), N = N1 X1 + N P, 8 17 (e) (a): A B: E I = knm 2 AD, BD: E A = kn CD: E A = kn (1 ) (2 ) CD, X1, 8 18 ( b) (3 ) X1, 11 X1 + 1 P = 0 (4 ),,, X1 = 1 M1, N1, MP N P 8 18 ( c), ( d ), 163

175 8 18 ( a) ; ( b ) ; ( c) M R 1, N 1 ; ( d) M P, N P ; ( e) M ( kn m ) ( f) N ( k N ) 11 = MR2 1 EI d s + N2 1 EA = 1 ( ) ( ) = P = MR1 M P EI d s + N1 N P E A = ( ) ( ) 180 = (5 ), X1 = - 1 P = (6 ), m = kn M = MR1 X1 + MP N = N1 X1 + NP M 8 18 (e), N 8 18( f) (7 ) : 8 m/ kn 18 (e)m, AB CD kn, knm 180 knm, 50%, EA0, X1 0, 164

176 8 19 ( a ), E A, X1 165 kn, C,, 8 19 ( b ), ( ), 8 20 ( a) (),,,,, 8 20 ( b) 8 20,,, (a), (1 ) (2 ) CD X1, 8 21( b ) (3 ) 11 X1 + 1 P = 0 (4 )M1, MP 8 21 (c), ( d) 11 = 2 EI ( ) E I ( ) ( ) + ( 1 2 ( ) = 96 E I 69) 8 19 ( a) M 0 ( k Nm ) ; ( b ) M ( kn m ) 165

177 8 21 (a) ; ( b ) ; (c) MR ( m ) ; ( d ) M P ( k Nm ) ; ( e) M ( kn m ) 1 P = 1 E I ( )( ) E I (5 ), ( )( ) + ( ) ( ) = E I x1 = - 1 p = kn 11 (6 )M M = M R1 X1 + MP, 8 21( e), 8 6,, ; ( E I, E A, GA ),,,,, 8 22 (a),, ( 8 166

178 22 ( b ) ): X1, X2, X3 : X1 X2 X3,,, ;,,, ( 8 22(c), ( d), ( e) ), X1 X2, M1, M2 X3, M3,, M1, M2 M3,, 13 = 31 = 0, 2 3 = 32 = X X2 + 1 P = X X2 + 2 P = X3 + 3 P = 0 ( 8 13),,, 8 22 ( a) ; ( b) ; (c) M 1 ; ( d) MR 2 ; ( e) MR 3,, ( 1) : 8 23( a) MP ( 8 23( b ) )M3, 3 P = 0 167

179 ( 8 13 ),, X3 = 0 X1 X2, 8 23,,, ( 2) : 8 24( a) MP ( 8 24( b ) )M1, M2, 1 P = 0, 2 P = 0 ( 8 13), X1 = 0, X2 = 0X3, 8 24,,,,, (1 ),, ( 8 25 ) (2 ),,,, (a) P 168

180 P ( 8 25 ( b) ) ( 8 25( c) ) 8 25 ( a) ; ( b) ; (c) (1 ),, CD,,, (2 ), 8 26 (a ), ; X1 X1, 11 X1 + 1 P = M1, MP ( 8 26 ( b), ( c) ),, : 1 1 = 2 EI 1 P = 2 EI ( = EI P 1 2 = P3 4 EI X1 = - 1 P = P 169

181 M ( 8 M = MR1 X1 + M P 27),, 1. (1 ) : 8 28 (a), 8 27,, ;, :,,,,, 8 28( b ) (2 ) : 8 29 (a),,, ;,,,,, 8 29 ( b ) (1 ) : 8 30 ( a),,,

182 K ;,,,, 8 30 ( b ) (2 ) : 8 31 ( a),, I 2, ( 8 31( b ) ),,, QK, 8 31( c), QK,, QK,, 8 31( d) 171

183 (a)ei = 8 32 ( a) ; ( b ) ; ( c) ; ( d) M 1 ( m ) ; ( e) M P ( k Nm ) ; ( f) M ( kn m ) 172

184 ,, 8 32 ( b ) 8 32 ( b), C 8 32 (c) M1, MP ( 8 32 ( d), ( e) ), 11 = 1 EI 1 P = - 1 EI ( ) = 72 EI ( ) + ( ) = EI X1 = - 1 P = = 12.5 kn M = M R1 X1 + MP M, M 8 32 ( f) 8 7,,,,,,, 8 33 (a), t1, t2, 8 33 (a) ; ( b) B, X1, X2 X3 8 33( b) 11 X X X3 + 1 t = 0 21 X X X3 + 2 t = 0 31 X X X3 + 3 t = 0 1 t, 2 t, 3 t X1, X2 X3, 173

185 it = t0 N + t h M R,,, M = MR1 X1 + MR2 X2 + MR3 X3 ( 8 14) (a)10 C,,, EI h (1 ) (2 ) 8 34( b ) (3 ) 8 34 ( a) ; ( b) ; (c) M R 1, N 1 ; (d ) M 1 1 X1 + 1 t = 0 (4 ) M1, N1 ( 8 34 (c) ), 11 = 2 EI 1 t = = EI t0 N 1 10 (1 + h ) + t h M R 10 = = h (5 ), 174 X1 = - 1 t = - 15 E I ( h )

186 (6 )M M = M R1 X ( d), E I, 8 8,,,,,,, 8 35 (a) 8 35 ( a) ; ( b ) ; ( c) ( b), 11 X X2 + 1 C = 0 21 X X2 + 2 C = 0 35 (c), 11 X X2 + 1 C = C1 21 X X2 + 2 C = C3,,, 1 C, 2 C X1, X2 ic = - Ri Ci (a), A, EI = (1 ) (2 )8 36( b ) (3 ) 11 X1 + 1 C = 0 (4 )M1 ( 8 36 ( d) ), 175

187 11 = 1 EI ( ) = 3 3 EI 1 C = - Ri Ci = - ( ) = ( a) ; ( b ), ( c) ; ( d) M 1 ; ( e) M ; ( f ) M 1 (5 ), X1 = - 1 C = 3 EI 11 2 ( 6) M M = M R1 X1 M ( 8 36 (e) )8 36 (c), 1 1 X1 = (, )M1 ( 8 36 ( f) ), M ( 8 11 = 1 EI ( ) = 3 EI X1 = 3 EI 36( e) ) ( a), B, k = 10 E I 3, (1 ): B, X1, 8 37 ( b) B,, B = 1 k X 1 B, X1 + 1 P = - X1 k

188 X1, ( ) X1 + k 1 P = 0, 8 11 = 1 EI ( ) = 3 3 EI 1 P = - 1 EI 37( c), ( d) ; 1 2 P = - 5 P3 48 EI X1 = 5 Pk 16 (3 EI + k 3 ) = P () ( 8 37( e) ) M = MR 1 X1 + MP 8 37 ( a) ; ( b ) ; ( c) M 1 ; ( d) M P ; ( e) M ; ( f) ; ( g) M 1 ; ( h) M P (2 ): A A X1, 8 37 (f)b, 177

189 11 X1 + 1 P = 0, P, 8, 11, 1 P 1 1 = 1 EI ( ) - ( k ) = EI 1 P = 1 EI ( P 1 2 ) - ( - 1 P 2 k ) = 9 P2 80 EI 8 X1 = - 1 P 11 = P 37 (e) 37 ( g ), ( h ) 8 9,,,,,, K = MRi M P ds + E I K Q i QP GA d s + Ni N P E A d s + t0 Ni d s + t h M Ri d s - Ri Ci, Mi, Qi, N i Ri P = 1 MP, QP, N P t0,t, Ci,,, P = (a) B M 8 38 ( a), B, 8 M( 8 38( b), B M = 1, 38 ( b) ) 8 B = 1 EI 1 2 EI 10 q EI ( q2 ) 1 - ( q2 ) 1 + ( q2 ) 1 - ( q2 ) 1 = - q 3 88 EI = 7 q3 264 EI 38 (c), ( ) 178 B = 1 EI ( q2 ) ( q2 ) =

190 8 38 ( a) M ; ( b ) M; ( c) M, q 3 24 EI - q 3 66 EI = 7 q3 264 EI ( ) (a) M 8 36 (e), (1 ), 8 39 (a) M = MR M P E I 1 EI d s - Ri Ci = E I 2-0 = 3 () (2 ), 8 39 ( b) M = MR M P EI - d s - Ri Ci = 1 EI ( ) ( 5 6 3E I ) - ( -, 1 2 ) = 3 ()

191 8 10,,,,,, 8 40( a) ( 8 40 ( b), ( c), ( d) ) 8 40 (a ) ; ( b ) M ; ( c) Q ; ( d ) N ; ( e) C ; ( d),, C( 8 (8 X = 3 22 q q = 0 Y = q q = 0 MC = 1 11 q2-40( f) ) 1 11 q2 = 0 40 (e) ) 180

192 MB = 1 11 q q q2 = 0 X = 3 22 q q = 0 13 Y = q - 22 q q = 0,,,,,, Xi, 8 41 (a) 8 40( a) M A A H, 8 A H = 1 EI 1 2 EI 41 ( b) M, M ( q2 2 3 ) - ( q2 1 2 ) + ( q2 2 3 ) - ( q2 1 3 ) = ( a) M ; ( b ) M, n n,,, n,, Xi, 8 42 (a) AB CD,, M 1( 8 42( b) ), i = MR i M P d s = EI M P E I d s = 0 181

193 8 42 ( a) M ; ( b ) M M EI,, M, M EI 8 11, (1 ),,,,,,, (2 ), ;,, (3 ) :,, ;,,,, (4 ) 8 43 ( a) ( b ),,,

194 , 183

195 E A =

196 ,

197

198

199 8 9 ( E A = ) , E I,, h = (1 ) (2 )A A 10, 8 11, 10 C, E A, , A A,, M a, I = 7114 cm 4, E = kn/ cm 2, = 10 m, P = 50 kn, B? M EI =, k = EI a 3 * 8 15 A B 0.5 cm,, 188

200 EA = kn K M ( E I = ) M ( a) MBC = 15.7 knm ( ) ( b) MBA = 6.64 knm ( ) ( c) MDB = 20 knm ( ) ( d ) MC D = 77 knm ( ) ( e) MC D = 7.2 knm ( ) ( f) MCD = 1 2 P ( ) 8 3 ( a) MBE = 5 knm ( ) ( b) MD E = 1 20 q2 ( ) 189

201 ( c) MBC = 76 P ( ) 191 ( d ) MAD = 3 p ( ) ( a) NCD = P() ( b) NDE = P() 8 5 ( a) NCD = kn( ) 8 19 ( b) MDB = 1 3 p( ) 8 6 ( a) MAC = knm ( ) ( b) MA D = q2 ( ) 8 7 ( a) MAC = 11.1 knm( ) ( b) NDE NFG = kn = kn 8 8 ( a) MDE = 2.56 knm ( ) 190 ( b) MBC = 5 Pa ( ) 24 ( c) MB A = 1 9 q2 ( ) ( d ) MAC = 3 P ( ) 28 ( e) MC = PR (- 2 ) ( ), MB = PR ( ), 2

202 ( f) MCA = 1 4 P ( ) ( g ) MCA = 60 knm ( ) ( h) MBA = 1 4 Ph ( ) 8 9 ( a) N2 5 = P () ( b) N36 = N38 = 5 51 P () 8 10 MCB = 480 E I 8 11 NDE = 1.41 E A () 8 12 MAB = 3 E I A ( ) cm ( ) A = 60 () 8 14 MAB = 5 Pa ( ), P () 8 15 N AB = 62.5 kn () 8 16 K y = 13.5 E I ( ) 8 17 = 3 16 A ( )

203 9 1,,,, 9 1( a), X1 P = 1, X1 X1, 9, 1 ( b),,, P = 1 X1, X1 9 1(c), 11 X1 + 1 P = 0 X1 = - 1 P 1 1 (9 1) 1 P P = 1 x, X1, 9 1 ( d) ; 11 X1 = 1, X1, 9 1 (e) P = 1, X1 (9 2 )( 9 1), P1 X1 9 (9 1( e) = 1, 1 P = P1 (9 2) X1 = - P1 1 1 (9 3) = 1, P = 1, 3 ), 11,, P1 P = 1, P = 1 x,, X1 x, X1 188

204 X1 ( x) = - P1 ( x) 1 1 x, X1 ( x) X1 (9 4) X1 ( x) P1 ( x), P1 ( x) 9 1 ( e)x1 = 1 X1, X1 = 1, X1 = 1 11, X1 P1 ( x) P = 1, P = 1,, P1 ( x) ; (9 4 ), X1 ( x) P1,, X1 ( x) (1 ), 9 2( b ) (2 ) m1, MP, 9 2( c), ( d) (3 ) 1 1 P1 (4 ) 1 1, P1 ( = m1 2 EI d s = 3 3 EI P1 = 1 P = m1 M P d s = - EI 4) X1 = - P1 ( x) 1 1 = x2 ( 3 - x) 2 3 x 2 (3 - x) 6 EI X1 X1 ( 9 2 (e) ) 189

205 (9 4 ), 11 = 1, X1 P1 X1 X1 = - P1 ( x), P1,,,,,,,,,,,,,,, 9 3 ( b), ( c), ( d), ( e) ,,,,,,, ( ), 190

206 ,, ( S = qw ),, ;,,,, 9 4, 9 4,,, 9 4,,,,, QK,,,,, 191

207 ,,,,,,,,,, ( a), q = 20 kn/ m, p = 40 kn/ m 9 5 Mq ( 9 5 ( b ) ) Mp1, Mp2, Mp3 ( 9 5 (c), ( d), (e) ) 9 5( b ) 9 5 (c), ( d), ( e) (), ( )1, M1 ( max ) = ( ) = knm 192

208 M1 ( mi n) = ( ) + ( ) + ( ) = knm,,,, 9 5 (f), ( 9 6 ( a) ) ( 9 6( b), (c), ( d) )9 6( a) 9 6 ( b), ( c), ( d) (), ( )1, M1( max) M1( min ) = ( - 72 ) + 4 = - 68 kn = ( - 72) + ( ) + ( - 12) = kn,,,, 9 6 (e) 9 6 * 9 3 ( 9 7), 9 8,,,,,, 9 9 P, 193

209 , A, B, C, D,,, 9 9 9( b ),,, 9( c), 11 X1 + 1 P = m1, MP ( 9 9( d ), (e) ), 11 = EI 1 + X1 = EI2, 1 P = - 3 I1 2 P I I2 1 3, M 3 P2 48 EI ,,,, 194

210 E I,, q kn/ m 2 () 9 10 P = q ( b) x, 1, 2, 3, 4, X1 ( ) : 5, 6, X2 11 X X2 + 1 P = 0 21 X X2 + 2 P = 0 m1, m2 MP 9 10 (c), ( d), ( e), A B, CD, G H, I J, A B G H, 2 EI 11 = =

211 EI 2 2 = EI 1 2 = = EI 1 P = EI 2 P = P 3 2 P P = P P = E I 26 X X2-10 P = P3 2 = X X2-5 P = 0 X1 = 75 P, X2 = P X1 X2 G H, I J, A B(CD) E F P - X1 = P, P - X2 = P,, M = m1 X1 + m2 X2 + MP, 9 10 ( f) 9 4, ( 9 11( a) ) ; ( 9 11 ( b) ) ;,, ( 9 11( c) ) 9 11, (f) ( d ), (e ), ( f )

212 ,,,,,,,,,,,,,,,, 9 12,, I = IC [ 1 - ( 1 - n) x 1 ] cos ( 9 5) Ix ; ; IC ; 1 ; 9 12 n, (9 5 )n, I A n= 1, I = IC cos (9 6) bh, b, h h = hc 3 cos A = AC 3 cos A = AC cos (9 7), 1% f < 8, cos 1, A = AC =,,,,, 197

213 9 5 ( 9 13 ( a ) ),, I = ICcos (9 8) 9 13, f < 4, (9 6 ) I = IC cos ( ( b), B 11 X1 + 1 P = 0 (9 9) 8 ), f < 5 11 X1 11 = m2 1 EI ds + n2 1 1 P = m1 M P d s E I EA ds = 1, m1 = - y, n1 = cos, MP M 0 MP = M = y2 EI d s + cos2 EA d s,, 11 1 P 1 P = - ym0 EI d s 198

214 X1 = H = - 1 P = 11 ym0 EI d s H,, M = M 0 - H y Q = Q 0 cos- y2 EI d s + cos2 E A ds ( 9 10) Hsin N = Q 0 sin+ Hcos ( 9 11) (a),, H I x = IC cosix = IC cos, y = 4 f x( - x), f > 2 5 (9 f > 8 ) 1 1 = y EI d s = y 2 cos d s = 0 E I C 1 EI C 4 f x( - x) 0 2,, 2 1 EIC 0 y2 d x = d x = 8 f2 15 EI C 1 P M ( b),, 2 M 0 = Px 0 < x 4 M 0 = P 4 1 P = H = - 1 P = < x 2 ym 0 cos d s = - E I C 4 1 EI C 0 ym 0 d x = 2 yp x d x EIC 0 +yp 4 4 xd x = - 19 P f EIC 8 f 2 15 EIC 2 = P f 19 P f EIC 9 14, H, f/,, 9 15,,, X1, 11 X1 + 1 P = P,,,

215 11 = n2 1 E A + m2 1 1 P = n1 N P EI d s E A + m1,,, 9 EI M P d s 16 (a ), 9 16 ( b) E1 A1 X1 11 = m X1 + 1 P = 0 d s E I + n2 1 d s 1 P = m1 MP E I = 1 d s E A + E1 A1 m1 = - y, N1 = cos X1 = y2 d s ymp EI d s E I + cos2 d s E A + E 1 A1,, E1 A1, 9 6, = 3 1 = 0 23 = 3 2 = 0 17 ( a ),

216 12 X X2 + 1 P = 0 21 X X2 + 2 P = 0 31 X1 + 3 P = 0 ( 9 12) 12 = 21 0, 12 = 21, 12 m1, m2, m1 m ( a), 9 18 ( b),,,, 9 18 (c), (9 12 ), O, x, y,, X1 = 1, X2 = 1, X3 = 1, m1 = 1, Q1 = 0, N1 = 0 m2 = y, Q2 = sin, N2 = cos m3 = x, Q3 = cos, N3 = - sin ( 9 13), x, y,, 12 = m1 m2 21 = EI ds + n1 y E I d s = y1 n2 EA d s + Q1 Q2 K - ys EI GA d s = d s d s = y1 E I - d s ys E I = 0 201

217 , ( 9 12 ) d s y1 EI ys = d s E I 11 X1 + 1 P = 0 22 X1 + 2 P = 0 33 X1 + 3 P = 0 ( 9 14) ( 9 15) 1 EI ( 9 19 ), d s, ( 9 E I 14) E I,, 9 19,,, ,,, , ( 9 15 ), 202

218 ii = mi 2 X1 X2 X3 EI d s + ni = - 1 P 1 1 = - 2 P 2 2 = - 3 P EA d s + k Qi 2 i P = mi M P d s E I + ni N P GA d s E A d s + k Q i QP GA d s ( 9 16) ( 9 17), 9 1, 9 1 ii, i P f h C P 2 P 3 P f < 1 5 f > < h C < 10 h C < hc > h C < M M, N M M M, N M M M M M M M M M, N, Q M, Q M M M M M M M M M, hc <, f <, 22, = m1 EI d s = 1 EI d s 2 2 = m2 2 EI d s + n2 2 EA = y2 EI d s + cos2 E A d s 3 3 = m3 EI d s = x2 EI d s m1 MP 1 P = E I m2 MP 2 P = E I m3 MP 3 P = I = IC/ cos, A = AC/ cos E I d s I d s = MP E I d s d s = ym P E I d s d s = xmp E I d s = d scos = d x I C I C d s A = d scos = d x A C A C 203 ( 9 18)

219 , ys = 1 EIC y1 d x 1 d x EIC EIC 11 = d x = y1 d x = d x y1 d x = ( 9 19) E I C 22 = y2 d x + E I C 33 = x2 d x E I C 1 P = MP d x E I C 2 P = ymp d x E I C 3 P = xm P d x IC A C cos2 d x ( 9 20) ii 1 P, ( 9 18 ),, M = x1 + x2 y + x3 x + MP Q = x2 sin+ x3 cos+ QP ( 9 21) M P, QP, N P N = x2 cos- x3 sin+ N P,,, ( ), b Fd s, [ a, b], 9 a 22 (a), s = b - a h F 0, F1,, Fn,, n, b Fd s = s( 1 a 2 F0 + F1 + F2 + + Fn Fn ) ( 9 22)

220 , n 2, 9 n b a 22 ( b ), Fd s = s 3 [ F ( F1 + F3 + + Fn - 1 ) + 2 ( F2 + F4 + + Fn - 2 ) + Fn ] ( 9 23),,,, 812, (a)y1 = 4 f 2 x 2, hc = 0.6 m, b= 1 m I = IC/ cos, A = AC/ cos (1 ) 9 = 1.5 m, 1) : y ) (9 19) ys y1 y1 d x = ( b ) 8,x = 4 f x 2 = x 2 = x = [ 32.00] 12 = 1.33 m x y1 d x = [ ( ) ( ) ] = ) : y = y1 - ys = y1-1.33, 9 2 [32.00 ] 4) (9 20) 9 2 EI C 1 1 = d x = = 12 EIC 22 = y2 d x + I C A C cos2 d x = 205

221 x m y 1 m [ 34.40] [16.696] = = EIC 33 = x2 d x = 1.5 [288 ] = y = y 1 - y 0 m tan sin cos x2 m 2 y 2 m 2 M P / ( knm) cos 2 x M P - 7 x 2-50 kn ( x - 3) ym P kn f = 1 3 > 1 5, / = 1.45%, MP 5) : MP = qx 2 = - 7 x 2, - 6 x 0 MP = 0, 0 x 3 MP = - 50( x - 3 ), 3 x 6 EI C 1 P MP =d x = 1.5 [ ] = EI C 2 P = 1.5 ymp d x = [ ] = EI C 3 P = xm P d x = 3 X1 X2 = - 1 P = = - 2 P = 22 (2 ) ( 9 21 ) 206 X = - 3 P = [2 286] = 1143 = 60.8 knm = 50.4 knm = knm

222 M = X1 + X2 y + X3 x + MP = y x + MP Q = X2 sin+ X3 cos+ QP = 50.4sin- 7.9cos+ QP N = X2 cos- X3 sin+ N P = 50.4cos+ 7.9sin+ N P M P, QP N P QP = - qx cos= - 14 xcos, - 6 x 0 QP = 0, 0 x < 3 QP N P = - Pcos= - 50cos, 3 < x 6 = qx sin= 14 xsin, - 6 x 0 N P = 0, 0 x < 3 N P = Psin= 50 sin, 3 < x 6 9 3, 9 4, ( 9 24 ) M x/ m y/ m X 1 knm X 2 y k Nm X 3 x knm MP/ ( knm) - 7 x 2-50( x - 3 ) M knm

223

224 9 4 Q N x m sin cos14x Q Q P / kn sin cos - 14x- 50 kn kn cos cos Q kn 50.4 cos kn 7.9 sin kn N N P / kn 14x 50 sin sin N kn * 9 8,,,,, 9 25 ( a), y1 = 4 f 2 x 2, I = IC cos A = AC cos, (1 ) ( 9 19 )ys, (2 ) ys y1 d x = = f 0 2 x 2 d x y = y1 - ys = 4 f 2 x 2 - (3 ) P = 1, X1 X2 = - 1 P 1 1 = - 2 P 2 2 f 3 = f 3 209

225 3 = - 3 P 3 3 ( 9 24) f > 1 5, ( 9 22 ) EI C 1 1 = d x = EIC 22 = EIC y2 d x = f = x2 d x = ( y1 - ys ) 2 d x = 2 x 2 d x = 3 12 P = 1 d ( 9 25 ( b ) ), M P = 0, - 2 x M P (9 = - ( x - ), x 2 20) EIC 1 P = M P d x = EIC 2 - ( x - ) d x = - 2 ( ) ymp dx = 2 P = 2 EIC 3 P = = - 3 ( ) (9 - ( 4 f x f 2 ( ) xm P d x = (9 X1 X2 X3 f 3 ) ( x - ) dx = 2 - x( x - ) d x 20) = - 1 P = ( ) = - 2 P = ( 1 + ) f ( 15 = - 3 P = ) 9 25 ( 9 25) 25) P = , 210 X

226 , 9 25 (c), ( d), (e)8 K (9 21), MK = X1 + X2 ( yk - ys ) + X3 XK + MK P QK = X2 sin K + X3 cos K + QKP N K = X2 cos K + X3 sin K + N K P yk X 1, Y1 MK P, QK P, N KP (9 = 12 m, f = 4 m, x K = - 3 m, 23 ) 9 yk 26 = ( - 3 ) 2 = 1 m ys = f 3 = 1.33 m tan K = y= 8 f x = ( - 3) 2 = K = sin K = cos K = MK = X X2-3 X3 + MKP QK = X X3 + QK P N K = X X3 + N KP 9 5,

227 9 5 MK P = 1 X1 X2 X X3-3 X3 M 0 K MK QK N K P = X X 3 Q 0 K Q K X X 3 N 0 K N K

228 A A H, V A M A H = X2 V A = X3 + V AP ( 9 26) M A = X1 + ( f - ys ) X2 + XA X 3 + MAP V AP, MAP A K (9 M A = X1 + ( f - ys ) X2-2 X3 + MP = 26) A 9 X X2-6 X3 + MP 27( d ), (e), (f) , 213

229 9 7 H, V A, MA P = 1 H = X2 X3 V AP V A X X2-6 X3 M 0 A MA

230 9 9,,, ( ) t2,, 1 1 X1 + 1 t = X1 + 2 t = X1 + 3 t = 0 ( 9 27), t1, t2 ( 9 28( a) ), > t1, t t t = 1 2 ( t1 + t2 ), t = t2 - t1 (9 27), 1 t = 2 t m2 d s h - t n2 d s 9 28, 3 t = 0 m1 = 1, m2 = y, N2 = cos, 1 t = t d s h 2 t = t y d s h 11 = d s EI - t cosd s = t y d s h - t 22 = y2, d s E I + cos2 d s E A 215

231 X1 = - X2 = - X3 = 0 t d s h d s EI t yd s h y2 d s E I - t + cos2 d s E A ( 9 28), : t1 = t2 = t, t = 0 X1 = 0 X2 = - X3 = 0 y2 t d s E I + cos2 d s E A ( 9 29),,, 0.025%, t , = , 25,,,, , 9 29( a) A a, b,, 11 X1 + 1= 0 22 X2 + 2= 0 33 X3 + 3= 0 ( 9 30) 1, 2, 3 X1, X2, X3,, 9 29 (c), ( d), (e), i= - Ri C 1= - ( - 1 ) = 2= - [ - 1 a - ( f - ys )] = a + ( f - ys ) 3= - ( - 1 b + ii, 2 ) = b

232 X1 = - X 2 = - X 3 = = - d s E I = - = - y2 b - x2 a + ( f - ys ) d s E I + cos2 d s E A 2 d s E I ( 9 31),, E I = 217

233 (1 ) MB : ; 4,, (2 ) MK, ( :, M = m1 X1 + MP M K = mk1 MB + MK P, mk1 = 1/ 2, MB (1 ), MK P ) RB, MA, MC, MK, QK, QB, QB q= 10 kn/ m, p = 20 kn/ m, E I = 9 3 * , E I, P, y = 4 f 2 x( - x), Ix = IC cos, E IC = knm2, E1 A1 = kn, K 9 7 H, 0 = y1 = 4 f 2 x 2, A = AC cos, I = m, f = 3 m, hc 218 IC cos, = 18 = 0.6 m,,,