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,,,, :, ;, ;, ;,,,,,,,, ( 3, 6, 7 ), ( 1, 4 ), ( 8, 10 ) ( 5, 9 ) ( 2 ),,,,,,,,, 2001 6

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1 1. 1 1 1. 2 2 1. 3 8 2 10 2. 1 10 2. 2 11 2. 3 13 2. 4 17 18 18 18 3 21 3. 1 21 3. 2 22 3. 3 27 3. 4 38 3. 5 43 3. 6 55 3. 7 73 75 75 77 4 86 4. 1 86 4. 2 87 4. 3 93 4. 4 95 1

. 5 100 4. 6 104 4. 7 107 110 110 111 5 116 5. 1 116 5. 2 118 5. 3 122 5. 4 128 5. 5 131 5. 6 134 5. 7 135 5. 8 139 146 146 148 6 153 6. 1 153 6. 2 153 6. 3 156 6. 4 166 180 180 182 7 186 7. 1 186 7. 2 186 7. 3 190 7. 4 202 205 205 207 8 210 8. 1 210 8. 2 212 2

. 3 219 8. 4 224 8. 5 231 235 235 235 9 238 9. 1 238 9. 2 239 9. 3 241 9. 4 244 9. 5 246 250 250 251 10 254 10. 1 254 10. 2 258 10. 3 263 274 274 275 278 286 3

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

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

1 2 ), 1 ),,,,, ( ),,,,,,,,,,, 1. 1( a), ( b) 1. 1,,,,, 1. 2 ( a), ( b),,, 2 ) 1. 2,,,,,,,, 3 ) : ( 3

( ), 1. 3( a) :, ; F Y, 1. 3 ( b),,, 1. 3 1. 4 1. 4( a) :,, ; F Y, F X, 1. 4 ( b),,, 1. 5( a), ; M F Y, 1. 5 ( b) 1. 6( a) : ; F X, F Y M, 1. 6( b), ( c) 1. 5 1. 6 1. 7( a) :, ;,, 1. 7 ( b),,,,,,,,,, ;, 4

1. 7 4 ),,,,,,,,,,,, 1. 1 1. 8 ( a),,,,, 1. 8 5

1 ) 1. 8( a),, :,,,,,,,,,,,,,,, ( 2 ),, ( 3 ),,,,, ( 4 ),,,,,,, ;,,, 1. 8( b),,, 1. 2. 2, : ( 1 ) 1 ),, 1. 9 ( a ), ( b) 6

1. 9 2 ), ( ), 1. 10( a), ( b) 1. 10 ( 2 ) 1 ) ( ),, 1. 11 ( a), ( b), ( c) 1. 11 2 ), :,, 1. 12 ( a), ( b) 3 ) 1. 12,,, 1. 13 7

1. 15 1. 13 1. 14 4),,, 1. 14 5),,, ( ), 1. 15 1. 3, :,,, :, ( 1 ) ( ) ( ) :,, :,, :,, ( 2 ) :, :, 8 ( 3 ) :,

1,,,,,,, 9

,,,, 2. 1,? 2. 1( a),,,,,, 2. 1( b),,,,,, 2. 1 : 1 ) 2 ),,, 2. 1( a), ABC ; AB, AC, BC 3 10

2. 2 2. 2. 1,, x, y, 2, 2. 2( a) 2. 2, A x, y A AB, 3, 2. 2( b) 2. 2. 2,,, ( ), ( 1 ),,,, 2. 3( a) 2. 3 ( 2 ) 2. 3( b),,, x, y,, 3,,,, 11

, 4, 2,, 2. 3( c), 9,,, x, y,, 3,,, 5, 4 2, n, 2( n - 1), ( n - 1 ), 2 ( n - 1) 2. 2. 3,,,,,,,, ;,, 2. 2. 4,,, W, m, h, r, :,, 2. 4 W = 3m - 2h - r ( 2. 1) 2. 4,, j, b, r, : W = 2j - b - r ( 2. 2) 2. 1 2. 5 W 2. 5 AB, BCD, DEF, FG, m = 4,, h = 3, 7, r = 7, W = 3m - 2 h - r = 3 4-2 3-7 = - 1 12

2 2. 2 2. 6 : m = 13, h = 18, r = 3, W = 3* 13-2 * 18-3 = 0 :. 6 j = 8, b = 13, r = 3, W = 2* 8-13 - 3 = 0 ( 2. 1) ( 2. 2), : W > 0,,, ; W = 0, ; W < 0,,? 2. 7( a) ( 2. 1), B A, 2. 7( b),, AB A,,,, 2. 7 2. 3 2. 3. 1, 2. 8 ( a) O, 2. 8, O, O, 2. 8 ( b) O, O,, 2. 8 ( c), ( d) 13

. 3. 2 ( 1 ), 2. 9( a) 1, 2, 3, 2. 9, 2. 9 ( a) 2. 9( b), :, 2. 9( c),,, ( 2 ), 2. 10 2. 10 ( a), A, B, C,,, A, C AC, B, C BC, C,, C,,, 2. 10( a) 2. 10( b ),, 2. 10( c), ( ),, ( 3 ),,,,, 2. 11 14

2,,,, :, 2. 11 2. 12 2. 12, AEG D, C, H, F, I, B,, 2. 3. 3, 2. 13( a),, ; 2. 13( b), O 2. 13 2. 14( a), O, O, O,,,, 2. 14 ( b), ( c), 2. 14,, 15

. 15? 2. 15, P B : B,, cos, R B R B = P a lcos, /2, cos 0, R B,,, 2. 3. 4,, W > 0,, W 0,,,,, : ; 2. 3 2. 16 2. 16 AB 1, 2 3,,,,, AB, AB CE, EF ( :, AB ) CE BC 4, D, EF 5, 6, H( ), CE EF E,, CE, EF, 2. 4 2. 17 AB, BC AC A, B, C, ABC, ABC A, E, DCFG, ABC, EG D,, 2. 17, 2. 5 2. 18 H GH H, GH FG, GD FD F, G D, DFG, DFG G 2 16

2 BCE, 1 CD, EF,, AB B A, A, AB B,,,, 2. 18 2. 19 2. 6 2. 19 BAD DH, HL DL D, H L, DHL, DCL, CGH,, CGHLD,, CBEF C FG, 2. 4,,,,,,,,,,,, 2. 20( a),,, F X = 0, F Y = 0, M = 0, 2. 20,, 2. 20( b),,, 3,, 17

,, 1 ), 2 ),, 3 ), 1.? 2.,? 3.,? 4.? 5.,, ( ) 2. 5 2. 6 6., 1 5, 3 5, 4 5, 2 5,, 12, ( ) 2. 1 2. 1 18

2. 2 2. 2 2. 3 2. 3 19

. 4 2. 5 2. 4 2. 5 20

,,, 3. 1,,, 3. 1, 21

, ;,,, :, 3. 1 ( a), ( b) ;, 3. 1( c) ;, 3. 1 ( d) ;, 3. 1 ( e) ;, 3. 1 ( f),, 3. 2,, 3. 2. 1,, : 3, 3. 1( a), ( c), X = 0, Y = 0, M A( F) = 0, : 3, 3. 1( b), ( d), 3. 2( a), CD, C F DY,, F AX, F AY, F BY 3. 2( b),, A, B, F BY, F AY, AC, C F AX,, X = 0 F BX 3. 2. 2 3. 2 22 ( 1 ), M F Q F N

3, : 3. 3 M = ( ) F Q = ( ) F N = ( ) : M, F Q, F N, M, F Q, F N,,,,, ( 2 ), ( M ) ( F Q ) ( F N, ), ; ( F Q F N ),,,, ( 3 ), 3. 4 ( a), x, y, q, F Q ( 3. 1) : F Q M : df Q dx = - q dm dx = F Q d 2 M dx 2 = - q ( 3. 1), ; M ; M, 23

. 4, M F Q, 3. 1,,, ( ), 24

3,,,, 3. 4( a),,, 3. 4( b), ( c) ( 4 ), ( 4. 6),,, 3. 5( a), : P M A, M B 3. 5 3. 6,, 3. 5 ( b) P,, 3. 5 ( c) ( b) ( c ),, 3. 5 ( d),,, 3. 6 ( a) AB, 3. 6( b), q, M A, M B, F Q A, F Q B AB, 25

M A, M B, F AY, F B Y, 3. 6 ( c), F Q A = F AY, F Q B = F B Y ( b) ( c),,,,,, : A, B M A, M B ( ) ; ( ), AB M, 3. 6( d) 3. 7,, : M A( F) = 0 40 + 160 2 + 40 6 7 + 40 10-8F BY = 0 F BY = 305kN M B ( F ) = 0 8F AY + 40-160 6-40 6 1 + 40 2 = 0 F AY = 135kN Y = 135 + 305-160 - 40-40 6 = 0 A, C, D, E, B, F, : M A = 0 M F = 0 M l C = 135kN m M r C = 175 kn m M D M E M B = 310kN m = 260kN m = - 160 kn m 3. 7 26

3 5 ),,,, 3. 7 ( b) AC, CD, DE, M, EB, BF, M ; C, M,, 3. 3 3. 3. 1,,,,, 3. 8 ;, 3. 9 ;, 3. 10 ;, 3. 11 3. 8 3. 9, 3. 12, B, C,,, 3. 13,,, 3. 14( a), BC, C, D, 3. 14( b), BC, 27

. 10 3. 11 3. 12 3. 13 28

3. 14 3. 3. 2 : M, F Q, F N,,, 3. 15, A, M AB, M AC, M AD AB A AC A AD A, B C D M BA, M CA, M DA,,, ;,,,,, ( 1 ),,,,,, : 3. 15,, 3. 1 3. 16( a) H X = 0, F B X = qa ( ) M A = 0, F D Y = 5 2 qa ( ) M D = 0, F AY = 3 2 qa ( ) CE : M CE = 0, M EC = qa 2 ( ) 29

. 16 AE : M AE = M E A = 0 DF : M D F = M F D = 0 BF : M BF = 0, M F B = qa 2 ( ) EF : E, M E = 0, M EF = qa 2 ( ) F, M F = 0, M F E = qa 2 ( ),, 3. 16 ( b) M :,,, M = 0;,, AE, DF ( 2 ), 3. 17 :, 3. 17 ( a) 30

3 : F Qi k = M ik M ki l i k ( 3. 2), M ik M ki ; M i k M ki,, M, ( ) ; M, ( ), 3. 17( b ), 90 3. 17 ( c) : M,,,,,,, ;,,,, ;,, ( 3 ),,,, X = 0, Y = 0 3. 2 3. 18( a) 3. 18 X = 0, F BX = 5kN ( ) M B = 0, F CY = 4kN ( ) 31

0, F BY = 4kN ( ) AD : M AD = 0, M D A = 5kN m( ) DB : M BD = 0, M D R = 15kN m( ) CD : M CD = 0, M D C = 20kN m( ),, 3. 18 ( c), AD, BD, DC : AD : F Q D A = F QAD = 5kN DB : F Q D B = F Q BD = 5kN AB : F QD C = F Q CD = 4kN 3. 18 ( d) AD, : F ND A = 0, D X = 0, F N D C = 0 Y = 0, F N D B = 4kN, 3. 18( e),,,, 3. 18 ( b), X = 5-5 + 0 = 0 Y = 0-4 + 4 = 0 M D = 5 1 + 5 3-20 = 0, 3. 3 3. 19( a),,, CD : M D C = 0, M CD = 40kN m ( ) BC : M CB = 50 kn m ( ) M BC = 130kN m ( ) AB : M BA = 130kN m ( ) 32

3 AB = 30kN m ( ) 3. 19, CD, AB, ; BC,, 3. 19( c) DC, AB,, DC, AB : DC : F Q CD = F Q DC = 40 kn = 20kN 2 AB : F QAB = F Q BA = 130-30 kn = 20kN 5 BC,, BC 3. 19( b) : 3. 19 ( d) F Q CB = 0, F Q BC = - 40kN C X = 0, F N CB = - 20kN Y = 0, F N CD = 0 B X = 0, F N BC = - 20kN 33

, 3. 19( e) 3. 3. 3 0, F NB A = - 40kN, 3. 20 3. 21,,, q( x), 3. 22 ( a), q, ;, 3. 22 ( b), q,, q q 0 q 0, q 0 q 0 dx = q ds ( 3. 3) = ds dx q = q cos,, 3. 23( a) : 3. 20 3. 21 3. 22, q, x, xoy, K : 34 M K = ql 2 x - 1 2 qx2 ( a)

3 QK = F N K = - 1 2 ql - qx cos ( b) 1 2 ql - qx sin ( c) 3. 23, K M K F Q K = ql 2 x - 1 2 qx2 ( d) = ql 2 ( d), ( e) ( a), ( b), ( c), M K = M 0 K - qx ( e) F QK = F 0 Q Kcos ( 3. 4) F NK = - F 0 Q K sin,, 3. 23 ( d), ( e), ( f) 3. 3. 4, :,, 35

. 4 3. 24( a) M A = 0, 10 6 3-12F BY = 0, F B Y = 15kN( ) M B = 0, 10 6 9-12F AY = 0, F AY = 45kN( ) X = 0, F B X - F AX = 0, C F B X = F AX M C = 0, 15 6-6. 5F BX = 0, M F BX = 13. 8kN( ) F AX = 13. 8kN( ) DC,, M D C M CD = 0 = ( - 13. 8 4. 5) kn m = - 62. 1kN m( ) CD,,, : 1 8 10 6 2 kn m = 45kN m,,, M 3. 24 ( b) F Q AD, BE, : F Q AD = F Q DA = - 13. 84kN F Q EB = F Q EB = 13. 84kN DC, CE,,,,,,,, : 3. 24 ( e) 3. 24 ( f) M C = 0, F Q D C = M D = 0, F Q DC = 62. 3 + 10 6 3 6. 33 62. 3-10 6 3 6. 33 kn = 38. 3kN kn = - 18. 6kN M C = 0, M E = 0 36

3. 24 F Q CE = F Q EC = - 62. 3 6. 33, F Q F N AD, BE,, DC 3. 24( g) kn = - 9. 85kN, 3. 24 ( c) F N AD = F N DA = - 45kN F N BE = F N EB = - 15kN F N DC = - 13. 84 3 10-45 1 10 kn = - 27. 4kN, 3. 24( h) 37

3 N CD = - 13. 84 10-45 1 10 + 10 6 1 10 CE, 3. 24( i) kn = - 8. 39kN F NE C = F N CE = - 13. 84 3 10-15 1 10 kn = - 17. 89kN, CD 3. 24( j), Y = 0 3. 5 3. 25 1,,,, C ( ),, : 3. 25 X = 0, F AX = P ( ) M C = 0, F AY a P 2a = 0, F AY = 2P( ) Y = 0, F BY = 2P ( ) M B = 0, M B + P 2a - P a - 2P 2a = 0, M B = 2 Pa( ),,, 3. 25 2 F AX,,, AD : F AX, A M A = 0, M DA = 2Pa, D: M DC = M D A = 2Pa, DE : C M C = 0; DC CE, E: M EF = M EC = 2Pa, BE : F BY, M B, F P,, M EF 2 Pa, ; F M F = 3Pa, M B = 3Pa, 3. 4 38 3. 4. 1 ( ),

3. 26, ( 3. 26 ( a) ) ( 3. 27 ( a) ) 3. 26 ( b) 3. 27( b),, 3. 26 ( b),,, ;, ; 3. 27 39

,,, 3. 26 ( c), 3. 27( c) 3. 27 ( b),,, 3. 28 ACB,, DE FG ACB, 3. 28,, ;,,, 3. 4. 2,,,,,,,,,,,,,, ( ),,,,,,,,,,, 3. 6 3. 29( a) AB, ; DH, ; BD AB, DH,, 3. 29 ( b) : AB, DH BD, BD 3. 29 ( c) M B = 0, 30-6F DY = 0, 40 F DY = 5kN( )

3 D = 0, 30-6F BY = 0, F BY = 5kN( ) 3. 29 F DY, F BY AB, DH DH, M E = 0, 5 3 - F G Y = 27. 5 kn( ) 1 2 20 3 2 + 6F G Y - 10 9 = 0 M G = 0, 5 9 + 20 3 4. 5 6F EY - 10 3 = 0, F E Y = 47. 5 kn( ),, 3. 29 ( d), ( e) 3. 7 3. 30( a), 41

, EF GH. 30( a), ACDB, EF, GH 3. 30 EF EF,, EF GH F X = 0, F G X - 10 4. 5 = 0 F G X = 45kN( ) M A = 0, 1 2 10 4. 5 2-4. 5F H X = 0 F H X = 22. 5kN( ) Y = 0, F GY = 22. 5kN( ) ACDB,, 42

3 X = 0, F AX = 45kN( ) M A = 0, 6F BY + 45 4. 5 + 22. 5 6 - F B Y = 3. 75kN( ) 1 2 20 6 2 = 0 M B = 0, 6F AY - 45 4. 5-1 2 20 6 2 = 0 F AY = 93. 75kN ( ),,,, 3. 30 ( c), ( d), ( e), CD G,, 3. 30( f), ( g) CD : G : F X = 45-45 = 0 F Y = 93. 75 + 26. 25-20 6 = 0 M C = 270-1 2 20 6 2-67. 5 + 26. 25 6 = 0 F X = 45-0 - 45 = 0 F Y = 3. 75 + 22. 5-26. 25 = 0 M = 0 + 0 + 0 = 0 3. 5 3. 5. 1 3. 31 ( a), 3. 31( b) : ( ),,, 3. 32,, ( a ),, ( ),, ( b), ( c),,,, 43

. 31 3. 32,,,,,,,,,,,,,, 3. 33, 3. 33 ( a ), ( b), ( c), ( a), ( b), ( c) ; 3. 33( d), ( e ),,,, ( ) ( e),, 44 3. 33 3. 34,

3 f/ l,,, 1 1 /10, 3. 35,, 3. 34 3. 35 3. 5. 2,, ( 3. 36( a) ), 3. 36 ( b) ( ), ( 1 ),, 4 : F AY F AX F BY F B X, 4 3, ( ), C, F 0 AX, F 0 AY, F 0 BY, 3. 36( a), ( b) : M A = 0, F BY = F 0 B Y = 1 l ( P 1 a 1 + P 2 a 2 + P 3 a 3 ) M B = 0, F AY = F 0 AY = 1 l ( P 1 b 1 + P 2 b 2 + P 3 b 3 ), M C F X = 0, F AX = F BX = F H = 0, F AY l 2 - P 1 F H = C ( 3. 5), l 2 - a 1 - F H f = 0 F AY l 2 - P 1 M 0 C = F AY l 2 - P 1 f l 2 - a 1 l 2 - a 1 ( 3. 5) 45

. 36, F H = M0 C f F AY = F 0 AY F BY = F 0 BY ( 3. 6) ( 3. 6), F H F H = M0 C f,, f,,, f = 0, F H A, B, C, ( 2 ) =,,, 3. 36( c), K, x K y K, K, K M K F QK F NK,,, AK, 3. 36( c) 46 F QK, : M K = 0, M K = [ F AY x - P 1 ( x - a 1 ) ] - F H y K ( a)

3 F NK,, Q K = ( F AY - P 1 ) cos K F H sin K ( b) F N K = ( F AY - P 1 ) sin K + F H cos K ( c) F AY = F 0 AY, ( a) ( 3. 36 ( b) ), K M 0 K, ( b), ( c) ( F AY - P 1 ) K F 0 Q K, ( a), ( b), ( c) M K = M 0 K - F H y K ( 3. 7) F Q K F N K = F 0 QK cos K - F H sin K ( 3. 8) = F 0 QK sin K + F H cos K ( 3. 9), K K,, ( 3. 7),, F H F H y K, F H,,,,,,,,, 3. 8 3. 37( a),,, ( 3. 6) F AY = F 0 AY = F BY = F 0 B Y = F H = M0 C f = y = 4f l 2 ( l - x) x 100 9 + 20 6 3 12 100 3 + 20 6 9 12 105 6-100 3 4 kn = 105kN kn = 115kN kn = 82. 5kN,,, A 3m 2, x = 3m, ( 3. 7) y = 4f l 2 ( l - x) x = tan 2 = dy dx x = 3 = 4f l 4 4 12 2 ( 12-3) 3 m = 3 m 1-2x l = 4 4 12 1-2 3 12 2 = 33 43 ; sin 2 = 0. 555 ; cos 2 = 0. 832 = 0. 667 M 2 = M 0 2 - F H y 2 = ( 105 3-82. 5 3) kn m = 67. 5kN m 47

. 37 2, P = 100kN, 2 P, 2 P cos 2, Psin 2,, 2, ( 3. 8) F Q2 F Q2 ( 3. 9) = F 0 Q 2 cos 2 - F H sin 2 = ( 105 0. 832-82. 5 0. 555) kn = 41. 6kN = F 0 Q 2 cos 2 - F H sin 2 = [ ( 105-100) 0. 832-82. 5 0. 555 ] kn = - 41. 6 kn F N 2 = F 0 Q2 sin 2 + F H cos 2 = ( 105 0. 555 + 8. 25 0. 832 ) kn = 127kN 48

. 2 x/ m y / m tan sin cos F 0 Q / kn M/ kn m M 0 - F H y M F Q /kn F 0 Q cos - F Hsin F Q F N /kn F 0 Q sin F Hcos F N 0 0. 00 0. 00 1. 333 0. 800 0. 600 105. 00 0. 00 0. 00 0. 00 63. 00-66. 00-3. 00 84. 00 49. 50 133. 50 1 1. 50 1. 75 1. 000 0. 707 0. 707 105. 00 157. 50-144. 40 13. 10 74. 20-58. 30 15. 90 74. 20 58. 30 132. 50 2 3. 00 3. 00 0. 667 0. 555 0. 832 105. 00 5. 00 315. 00-247. 50 67. 50 87. 40 4. 20-45. 80 41. 60-41. 60 58. 40 2. 80 68. 60 127. 00 71. 40 3 4. 50 3. 75 0. 333 0. 316 0. 948 5. 00 322. 50-309. 40 13. 10 4. 70-26. 10-21. 40 1. 60 78. 30 79. 90 4 6. 00 4. 00 0. 000 0. 000 1. 000 5. 00 330. 00-330. 00 0. 00 5. 00 0. 00 5. 00 0. 00 82. 50 82. 50 5 7. 50 3. 75-0. 333-0. 316 0. 948-25. 00 315. 00-309. 40 5. 60-23. 70 26. 10 2. 40 7. 90 78. 30 86. 20 6 9. 00 3. 00-0. 667-0. 555 0. 832-55. 00 255. 00-247. 50 7. 50-45. 80 45. 80 0. 00 30. 50 68. 60 99. 10 7 10. 50 1. 75-1. 000-0. 707 0. 707-85. 00 150. 00-144. 40 5. 60-60. 10 58. 30-1. 80 60. 10 58. 30 118. 40 8 12. 00 0. 00-1. 333-0. 800 0. 600-115. 00 0. 00 0. 00 0. 00-68. 90 66. 00-2. 90 92. 00 49. 50 141. 50

N 2 = F 0 Q2 sin 2 + F H cos 2 = [ ( 105-100) 0. 555 + 82. 5 0. 832] kn = 71. 4kN, 3. 2. M F Q F N, 3. 37 ( b), ( c), ( d), [ 3. 37( c) ],, 3. 37( b) 3. 38, 3. 38 ( M 0 ), F H y ( M 0 - F H y),,,,,, 3. 9 3. 39( a) K M K, F Q K F N K, y = 4f l 2 ( l - x) x 50 3. 39,, ( 3. 6 ), ( 3. 7 ), ( 3. 8 ), ( 3. 9 )

3, M A = 0, F BY 16-4F Q 2 = 0, F BY = 0. 5F Q, ( ) M B = 0, F AY 16 + 4F Q 2 = 0, F AY = 0. 5F Q, ( ) F X = 0, F H A + F HB 4 F Q 2 = 0, F H A + F HB = 4 F Q, M C = 0, : M C = 0 F By 8 - F H B 4 = 0 F H B = q ( ) F H A = 4q - q = 3q( ) K K x K = 4m, y K = 4f l 2 ( l - x K ) x K = 4 4 16 2 ( 16-4) 4 m = 3m tan K = dy dx = 4f ( l - 2x l 2 K ) = 4 4 16 2 ( 16-2 4 ) = 0. 5 k = 26 34, cos K = 0. 894, sin K = 0. 447 K, 3. 39( b), M K F Q K = - 0. 5q 4 + 3q 3-3 q 1. 5 = 2. 5q = - 0. 5qcos K + 3qsin K - 3qsin K = - 0. 5q 0. 894 = - 0. 447q F N K = - 0. 5qsin K - 3qcos K + 3qcos K = - 0. 5q 0. 447 = - 0. 224q ( ) 3. 5. 3,, M, F Q F N, 3. 40( b), R,, R, 3. 40( c),, ( ),,,,, ( 3. 7),,,, ( M = 0, F Q = 0 ), 51

. 40, ( 3. 7 ) : M K = M 0 K - F H y K,, M = 0 M 0 - F H y = 0 y = M0 F H ( 3. 10), y,, F H, 3. 10 3. 41( a) F Q 3. 41 3. 41 ( b), F H ( 3. 6 ) M 0 = 1 2 qlx - 1 2 qx2 = 1 2 F H = M0 C f ( 3. 10) 52 = 1 8 ql2 f qx( l - x) = ql 2 8f

3 M 0 F H = 1 2 qx( l - x) ql 2 8 f y = 4f l 2 ( l - x) x ( 3. 11),, 3. 11, 3. 42( a),, ds, 3. 42( a) R, d, ds = Rd, F u = 0 3. 42 F N cos d 2 - ( F N + df N ) cos d 2 - F Q sin d 2 - ( F Q + df Q ) sin d 2 = 0 d, cos d d = 1, sin 2 2 = d,, : 2 ds = Rd, df N + F Q d = 0, F v = 0, df N ds = - F Q R df Q - F N d + qds = 0 ( a) df Q ds = F N R - q ( b) M 0 = 0, dm - F Q ds = 0 53

( a), ( b), ( c), M = 0, ( c), ( d) ( a), M ds = F Q ( c) F Q = 0 ( d) ( d) ( b), df N ds = 0 N = F N R - q = 0 q = q c R = F N q, q, R, 3. 43,,,, 3. 12 3. 43, q = q c M 0 + y( ), q, y,, ( 3. 10 ) ( 3. 10) x, : y = - q( x),, + y, : 54 y = A ch d 2 M 0 dx 2 = - q( x) y = + q( x) F H y - y = q C F H F H F H x + B sh F H x - 1 d 2 M 0 F H dx 2 q c

3 B : x = 0, y = 0, x = 0, y = 0, A = q c B = 0 y = q c ch F H x - 1,,,,,,,, 3. 6 3. 6. 1,, 3. 44 ( a), ( b), ( e),,, 3. 44 ( a),,, d,,,,,,,,, : 1 ) 2 ), 3 ),,,,,,,,,,,,,, 55

. 44,,,,,,, ( ),,,,, (, ),, 3. 44, ( c), ( d) ( a), ( b), : 56

3 1 ) ; ; ; 3. 45 ( 2 ) 1 ) ( 3. 45 ) 2 ) ( 3. 46 ) ( 3 ) 1 ) :, ( 3. 47( a) ) 2 ) : ( 3. 47( b) ) 3 ) : ( 3. 47( c), ( d) ) 3. 46 3. 47 57

. 6. 2, :,,,,, ( 1) 1),,,,,,,,,, F N F X F Y ( 3. 48 ), l, 3. 48 l x, l y, : F N l = F X l x = F Y l y, F N F X F Y,,, 3. 13 3. 49 ( a),, F X1 = 0, F Y1 = F Y8 = 1 2 ( 10 + 20 + 20 + 20 + 10) kn = 40kN ( ),, 1, 8,, 1, 1, 3. 49( b) F Y = 0, F Y13 = - 30kN, F X1 3 = 2 1 F Y13 = 2 ( - 30) kn = - 60kN F N 13 = 5 1 F Y13 = 5 ( - 30) kn = - 67. 1kN ( ) F X = 0, F N12 = - F X13 = - ( 60) kn = 60kN ( ) 58

3. 49 2, 3. 49( c) F N12,,, F X = 0, F N2 5 = 60 kn( ) F Y = 0, F N23 = 0 3, 3. 49( d) F N1 3, F N2 3,,, F X = 0, F X3 4 + F X35 + 60 = 0, F Y = 0, F Y34 - F Y35-20 + 30 = 0 F Y34 = F X34 2, F Y35 = F X35 2,, F X34 = - 40, F X35 = - 20, 59

Y34 = 1 2 ( - 40) kn = - 20kN F N34 = 5 ( - 40) kn = - 44. 7kN ( ) 2 F Y35 = 1 2 ( - 20) kn = - 10kN F N35 = 5 ( - 20) kn = - 22. 4kN ( ) 2, : ( 3. 49( d), F N34 F X ),,, 3. 49( e), F N1 3 F N34 F N3 5 1, 5, 4, 5,, M 5 = 0, F X34 2 + 30 4-20 2 = 0 F X34 = - 40kN F Y34 = 1 2 ( - 40) kn = - 20kN F N34 = 5 ( - 40) kn = - 44. 7kN ( ) 2,, F X = 0, F X35 + 60 + ( - 40) = 0 F X35 = - 20kN F Y35 = 1 2 ( - 20) kn = - 10kN F N35 = 5 ( - 20) kn = - 22. 4kN ( ) 2 4, 3. 49( f), F X = 0, F X4 6 = - 40kN F Y46 = 1 2 ( - 40) kn = - 20kN, F N46 = 5 ( - 40) kn = - 44. 7kN ( ) 2 F Y = 0, F N 45 = 20kN ( ), F N34 F N46,,, 60

3 3. 49 ( a),, 3. 49( e), F N13 F N34 5, F N1 3 F N 34 5,, F N13 F N 34 1 4,, F X13 F Y34 5, F Y13 F X34, F N13 F N34 5 3. 50, 3. 50, ( b) 2 ),, a) L ( 3. 51( a ) ), 3. 51 b) T, ( 3. 51 ( b) ),,, ( ) c) X ( 3. 51( c) ),, d) K,,,,,,, ( 3. 51( d) ) ;,, ( 3. 51( e) ), 3. 52, 61

. 52 ( 2 ), ( ) ( ),,,,,, 3. 14 3. 53 a, b, c 3. 53,, 1, 2, 3, 4, 5, a, b, c 62

3 1 X = 0, F 1 Y = 4. 52kN( ) R 8 Y = 1. 48kN( ) -, a, b, c,, 3. 53 ( b), F Na, F N b, F N C, F Na,, F N b F N C 5,, F N b, : M 5 = 0, 2. 48F N a + 1 3. 00-1. 48 11. 85 = 0 F N a = 5. 86kN ( ), F N b, F N a F N C 7,, F N b 7, F N a, F Nb 6 F bx F by :, F N b = M 7 = 0, - 2. 88F bx - 1. 48 8. 85 = 0 F bx = - 4. 68kN 3. 017 ( - 4. 68 ) kn = - 4. 70kN( ) 3. 00, F N C,,, F Nc = 3. 53 ( b),, F Y = 1. 48-1 - F X = 0, - F cx - F N a - F bx = 0 F cx = - 1. 18kN 3. 89 ( - 1. 18 ) kn = - 1. 53kN( ) 3. 00 0. 32 2. 48 ( - 4. 68 ) + ( - 1. 18) = 0 3. 00 3. 00 3. 15 3. 54( a) a, b : F Na, F AY = F BY = 2. 5P ( ) -,, 3. 54 ( b), F N a, F Y = 0, 2. 5P + F N a - P = 0 F N a = - 1. 5P( ), F Nb, -,, 3. 54( c), 63

F Y = 0, 2. 5P - 2P - F Nb sin = 0 F N b = P 2sina ( ),,,,,,, 3. 55( a), -,, a,,, 3. 55 ( b), X = 0, F N a 3. 56( a), -,, a, C, M c = 0 F Na, 3. 56 ( b). 54 3. 16 3. 57( a) a b, 3. 57( a) 3. 55 3. 56 64

3, -, 3. 57( b),,, -,, 3. 57( d),,, b, E, F Nb M E = 0, F N b 6 + P 3 4 = 0 F Nb = - 2 9 P -, 3. 57 : ( 3 ) M D = 0, P 3 8 + 6F N b + 6F a X = 0 F a X = - 2 9 P F N a = 5 4 F a X = -,, 3. 58,,,, 5 18 P, 3. 17 3. 59( a) KH F N H K 65

. 58,, F NH K -,, 3. 59( d),,, G,, 3. 59 ( b), F N GH F NG F -, 3. 59 ( c), F N GF,, 3. 59 ( a) -, M E = 0, 6 F N GF - 300 5-750 5 = 0 F N GF = 875kN( ) G, F G HX = F N F G = 875kN -,, M E = 0, 750 5-4F H KX - 4F G HX = 0 F H KX = 62. 5kN F N H K = 62. 5 26 kn = 63. 74kN 5 66

3. 59 3. 6. 3,,, : ( ) M 0, Q 0 ( 1 ) ( 3. 60 ( a) ) ( ) 3. 60( b), ( c), ( d), F N = M0 h M 0, h F N ( ) h, F N, M 0,,, ( ), F Y = F 0 Q F 0 Q, F Y, 3. 61 ( a) 67

, ; 3. 61 ( a),, ( 2 ) ( 3. 61 ( b) ) F N. 60 = M0 r r, r M 0 ;,,,,, ( 3 ) ( 3. 61 ( c) ), F N = M 0 /r, r, M 0,, 68

3. 61,, ;,, 69

4 ) ( 3. 61 ( d) ),, r,, M 0 / r, ( 5 ) ( 3. 61 ( e) ), 3. 61,, : 1 ),,, ;,,,, 2 ),,, ;,,,,,, 12m, 50m 3 ),,,, 18 30 m 100 150m 4 ),,,,,, 18 24m, 3. 6. 4, 3. 62, 3. 63 3. 62 ( a),,, 3. 62 ( b) AC BC, ( ),,,,,, 3. 18 3. 64( a) F A X = 0, F A Y = 45kN( ), F BY = 15 kn( ) ( DE ) F N D E -, C DE,, 3. 64( b), 70 M C = 0, F N DE = 75kN( )

3. 62 3. 63 D, E, 3. 64 ( c), M, F Q, F N AC, 3. 64( d) : M AF = 0 F Q AF = [ ( 45-17. 5) 12 12. 04-75 1 ] kn = 21. 17 kn 12. 04 F N AF = [ ( 17. 5-45) 1 12. 04 M F A = M F C = [ ( 45-17. 5) 3-75 0. 25-12 - 75 ] kn = - 77. 03kN 12. 04 1 2 10 3 2 ] kn m = 18. 75kN m F Q F A = [ ( 45-17. 5-10 3) 12 12. 04-75 1 ] kn = - 8. 72kN 12. 04 F N F A = [ ( 10 3 + 17. 5-45) 1 12. 04 F N F C = ( - 74. 5-17. 5 1 ) kn = - 75. 99kN 12. 04 M CF = 0 12-75 ] kn = - 74. 5kN 12. 04 71

M, F Q, F N. 64 F Q CF = ( - 15 12 12. 04-75 1 ) kn = - 21. 18kN 12. 04 F N CF = ( 15 1 12. 04 12-75 ) kn = - 73. 50kN 12. 04 3. 64( f), ( g), ( h) : : ( 1 ) f l F ND E, ( 2 ) f 1 f 2 3. 65,, f = f 1, :, f 1 F N D E = M0 C f + f 2 f 1 f 2, = 0,,, 3. 65( a),, F, f 2 = 0,, 3. 65( c), A, C f 1 f 2, F 3. 65,,, M 72

3. 65 3. 7, :, ;,, 1 ), 3. 66 3. 66 ( a), ( b ) ( c),,,, 73

),,,, 3 ) :, 3. 67 3. 67, ( a) DE ( b) CDE,,, 4 ) :,, 3. 68,, 3. 68 ( a), AB F q, A, B, AB, 5 ) :, 3. 69 74

3. 69 ( a), AB 3. 69 ( b), A, B, AB, 1 ),,, 2 ),, 3 ),,,,,, 1.? 2.? 3.,? 4.? 5., A? D T? 6. B 5? 6 7., : ( ) 7 A. ; B. BCDE ; C. ABCD ; D. DE 8. p q, 9., CD? 75

10. 9 10 76

3. 1 3. 1, 77

3. 2. 1 78 3. 2

3. 3, 3. 3 79

. 4 3. 5 3. 4 3. 5 3. 6 3. 7, ( a) 80

3. 6 3. 7 81

3. 8, M 3. 9 ( 1 ) E M, F Q, F N ( 2 ) D F Q, F N 3. 8 y = 4 f l 2 ( l - x) x l = 16m f = 4m ( 3 ) ( f = 8m),? ( 4 ),,? 3. 9 3. 10 K 3. 10 3. 11 K y = 4f l 2 ( l - x) x 82

3. 11 3. 12, C ( 1 ) C A ( 2 ) ( 3 ) D 3. 13, 3. 12 3. 13 83

3. 14 3. 14 3. 15 84

3. 15 3. 16, 3. 16 5

,,,,,, 4. 1,,,, 4. 1, q, BC D D, DD D, D D X D Y D D,, D D,,,,, 4. 2,, A AX, B B X, A, B AB = AX + BX, C C, D D, C, D CD = C + D 86 4. 1 4. 2

4 : 1 ) : 2 ) : 3 ) :,,,,,, 1 /600, 7 9m, 1 /250,,,,,,,,, : 1 ),, 2 ),,,,,,, 1,,, 2,,,,,, 4. 2 4. 2. 1,, =, ( 1 ),, 4. 3 P, W P i W = P i i cos ( 4. 1), kn m, P i i 87

. 3 4. 4 P, 4. 4 ( 2 ), 4. 5, 0 P i,, P i 0 ip P i i P, 4. 6 P P i 0 P i,, P dp, d ip, P, 4. 5 4. 6 dw = ( P + dp ) d ip = P d ip + dp d i P ( a) dw = P d i P ( b) 4. 6 dw P i P, ip P P i i P P = 1 P i ( c), d i P = i P dp ( b), W = ( c) ( d) P dw = 0 i P = ip P ( c) P ip 0 P ip dp = P dp = 1 2 i P P 2 ( d) W = 1 2 P i P ( 4. 2) 4. 6 OAB : P 0 P i, P P i,,,,,,,,,, 88

4,, 4. 5, P i,, 4. 5, P i it ( P i ), i t P i, it, P i, P i W = P i it 4. 6 ABCD, i t P i,,,,,,,,,, P, P, P, ; P,,,,,,,, : W = P i i k ( 4. 3), P i, i k K P i 4. 7( a),, ds, 4. 7 ( c), M, F Q, F N M + dm, F Q + df Q, F N + df N ABC, ds, 4. 7( b), 1 P 1, 2 P 2, c 1, c 2, c 3, ds : DE D E (, ) D E D E,, M, F Q, F N M + dm, F Q + df Q, F N + df N D E, ds ( ) d, d, d ds dw = M + F Q + F N + ( M + dm) ( + d ) + ( F Q + df Q ) ( + d ) + ( F N + df N ) ( + d ) ( a) :,, 4. 7 ( a), ds, M + F Q + F N + ( M + dm) + ( F Q + df Q ) + ( F N + df N ) = 0 ( b),, ( b) ( a) dw = ( M + dm) d + ( F Q + df Q ) d + ( F N + df N ) d ( c) 89

4. 7 dw = M d + F Q d + F N d ( d) ds,, dw = - ( M d + F Q d + F N d ) ( e) ( e), W = - ( M d + F Q d + F N d ) ( 4. 4) 4. 2. 2, :,, W W W + W = 0 ( 4. 5),, W = 0, ( 4. 5) W = 0 ( 4. 5 ) 4. 7, 4. 7( a), 4. 7( b), W = P 1 1 + P 2 2 + R 1 c 1 + R 2 c 2 + R 3 c 3 n = i = 1 P i ( 4. 4), ( 4. 6) ( 4. 5) n i = 1 P i, P i, R i, M, F Q, F N i n + i = 1 i R i c i n + i = 1 R i c i ( 4. 6) = ( M d + F Q d + F N d ) ( 4. 7) i, c i, d, d, d 90

4, 4. 8, d, d, d, 0, k, d = ds, d = 0 ds, d = ds ( 4. 7) n i = 1 P i i n + i = 1 R i c i = ( M + F Q 0 + F N ) ds ( 4. 8) 4. 8 ( 4. 3),,, ( ), ( ), :,,,,,, 4. 2. 3,, 4. 1 4. 9( a) D F Dy M G, F Q G ( ) 4. 9 91

, F Dy, F D y, 4. 9 ( b),, F D y, AC, CE, 4. 9 ( c),,,, : n P i i = 0 i = 1 F D y D + P 1 P 1 + P 2 P 2 + m m = 0 D = 1 P 1 = 3 4 P 2 = - : F D y 1 + 3 4 P 1 - F D y = 3 2 P 2-3 2 3 2 P 2-3 4 P 1 + 1 2a m m = - 1 2 a m = 0 M G, M G 4. 9( d ),, 4. 9( e), G, 1 2a P 1 = 1 = 1 a = 1 a M G = - P 1 P 1 + M G ( + ) = 0 P 1 1 + M G 1 a + 1 a 1 2 P 1a = 0 M G 4. 9 ( d), M G, F QG F Q G, 4. 9( f),, 4. 9( g) G 1, GG = 1 2 P 1-1 2 + F Q G 1 = 0 P 1 = - 1 2, F Q G = 1 2 P 1 4. 2 4. 10 ( a) P CD CD X, 4. 10 ( b), 4. 10 ( c), AB C FD E,, 92 P X P = a X = ( 2 a + a cos45 ) P P + X X = 0

4 4. 10 P a + X( 2a + a cos45 ) = 0 X = - P / ( 2 + 2 /2) = ( - 2 /3) P, X,, X X + P P = 0 X X + P P = 0 X P X X = 1, P X :,, X, X X X P X P X, P X, P, X P X P X, P ; X, P, X P X P X, P, X X X ;, X, X, X,, 4. 3,, 4. 3. 1 ( 1 ) 4. 11 ( a),, K n-n K 93

,, K K ( n-n ) P( P K, P K, ),, P = 1, P P R 1, R 2, 4. 11 ( b), ( 4. 3 ) 1 K n + i = 1 R i c i = ( M + F Q 0 + F N ) ds ( 4. 9), 1, R i, M, F Q, F N 4. 11 ; K,, 0,, c i ( ), : K = ( M + F Q 0 + F N n ) ds - i = 1 R i c i ( 4. 10),, ( 4. 10) : K 1 K, K, K ( 2 ) ( 4. 10),, ( 4. 10 ),, ( 4. 10),,, 4. 3. 2 ( 4. 10 ), K K,,, ;, ;,, 94 4. 12 KV, KH, K, J K, AB

4 4. 12 4. 4 4. 4. 1, c i = 0,,, 0, ( 4. 10 ) : KP = ( M + F Q 0 + F N ) ds, K P K, : = M P EI = F N P EA 0 = k F Q P GA KP = M M P EI + k F Q F QP GA + F N F N P EA ds ( 4. 11) : E, G A, I EI, GA, EA k, k 1. 2, k 10 /9, k A/ A P, ( A j ) M, F Q, F N, M P, F NP, F QP ( 4. 11), : M, F Q, F N M P, F N P, F QP ( 4. 11) KP 95

. 4. 2,,,,, ( 1 ),,, KP = M M P ds ( 4. 12) EI ( 2 ),, KP F = N F NP dx ( 4. 13) l EA F N, F N P, A l, KP = F N F NP l ( 4. 14) EA f l ( 3 ), ( ) < 1, 5 K P = M M P EI, + F N F NP EA ds ( 4. 15) KP = M M P ds ( 4. 16) EI ( 4 ), ( ), 96 4. 3 KP = M M P ds + EI F N F N P l ( 4. 17) EA 4. 13 ( a), EI =, C C ds = dx C, 4. 13 ( b) M( x), M P ( x), x AC : M( x) = - 1 a x, M P ( x) = 3 8 qax - 1 2 qx2 0 x a /2

4 4. 13 CB : M( x) = 1 a x, M P ( x) = 1 8 qa ( a - x) a /2 x a C C = a 2 0 - ( x/ a ) EI 3 8 qa x - qx2 2 dx + a a 2 ( x / a ) EI 1 8 qa ( a - x) dx = - qa 3 384 EI 4. 4 4. 14( a), EI, B BH 4. 14 BC, BA ds = dx, B H 4. 14( b) M( x) M P ( x) BA : M( x) = - 1 x, M P ( x) = - Pa - BC : M( x) = 0, M P ( x) = - Px B H 4. 5 EI) B H = a 0 = 1 EI - 1 x EI P a 3 2 + qa 4 8 - Pa - qx 2 2 ( ) 1 2 qx2 dx + a 1 0 0 ( - Px) dx EI 4. 15( a), A AV A ( AB ds = R d, BC ds = dx 1 ) AV AV 4. 15 ( b) 97

M( x) M P ( x) AB : 4. 15 M( x) = R sin, M P ( x) = PR sin BC : M( x) = R, M P ( x) = PR AV 2 ) A AV = EI 1 2 = 1 EI 0 R sin P R sin Rd + EI 1 1. 5 R 4 + 3 2 P R3 ( ) A 4. 15( c) M( x) M P ( x) AB : M( x) = 1, M P ( x) = PR sin BC : A M( x) = 1, M P ( x) = PR A = P R2 EI 2 0 = 5 2 EI PR2 ( ) sin d + P R 0 EI 1. 5 R 0 dx R PR dx 4. 6 4. 16 ( a) CE C E ( EA ) C E ( CE ) 4. 16 ( b) F N F N P C E 98

4 4. 16 F N F NP l F N F NP l AC 2 /2a - 2P 2a / 2-2P /2 BD - 2 / 2a - 2P 2a / 2 2P / 2 CE 2 /2a 0 2a / 2 0 DE 2 /2a 0 2a / 2 0 EB 1 /2a P a P /2 AE - 1 /2a P a - P /2 CD - 1 / a - P a P F N F N P l = P C E = F N F N P EA l = P EA ( ) 4. 7 4. 17 ( a) B B V ( EA ) 4. 17 : BC,,, : 99

= M M P dx + EI F N F N P EA dx B V 4. 17( b) M F N P = 1,, M P M = 0 F N 4. 17( b) F N P BC M F Q,, 4. 17( c), ( d) B V BV = M M P dx + EI F N F N P EA dx = 0 M P EI = 1 EA [ - 1 - = ql 2 2EA ( ) dx + F N F N P EA dx ql 2 l] + 0 + 0 + 0 4. 5, ( 4. 12) 4. 18 KP = M M P ds EI, M( x) M P ( x),,,, ( 4. 12),, : ) 1) ( EI 2 ) M( x) M P ( x) ( ) AB M( x) M P ( x),, 4. 18, O x M( x) = x tan ( a) AB, EI ds = dx, ( a) ( 4. 12) 100

4 m = M P ( x) dx = d, n x tan M P ( x) ds = tan x M P ( x) dx ( b) EI n KP EI m n EI m = tan x d ( c), x d d y, m x d M P ( x) y n M P ( x) c y x c, M P ( x), : ( d) ( c), m x d = x c ( d) n KP = tan EI x c = 1 EI y c ( e) y c = x c tan, M P ( x) c M( x), KP = 1 EI y c ( 4. 18), c y c, EI, ( 4. 18) :, M( x) M P ( x),, EI, M( x) M P ( x),, 4. 19,,, 4. 19, 101

:,, 4. 20 I 2 4. 20 4. 8 4. 21( a) C E = 2. 06 10 4 kn /m 2, I 1 = 0. 656m 4, = 1. 243m 4 102 4. 21, M( x) M P ( x), 4. 21( b), ( c) 4. 9 1 = 60 2 1 2 = 60 y 1 = 1 2 = 60 4 = 240 y 2 = 1 3 = 60 2 1 2 = 60 y 3 = 1 3 C V = 1 ( 1 y 1 + 3 y 3 ) + 1 2 y 2 EI 1 EI 2 = 80 EI 1 + 240 EI 2 = ( 0. 59 + 0. 947) cm = 1. 53cm ( ) 4. 22 ( a), C, D C, D, EI =, M( x) M P ( x), 4. 22 ( b), ( c )

4 4. 22 M( x) AC BE, CB, M P ( x), 4. 22( d),, 1 8 ql 2, CD = 1 EI - 12 6 2 2 3 6 5 + 9 6 2 1 3 6 5 + 2 3 6 9 1 2 6 5 + 1 2 3 12 2 3 6 5 = 1 EI 18 5 ( ) 4. 10 4. 23( a) C 4. 23 M( x) M P ( x), 4. 23( b), ( c), 1 = 1 2 4 4 = 8 y 1 = 2 3 4 = 8 3 2 = 1 32 4 8 = 3 3 3 = 1 135 27 5 = 2 2 y 2 = 3 4 4 = 3 y 3 = 18 3 = 6 4 = 1 2 12 5 = 30 y 4 = 15 3 = 5 103

CV = 1 EI ( 1 y 1 + 2 y 2 ) + 1 2 EI ( 3 y 3 + 4 y 4 ) = 1 EI 8 8 3 + 32 3 3 + 1 2EI = 160 3EI + 555 2EI = 1985 6 EI ( ) 135 6 + 30 5 2 : M P ( x) BC, 4. 6,, ( 4. 10), 4. 6. 1,, ( 4. 10) K C n = - R i c i ( 4. 19) i = 1, K C K C i R i R i C i,, 4. 11 4. 24( a), B, a = 1cm, b = 2. 4cm, C CV C c 104 4. 24

4 1 ) C CV c i R i, 4. 24( b) ( 4. 19) C V n = - R i c i = - - i = 1 1 2 a - 1 6 b = 2 ) C c 1 2 1 + 1 6 2. 4 cm = 0. 9cm ( ) c i R i, 4. 24( c) ( 4. 19) C n = - i = 1 R i c i = - 1 9 b + 0 a = - 4. 6. 2 1 9 2. 4 10-2 rad = - 0. 00267rad ( ),,,, ( 4. 10) kt = ( M + F Q 0 + F N ) ds ( a), K t K M, F Q, F N, 0,,, ds 4. 25, t 1, t 2,, h 1 = h 2 t 0 = h 1 t 2 + h 2 t 1 h ( b) 4. 25 ds t 0 = t 1 + t 2 2 ( c) = t 0 ( d) t = t 2 - t 1 ( e) = d ds = t 2 ds - t 1 ds hds = h t ( f),, ds 0 = 0, ( d), ( f) ( a) 105

, F N t 0 = M t ds + h F N t 0 ds = t h Mds + t 0 F N ds ( 4. 20) M t,,,, ( 4. 20 ) Kt = F N t 0 l ( 4. 21) 4. 12 4. 26 ( a), h, 20 10, - 20,, C C V, EI 4. 26, M, F N, M P C, 4. 26( c), ( d), ( e) 106 CV = 1 EI P l l 1 2 2 3 l + P l l l C t 1 t 2 = - 20-20 = - 40 = 10-20 = - 10 = 4Pl3 3EI ( )

4 0 = t 1 + t 2 2 = - 40-10 2 = - 25 t = t 2 - t 1 = - 10 + 40 = 30 CV = t Mds + h t 0 F N ds = ( - 25 ) ( - l) + - 30 l2 h 2 + - 30 l 2 h = 25 l - 45 h l2 ( ) C CV = CV + CV = 4Pl3 3EI - 25 l - 45 h l2 4. 7,,, 4. 7. 1 4. 27 ( a), ( b),, P i M i, F Q i, F N i i, i, 0 i, i, P j M j, F Q j, F Nj j, j, 0 j, j : ji P i P j ; i j P j P i 4. 27, ( 4. 3) P i i j = ( M i j + F Q i 0 j + F N i j ) ds = M i M j EI + k F Q i F Q j GA, + F N i F N j EA ds ( 4. 22a) 107

j ji = ( M j i + F Q j 0 i + F N j i ) ds = M j M i EI ( a), ( b),, n, + k F Q j F Qi GA + F N j F N i EA ds ( 4. 22 b) P i ij = P j ji ( 4. 22c) P i ij = P j ji ( 4. 23) :,,,,,, 4. 7. 2 4. 28( a), ( b), P i, P j : ji P i = 1 P j = 1 ij P j = 1 P i = 1 ( 4. 23) 4. 28 P i = 1, P j = 1, P i ij = P j ji i j = ji ( 4. 24) :,, P i = 1 P j = 1 ji, P j = 1 P i i j = 1 4. 29 :,, 4. 29 ( a ), ( b ) 108

4, : i j = ji 4. 7. 3 4. 30 ( a), ( b), c i, c j : r i i c i = 1 c i = 1 ; r ji c i = 1 c j = 1 ; r jj c j = 1 c j = 1 ; r i j c j = 1 c i = 1 4. 30 r i i 0 + r ji c j = r i j c i + r jj 0 c i = 1, c j = 1, r ji = r i j ( 4. 25) :,, c i = 1 c j = 1 r ji, c j = 1 c i = 1 r ij :,,,, 4. 31 ( a), ( b), : r ji c i, r ji = r i j = 1 j = 1 ; r i j j = 1 c i = 1, 4. 31 109

4. 32 4. 7. 4 4. 32( a), ( b), P i j : r ji P i = 1 j = 1 ; i j j = 1 P i = 1 ; ji P i j = 1 j = 1, P i = 1, ji = 0, r ji j + P i i j = r jj ji + 0 ii r ji r ji + i j = 0 = 1 = - i j ( 4. 26) :,, P i = 1 j = 1 r ji, j = 1 P i = 1 i j, :, ;, 1 ),, 2 ),,? ( ) 3 ),,, 1. 2.,?,? 110

4.,,?,? 4.? 5.,? 4. 1 F Cy, F F y, M B, M C 4. 1 4. 2 B H F By 4. 2 4. 3 4. 3 B ( ) 4. 4 4. 4 D D H 4. 5 4. 5 B BH,, EI = 4. 6 4. 6 y = 4f a 2 x( a - x), EI =,, ds = dx, B BH 111

. 6 4. 7 B B 4. 7 4. 8,, A = 30cm 2, E = 20. 6 10 6 N / cm 2, P = 98. 1kN C CV 4. 8 4. 9 4. 9 DB EB A = 20 cm 2, d = 2m, P = 40kN, E = 21000kN /cm 2 4. 10 C B 4. 10 112 4. 11

4. 11 ( a) C C H, EI = ; ( b) AB A A 4. 12 D DH, EI = 1000kN m 2 4. 12 4. 13 4. 13 C EI = 2. 1 10 4 kn m 2 4. 14 C, D CD : EI, E = 2. 0 10 7 kn /m 2, I = 2. 25 10-3 m 4, = 10kN /m 3 ( 1m ) 4. 14 4. 15 4. 15 A AV E = 210GPa, A = 12cm 2, I = 3600 10-8 m 4 4. 16 D EA = 2EI 1 m 2 4. 16 4. 17 113

. 17 A, B AB 4. 18 C C V BC C EI, EA 4. 18 4. 19 B 4. 19 4. 20 C C B k 1 = 8 EI a D k 2 = 48EI a 3 4. 20 4. 21 4. 21 AB, 1 = 6 10-7 /cm, BC 0. 08cm AB BV 4. 22 A, B, D a = 3 cm, b = 8cm, c = 5cm C 4. 22 4. 23 114

4. 23 C, F = 8 10-6, h = 20cm, a = 2m 4. 24, CD t, C CH CV 4. 24 4. 25 4. 25, AB 0. 5 cm, C * 4. 26, AB BC R = 400m, AB, BC, BC DV * 4. 26 4. 27 ( a) y( x) = Mx2 ( b) 2EI B 4. 27 115

,, 5. 1 5. 1. 1,?,,,, :, 5. 1 B,,, X 1 5. 1 5. 2, 1, 2,, X 1, X 2 116 5. 2

5. 1. 2,, n 5. 1, n = 1, 5. 2, n = 2,,,, : 1 ), 5. 1, 5. 2 2 ), 5. 3, 5. 4 5. 3 5. 4 3 ), 5. 5 5. 5 4 ), 5. 6 5. 6,,,,, 5. 1 5. 7 5. 7( a), B, 5. 7( b) B 117

. 7,,, n = 4 5. 7 ( c), CD, CE, DE C, 5. 7( d), n = 5 5. 7( e),, 5. 7 ( f) n = 12, : 5. 7( e) 5, 5. 8, 5. 8 n? 5. 2 5. 2. 1, 3, 4,, : 5. 9( a), B, X 1 5. 9( b), X 1, X 1?,, X 1,,,, X 1 B,,, X 1,, X 1,, X 1, B,,, B X 1 118

5. 9,,, X 1 ( B ) 1 : 1 = 0 11 1P X 1 X 1,, : 1 1 + 1 P = 0 ( 5. 1), 4, 11 1P : ( 5. 1) : 1 1 = X 1 l 3 3EI, X 1 l 3 3EI - ql 4 8EI = 0 : X 1 = 3 8 ql X 1, X 1 1 P = - ql 4 8EI ( 5. 9 ( e) ), ( 5. 9 ( f) ),, X 1, :,,,, (, ), ;,,,,, : 5. 2. 2, 119

,,, 5. 9 ( a), B X 1,, A X 1,. 10, 5. 10,,,, 5. 2. 3 ( ), 5. 11 ( a),, B X 1, X 2, 5. 11( b), X 1, X 2 : 5. 11 1 = 0 11 + 12 + 1 P = 0 2 = 0 21 + 22 + 2 P = 0, : ik = i k X k : : n, : 1 1 X 1 + 12 X 2 + 1 P = 0 2 1 X 1 + 22 X 2 + 2 P = 0 ( 5. 2) 120

5 1X 1 + 12 X 2 + + 1 n X n + 1 P = 0 2 1 X 1 + 22 X 2 + + 2 n X n + 2 P = 0 n1 X 1 + n2 X 2 + + nn X n + np = 0 ( 5. 3) : 11 12 1 n 21 22 2 n n1 i k, X k : n2 nn X 1 X 2 = X n 1 P 2 P np ( 5. 4) = 1 X i, 1 ),,,, 2 ) i i, i k, i P, ik = ki, 3 ) : i i, ik, i P, 4, ( ) X i = 1, X k = 1 : M i, M k M P i i X i = 1 X i, M i ik X k = 1 X i, M i M k ip X i, M i M P : ii = M2 1 EI ds ik = M i M k EI ds ( 5. 5) M 1 i P = M im P EI 5. 11 ( a), M 1, M 2 M P 5. 11 ( c ), ( d), ( e), ( 5. 2 ) 11, 12, 21 M 1 M 2, 1 P M 1 M P, 2P M 2 M P,,,, : ds M = M 1 X 1 + M 2 X 2 + + M n X n + M P = M i X i + M P ( 5. 6) 121

. 3, 5. 3. 1 : 1 ),, 2 ) 3 ) X i = 1, X k = 1 M i, M k M P, 4 ) i i, ik, ip, X i ; 5 ) M, F Q, F N M = M i X i + M P 5. 3. 2 122,, ( 1 ),, ( 5. 5) 5. 2 5. 12 ( a) 1 ), 5. 12( b) 2 ) : 11 X 1 + 12 X 2 + 1 P = 0 21 X 1 + 22 X 2 + 2 P = 0 3 ) M 1, M 2 M P, 5. 12 ( c), ( d), ( e), : 11 = 1 1 a 1 + 1 1 EI 1 2EI 1 2 a 1 2 3 1 = 7a 6 EI 1 22 = 1 1 EI 1 2 a 2 2 3 a + 1 1 2 EI 1 2 a 2 2 3 a = a 3 2EI 1 12 = 21 = - 1 P = - 2 P = 4 ) : X 1 = - 1 1 EI 1 2 a 2 1 + 1 1 2EI 1 2 a 2 2 3 1 = - 1 1 2EI 1 2 a P a 4 1 2 = - Pa 2 32EI 1 1 2 EI 1 1 2 a Pa 4 1 2 a = Pa 3 32EI 1 3 80 P a X 2 = - 9P 80 5 ) : : M = M i X i + M P, 2a 2 3EI 1

5 M AC M C A M C B M B C = 0. 12 = - 3Pa 80 1 + 0 + 0 = - 3 Pa ( ) 80 = - 3Pa 9P 1 + 80 80 a + 0 = 6 Pa ( ) 80 = - 3 Pa 80 1 + 9 P 80 a + 0 = 6 80 P a ( ) 6 ) ( 5. 12 ( f) ), ( 5. 12( g) ), ( 5. 12 ( h) ),,, 5. 3 5. 13 ( a) B k, EI - :, B, X 1, 5. 13( b) :, B,, B 1 k X 1( X 1 ), 123

. 13 11 X 1 + 1 P = - 1 k X 1 M 1 M P, 11, 1P M 1 M P 5. 13 ( c), ( d), X 1 11 = l3 3EI, X 1 = - M M AB, 5. 13( e) 1 P 11 + 1 k 1 P = - = M AB = M 1 X 1 + M P = - 5P 5l 3 48EI 16 1 + 3 EI kl 3 3P l 1 + 8EI kl 3 16 1 + 3EI kl 3 :, B, AB EI k =, B,, X 1 k = 0, B, X 1 ( 2 ) = 0 = 5P, EI 16,,,, : 124 5. 4 ii = F 2 N i EA l i k = F Ni F Nk EA l i P 5. 14 ( a), X 1 = F N i F N P EA l ( 5. 7), 5. 14( b)

5 : X 1 X 1 Z 1. 14 11 X 1 + 1 P = 0, : = 1 F N1 F N P ( 5. 14( c), ( d) ), 11, = 1 : 11 = 1 EA 1 2 2a + - 1 P = 1 EA - 1 2, X 1 : : P 2 1 2 2 2a 2 + 2 2 2a 2 + 2 2 - X 1 = - 2P 2 2 2a 2 + - 1P = 1 1 2a 2 + - P 3 + 2 2 2 2 2 2-2 2a 2 2 P 2 = ( 3 + 2 2) a EA 2 a 2 = - Pa EA F N = F N 1 X 1 + F N P 5. 14 ( e) :, X 1, 5. 14 ( f)?? ( 3 ), 125

; ( ),,,,, : i i = M2 i EI ds + F 2 N i EA l i k = M i M k EI ds + F N i F N k EA l ( 5. 8) ip = M i M P ds + EI F N i F NP EA l 5. 5 5. 15( a), EI, EA 5. 15, CD X 1 : X 1 11 X 1 + 1 P = 0, 5. 15( b), : M 1 M P F N1 F N P ( 5. 15( c), ( d) ), 1 1, 1P 11 = 1 EI a 2a a + 1 2 a2 2 3 a 2 + 1 EA [ 12 2a + ( - 1) 2 a 2 + ( 2) 2 2a 2] 126 = 8a 3 3EI + 4 ( 1 + 2) a EA 1P = - 1 EI, X 1 : X 1 1 2 Pa a 2 3 a 2 + Pa 2a a + 0 = - 8Pa 3 3EI = - 1 P = 8P a 3 11 3EI 1 8a 3 3EI + 4( 1 + 2) a EA = P 1 + K K = 3( 1 + 2 ) EI 2EAa 2

5 X 1, F N = F N1 X 1 + F NP, : K, EA, EI, K 0, X 1 P,, EA, EI, K, X 1 0, ( ) ( 5. 16 ( a) ),,,, ( ) EA =, 5. 16 ( b), ( 5. 7), 5. 16 5. 6 5. 17 ( a), EI 2 = 6EI 1 5. 17, 5. 17( b),, 127

1 X 1 + 1 P = 0 M 1 M P ( 5. 17 ( c), ( d) ), 11, 1P 1 1 = 2 1 EI 1 2 3 3 2 3 3 + 1 P = - 2 EI 2 1 2 7 3 2 3 3 + 1 3 10 + 1 2 7 10 2 3 10 + 1 3 3 = 2270 3EI 2 : 1 1 EI 2 2 7 160 2 3 10 + 1 3 3 + 1 2 7 20 2 3 3 + 1 3 10-1 1 EI 1 2 1 20 2 3 3 + 1 3 2 = - 14480 3EI 2 X 1 = - 1 P = 6. 379kN 11 M = M i X i + M P, 5. 17( e) 5. 4 5. 4. 1 4,,,, M,,, M,,,,,,, : : ip ip = l = F N F N EA dx MM l EI dx = 1 EI y C ( 5. 9) EA =, ip EA ip = F N F N l ( 5. 10), F N, M, F N, M, 128 : 1 ) F N, M;

5 ),, F N, M; 3 ) ip 5. 7 5. 18 ( a) C c 5. 18 5. 1 ( 5. 18( b) ), 5. 18 ( c) 5. 18 ( d),, M 5. 18 ( b), ( c) c = 1 2EI 1-5. 18 ( b), ( d) 1 2 a 3P a 40 2 3 1 + 1 2 a P a 4 1 2 1 = c = 1 1 EI 1 2 a 3P a 40 1-1 2 a 3Pa 80 1 = 3P a 160EI 1 3Pa 160 EI 1 ( ),,,, 5. 4. 2, 3,,,,,,,,,, M i, M, M i ( ) M,,, 5. 8 5. 2 129

. 2, M 1, M 2 M, 5. 19 M 1 M, A, M 2 M, BH 5. 19 A = 1 1 a 1 EI 1 2 BH = 1 a 2 EI 1 2 2 3 6 Pa 80-3P a 80 Pa 6 80-1 3 3P a 80 + 1 2 EI 1 1 2 a 6P a 80 2 3 1-1 2 a Pa 4 1 2 1 = 0 + 1 2EI 1 1 2 a 6P a 80 2 3 1-1 2 a Pa 4 1 2 a = 0,,,,, n, n, n,,, 5. 9 5. 20 ( a) M 5. 20 130

5 M 5. 20( c), : = 1 2EI 1 3 EI = y C EI. 20 ( b), M = 1 y C = 1 = EI 1 2 6 14.4-1 2 6 57.6 + 2 3 6 90 + 1 2 6 30.6-1 2 6 23.4 + 1 2 6 14. 4-1 2 6 23. 4 = 0,, M :, M, M EI, M, ( M ) M 5. 5,,,,, 5. 21 ( a), ( b), t 1, t 2 ( t 1 > t 2 ), A,, A 5. 21 5. 21 ( c), ( d),,,,, 5. 5. 1,,, t, i P i t i t, X i 131

: i1 X 1 + i2 X 2 + + i n X n i t 4, it : + it = 0 i t = t 0 F N l + t h M i,, M t, : M = M i X i 5. 10 5. 22( a), 10,, EI,, h, 5. 22, 5. 22( b), : F N1, M 1 11 X 1 + 1 t = 0 5. 22( c), ( d), : 11 = 1 EI l 2 l + 1 2 l2 2 3 l = 4l 3 3EI t 0 = 1 2 ( 0 + 10) = 5 t = 0-10 = 10 132, : 1t = 5 l + 10 h l 2 + 1 2 l 2 = 5 l 1 + 3l h X 1 = - 1t = - 15 EI 1 + 3l 11 4 l 2 h M = M 1 X 1, ( 5. 22( e) )

5. 5. 2,,,,, ip i c i c, X i i1 X 1 i : + i2 X 2 + + in X n i c 4, i c : i c = - R i C V + i c = 0, i c,, 5. 23 ( a), A, 5. 23( b), : 11 X 1 + 1 c = 0 5. 23 5. 23 ( c), : 1 1 X 1 = - A,, : M = M i X i 5. 11 5. 24( a), 5. 24( b), X 1, X 2 X 3, X 3, : : 11 = i c = - R ic : 11 X 1 + 12 X 2 + 1 c = 0 21 X 1 + 22 X 2 + 2 c = 0 l 3EI = 22 12 = 21 = - l 6EI 133

1 c = - -. 24 1 l AB, : X 1 = X 2 = - 6EI l 2 AB i = EI,, l : X 1 = X 2 = - 6i l AB M = M i X i, : M AB = X 1, = AB = 2 c l M B A = X 2, M, F Q 5. 24( e), ( f) 5. 6,, 1 ),,,,,,,,, 2 ),,,,,,,,, ;, 3 ),,, 134

5,,,,,,, 4 ),,,, ( 5. 25( a) ) ;,, ( 5. 25( b), ( c) ),,,,,,,,,,, ( 5. 25 ( d) ) 5. 25 5. 7,,, 5. 26 ( a),,,, ;,,,,,,?, i i, i k, i P i k, ip,,,, 5. 7. 1, ik, i P 5. 26 ( a),, 5. 26( b) 135

: X 1, X 2 ; : X 3 M 1, M 2 M 3 ( 5. 26( c), ( d), ( e) ), M 1, M 2, M 3, : 1 3 = 3 1 = 0 23 = 32 = 0 :, 5. 26 11 X 1 + 12 X 2 + 1 P = 0 21 X 1 + 22 X 2 + 2 P = 0 33 X 3 + 3P = 0 :,,,,,, ( a) 5. 27 ( 5. 27 ( a) ), M P ( 5. 27 ( b) ), M 3 M P, 3P = 0 136

5 F Q a), : X 3 = 0 : M = M 1 X 1 + M 2 X 2 + M P M 1, M 2 M P, M ( 5. 27( c) ) :,,,, :,, M, F N, ;,, F N, M, F Q = 0,,,, ( 5. 28 ( a) ), M P 1 P = 0, 2 P = 0 ( a),, X 1 = X 2 = 0 : M = M 3 X 3 M 3, M P + M P ( 5. 28 ( b) ),, M ( 5. 28( c) ) 5. 28 :,,,,, :,, M, F N, F Q ;,, F Q,, ( M = 0, F N = 0),,, 5. 12 5. 29( a) EI =,, 5. 29 ( b),,,, 5. 29 ( c) 5. 7. 2,,,,,, 2, 5. 30 ( a), C,,, C 137

. 29,, 5. 30 ( b), 5. 31 ( a),,, 5. 31( b), 5. 30 5. 31, 3, 5. 32 ( a), C,,,, 5. 32 ( b), 5. 33 ( a), I 2,,, 5. 33 ( b) 5. 32 3,, 5. 33( c),,,, 5. 33 ( d ) 5. 13 :,, 138

5. 33 5. 34, 2, 3, 5. 8 3,,,,,, :,,, 139

c < l,,,, 10,,, : 1 ), ds = Rd ; 2 ) f l < 1 4 ds dx; 3 ), ( ) 5. 8. 1, ( 5. 35 ( b) ), X 1, : 11 X 1 + 1 P = 0 5. 35, :, f l 1 5, 11 11 = M2 1 EI ds + F 2 N1 1P = M 1 M P ds EI EA ds,, X 1 : ( 5. 11) : M 1 = - y, F N1 = cos 11 = y2 EI ds + cos2 EA ds 1 P = - ym P EI ds ( 5. 11) = 1 X 1 = - 1 P = 11 y2 ym P EI ds EI ds + cos2 EA ds X 1, ( 5. 12) 140 : M K = M 0 K - X 1 y K F Q K F N K = F 0 QK cos K - X 1 sin K = F 0 QK sin K + X 1 cos K ( 5. 13)

5 : 2 E 1 A 1, :,,, 5. 36 11 X 1 = - 1 P = 11 y2 ym P EI ds EI ds + cos2 EA ds + ( 5. 14) l E 1 A 1 5. 36 5. 14 5. 37 ( a) y = 4f l 2 x( l - x), l = 18m, h = 3. 6m, A = 384 10-3 m 2, I = 1843 10-6 m 4, E = 192GPa 5. 37 ( b) f l 5. 37 = 3. 6 18 = 1 5 ds dx, cos 1 : 11 = EI 1 l 1P = - y = 4f l 2 x( l - x),, 0 y 2 dx + 1 EA l 0,, dx ( a) 1 EI l ym P dx ( b) 0 M B = 0, M P = q 2 x( l - x) y, M P ( a), ( b), : 11 = EI 1 l 4f = 0 l 2 x( l - x) 2 dx + 1 EA l 0 16 3. 6 2 18 30 192 10 9 1843 10-6 + dx = 16 f 2 l 30EI + 1 EA 18 192 10 9 384 10-3 m / N 141

1 P = - 3518. 45 10-10 m /N = - X 1 = - X 1, 1 EI 4f x( l - x) q l 2 2 x( l - x) dx = - 8 10 3 3. 6 18 3 15 192 10 9 1843 10-6 = - 316. 44 10-4 m 1P = 89940 N = 89. 94 kn 11 m qfl 3 15EI,, ( 5. 13 ), 5. 8. 2, 3, 5. 38 ( b), : 1 3 = 31 = 0, 23 = 32 = 0, 12 = 21 0, : 11 X 1 + 12 X 2 + 1 P = 0 21 X 1 + 22 X 2 + 2 P = 0 33 X 3 + 3P = 0 5. 38 12 ( = 21 ) = 0,, 12 = 2 1 = 0,, 5. 39 ( a),,, 12 = 21 = 0 12, 2 1 :,, 12 = EI 21 = M 1 M 2 ds + k F Q1 F Q 2 GA ds + F N 1 F N2 EA ds ( a), X 1 = 1, X 2 = 1 O, x, y,,,, 5. 39 ( b), ( c), ( d) : ( a), : 142 M 1 = 1 F Q 1 = 0 F N1 = 0 M 2 = y F Q2 = sin F N2 = cos

5 12 = 21 = 0, y s :. 39 12 = 21 = y EI ds = 1 EI ( y 1 - y s ) ds 1 y 1 EI ds - ys 1 EI ds = 0 1 EI y s 1 y 1 EI ds = 1 ( 5. 15) EI ds ( 5. 40), 1 ds, EI 1, y 1 EI ds x 1, y s x 1, O,,,, : 11 X 1 + 1P = 0 22 X 2 + 2P = 0 33 X 3 + 3P = 0, : 5. 40 ( 5. 16) 143

1 1 = M 2 1 E 2 2 = M 2 2 E 3 3 = M 2 3 ds I ds I ds I = ds I + N 2 2 ds E 1 P = M 1 M P I ds E 2 P = M 2 M P I E 3 P = ds M 3 M P I = x 2 ds ds A = y 2 ds I I = M P ds I ds = ym P I = ds xm P I + cos 2 ds A ( 5. 17), f l > 1 5, ; f l 1 5, 22, 5. 15 5. 41( a) y 1 = 4f l 2 x 2, h C = 0. 6m, b = 1m I = I C cos, A = A C K cos 5. 41, 5. 41( b), : ( 5. 15), ds I = dx I C, : y s y 1 y ds 1 EI = ds EI ( 5. 17), y = y 1 - y s = x2 9-4 3, f l = 4f l 2 x 2 = = 4 4 x 2 = x2 12 2 9 1 EI y 1 dx C = 1 EI dx C = 4 12 = 1 3 > 1 5 6 x 2-6 9 dx 6 dx - 6 = 4 3,, : 144

5 C 11 = dx = l = 12 EI C 22 = y 2 dx = 6 x 2-6 EI C 33 = x 2 dx = 6-6 9-4 3 x 2 dx = 144, M P ( 5. 17), : ( 5. 16), : EI C - 6 x 0, M P = - 0 x 3, M P = 0 2 dx = 17. 07 : 1 2 qx2 = - 7x 2 3 x 6, M P = - 50( x - 3) 1 P = M P dx = 0-7x 2 dx - 6 EI C 2 P = ym P ds = 0 x 2-6 EI C 3 P = X 1 X 2 X 3 K - 6 3 50( x - 3) dx = 729 9-4 3 ( - 7x2 ) dx - 6 x 2 3 9-4 3 xm P dx = 0-6 x( - 7x 2 ) dx - 6 = - 1P = 729 kn m = 60. 8kN m 11 12 = - 2P = 875. 1 kn = 51. 26kN 22 17. 07 = - 3P = 1143 kn = - 7. 9kN 33 144 3 50( x - 3) dx = - 875. 1 x 50( x - 3 ) dx = 1143 3,, K K, x K = - 3, y K = x2 9-4 3 = - 1 3, tan K = y x = - 3 = - 0. 667, cos K = 0. 832, sin K = - 0. 555 M K = X 1 + X 2 y K + X 3 x K + M P F QK F NK = 60. 8 + 51. 26-1 3 = X 2 sin K + X 3 cos K + F Q P - 7. 9( - 3) - 1 2 14 ( - 3) 2 kn m = 4. 41kN m = [ 51. 26( - 0. 555) - 7. 9 0. 832-14( - 3) 0. 832] kn = 0. 08kN = X 2 cos K - X 3 sin K + F N P = [ 51. 26 0. 832 + 7. 9 ( - 0. 555) + 14( - 3) ( - 0. 555) ] kn = 61. 57kN 145

1 ),,,?? 2 ),??? 3 ),,? :,,, ;,,, 4 ),,,,,,, 1.? 2.,, 3.,? 4.,? 5. 5. 3, EI 1 10,? BC,,? 6., CE E 6 7 7., 1 2 3 4? 8., b c d e?? 9. EI,,? 146 10. ( a) ( b)?

5 9 10 11 12 11., A B X 1, X 2 EI 1 1 P 2 P 22 12? 12., 13. C H,, :, 13 147

5. 1 5. 1 148

5 5. 2, M, F Q 5. 3, 5. 2 5. 3 5. 4, EA = 5. 5 a) A = 10I /l 2, CD ; b) A = 3I /2l 2, M, A 0 A 5. 6, M 5. 7 M C EI =, k = EI / a 3 5. 8 5. 3 ( d) EI = 1. 08 10 5 kn m 2, C D 149

. 4 5. 5 5. 6 5. 7 5. 9 M, K C 5. 10, EI =, EA = EI /l 2, h = l /10,, M 150 5. 11, A A, M, F Q

5. 9 5. 10 5. 11 5. 12, B,, M 5. 12 5. 13, M 5. 14, y = 4f l 2 x ( l - x), l = 30m, f = 5m, h = 0. 5m, EI = 10 5 kn m 2, EA = 2 10 6 kn, cos = 1, ds = dx C 5. 15 151

. 13 5. 14 5. 15 152

,,,,, 6. 1 19,,, 5,, 20,,, ( ),,,,,,,,,, 6. 2 5,, : 153

1 ) 6. 1, S i k,,, M i k ik i, F Q ki ik k,, M f f i k, F Q i k ( 2), ; i k ik, ;,,,, ;, 6. 1, i, k, i k, M ki, M ik :,, 6. 2 6. 2,,, 6. 1,,, ( 6. 3), A, B A, B, AB,, : M AB M BA F Q AB = - F Q BA = - = 4i A + 2i B - 6 i l AB + M f AB = 2i A + 4i B - 6 i l AB + M f B A 6 i l A - 6i l A - 6 i l B + 12i l 2 AB + F f Q AB 6i l B + 12 i AB + F f Q BA l 2 6. 3 ( 6. 1),,,,,,,,,,, 154

6. 1 i = EI l M AB M BA F QAB F QBA 1 4i 2i - 6i l - 6i l 2-6i l - 6i l 12i l 2 12i l 2 - Pab2 l 2 - Pa2 b Pb 2 ( l + 2a) - Pa2 ( l + 2b) l 2 l 3 l 3 3 a = b = l /2 - Pl 8 Pl 8 P 2 - P 2 4 - ql2 12 ql 2 12 ql 2 - ql 2 5 3i 0-3i l - 3i l 6-3i l 0 3i l 2 3i l 2 - Pab( l + b) 2l 2 0 Pb( 3l 2 - b 2 ) - Pa2 ( 2l + b) 2l 3 2l 3 7 a = b = l /2-3Pl 16 0 11P 16-5P 16 8 - ql2 8 0 5ql 8-3ql 8 l 2-3b 2 m 0-3( l2 - b 2 ) m - 3( l2 - b 2 ) 2l 2 2l 3 2l 3 m 9 a = l, b = 0 m 2 m - 3m 2l - 3m 2l 155

M AB M BA F QAB F QBA 10 i - i 0 0 - Pa ( 2l - a) - 2l Pa2 2l P 0 11 a = l /2-3Pl 8 - Pl 8 P 0 12 - Pl 2 - Pl 2 P F Q lba = P F Q rba = 0 13 - ql2 3 - ql2 6 ql 0 6. 3 6. 3. 1,, : 1 ) :,,, 2 ) : 6. 3. 2, 6. 4 ( a) P, A ; B, BA BC B, B B ( Z 1 Z 1, ) ; C 6. 4, ( a) ( b) ( e) AB, B Z 1 ; BC, P, B ( Z 1 ), ( a) 156

6. 4, ( b) ( e),, :, Z 1 M BC M BA M AB = 4EI Z l 1 = 2EI Z l 1 = 3EI Z l 1 - M C B = 0 3 16 P l, M AB, M B A M BC,, Z 1,, Z 1, Z 1,,,, B, 6. 4( g), : M B = 0; M BA + M BC = 0 4EI Z 1 l + 3EI Z 1 - l 3 16 P l = 0 Z 1 = 3P l2 112EI ( ) 157

1 M AB, M BA M BC, M BC M AB M BA = 2EI Z 1 = 3 l 56 P l ( ) = 4EI Z 1 = 3 Pl ( ) l 28 = 3EI Z 1 - l 3 16 P l = - 3 28 P l ( ),, 6. 4( h ), 6. 4 ( i), ( j),,, 6. 5( a), C, D Z 1 Z 2, Z 3,, Z 1, Z 2 Z 3, C D, 6. 5( b), M C = 0 M C D + M CB = 0 M D = 0 M D C + M DB = 0 CD, 6. 5( b), F x = 0 P - F Q CA - F Q D B = 0 6. 5, Z 1, Z 2 Z 3,,, : 1 ), ( ) ; 2 ),, ( ) ; 3 ),, ; 158

6 ), 6. 3. 3,,,, ( 1 ),, ;, ;,,,,,, 6. 6( a),, 2 6. 6 ( 2 ),,,,, 6. 6( a), 4, 5, 6,, 1, 2, 3, :,,, ( ), 2,,,, ;, ( ),, 6. 6 ( a), 6. 6 ( b),,, 1,, 159

),,,,, 6. 6 ( a ), 1, 3, Z 1, Z 2, 3, Z 3, 6. 6( c), 6. 7 6. 7( a),, 1, 2, 3, 6. 7 ( b), 1, 2, 3,, 3, 6. 8( a), 4 2, 6. 8( b) 6. 8 6. 9 ( a),, 2 B 3, 2 B 23 3B 3, 3 ;, 2 4, 6. 9 ( b) 6. 10 ( a), 1, 2 ;, 6. 10( b) 6. 11 ( a), 3 1, 2, 3, 3 ;, 1, 3 6. 11( b) 160

6. 9 6. 10 6. 11,,,, 6. 12( a), ( b), 2 1 6. 3. 4,,, ;,,,, 161

( 6. 3. 2 ), 6. 13 ( a). 12, 162 6. 13

6 Z 1 ( ), C ( B ) Z 2 ( ),, 6. 13 ( b),,,,,,, R 1, R 2,, Z 1, Z 2, R 1 R 2 Z 1, Z 2 R 11, R 12, R 1 P, R 2 1, R 22, R 2 P, 6. 13( c), ( d), ( e),, R 1 = R 11 + R 12 + R 1 P = 0 R 2 = R 21 + R 22 + R 2 P = 0 R ij ( ) ; 1 i ( ) ; 2 j ( ) r 11, r 12 Z 1 = 1 Z 2 = 1, r 21, r 22 Z 1 = 1 Z 2 = 1,, r 11 Z 1 + r 12 Z 2 + R 1P = 0 ( 6. 2) r 21 Z 1 + r 22 Z 2 + R 2P = 0 Z 1, Z 2, :, 6. 13, R 1 M B = 0, R 2 = 0 F x = 0 = 0 B n, n, n : r 11 Z 1 + + r 1 i Z i + + r 1 n Z n + R 1P = 0 r i1 Z 1 + + r ii Z i + + r in Z n + R i P = 0 r n1 Z 1 + + r ni Z i + + r nn Z n + R np = 0 Z,,, : r 11 r 12 r 1n Z 1 R 1 P r 21 r 22 r 2n Z 2 + R 2 P = 0 ( 6. 3) r n1 r n2 r n n Z n R np, r ii, i Z i = 1 i ( ), Z i 163

, ; r i j ( i j), j Z j = 1 i ( ), Z i,,, r ij r ji, r i j = r ji ; R i P,, i ( ), Z i,,, ( ),,,, : : 1 ), ; 2 ) ( r R), ( ) ; 3 ), ( ), 6. 1 Z i = 1 Z k = 1 M i, M k M P, ( ),, r i i, r ik R ip,, M i, M k M p Z i, M i = 0 ; r ii, r i k R ip,, M i, M k M P, F x = 0 F y = 0 6. 13( a) 6. 13( a),, ( 6. 2), 6. 1 Z 1 Z 2 = 1 = 1 M 1, M 2 M P, 6. 14( a), ( b) ( c), 6. 14( a), ( b) ( c) B, M B = 0, r 11 = 7i, r 12 = - 6i l, R 1P = ql 2 12, 6. 14 ( a), ( b), ( c),, F x r 21 = - = 0, 6. 1 6i l, r 22 = 15i l 2, R 2P = -,, 164-7iZ 1-6i l Z 1 6i l Z 2 + 15i l 2 Z 2 - + ql2 12 = 0 3 2 ql = 0 3 2 ql

6, Z 1, Z 2 :. 14 Z 1 = 31 276 ql2 i ; Z 2 = 40 276 ql3 i M AB M AB = 2i 31 276 ql2 i - 67 92 ql2 M = M 1 Z 1 + M 2 Z 2 + M P - 6 i l 40 276 ql3 i - ql2 12 =, M 6. 15 ( a) M, M F Q F N, 6. 15( b), ( c) 6. 15 165

. 4 6. 4. 1, : ; ; M i, M k M P, ; Z i ; ; 5. 4,,,,, 6. 4. 2 ( 1 ) ( ),,, M i, M k M P,, 6. 1 6. 16 ( a) B, Z 1,, 6. 16 ( b) r 11 Z 1 + R 1 P = 0 M 1, M P, 6. 1, M 1, M P, B, 6. 16 ( c), ( d) M B = 0, r 1 1 = 7i; R 1 P = 6 Z 1 r 11, R 1 P : 166 7 i Z 1 + 6 = 0 Z 1 = - 6 7i

6. 16, M = Z 1 M 1 + M P,, 6. 16( e) M, M F Q, 6. 16( f) 6. 16 ( g), M B = 0 B,, B F y = 0, F BY = 17. 07kN, 6. 16 ( g) 6. 2 6. 17 ( a) B,, 1, 6. 17 ( b) r 1 1 Z 1 + R 1P = 0 167

M 1, M P,. 17,,, i 0 = EI 1 = 1, i BD = i C E = 2EI 4 i AB = 4EI 4 6. 1, M 1, M P B Z 1 r 11 = 4 + 2 + 3 = 9 R 1 P, = 0. 5 = 1; i BC = 5EI 5 = 1, 6. 17( c), ( d) = ( 26. 67 + 0-62. 5) kn m = - 35. 83kN m 168

6 M M = Z 1 M 1 1 = - R 1 P r 11 = - - 35. 83 9 = - 3. 98 + M P, M, 6. 17( e) B, 6. 17 ( f), M B = 42. 60 + 7. 96-50. 56 = 0 : 6. 2,, 6. 18 M P, R 1 P = 0,, Z 1 = 0 M = Z 1 M 1 + M P, Z 1 = 0, M P = 0, M = 0 M, F Q,, 6. 18, :,, ( 2 ),,,,,, 6. 3 6. 19 ( a), 6. 19 3 : B, C Z 1, Z 2 Z 3 6. 19 ( b) : r 11 Z 1 + r 1 2 Z 2 + r 13 Z 3 + R 1 P = 0 r 21 Z 1 + r 2 2 Z 2 + r 23 Z 3 + R 2 P = 0 169

31 Z 1 + r 3 2 Z 2 + r 33 Z 3 + R 3 P = 0 M i, M P i 0 = EI 0 1, = 1, i A B = i CD = 4EI 0 4 = 1; i B C = 5EI 0 5 = 1 i BE = 3EI 0 4 = 3 4, i CF = 3EI 0 6 = 1 2 6. 20 6. 1 Z 1 = 1, Z 2 = 1, Z 3 = 1 M 1, M 2, M 3 M P, 6. 20 ( 6. 20), M = 0, F x = 0, : 170 r 1 1 = 10, r 12 = 2, r 13 = - r 2 1 = 2, r 2 2 = 9, r 2 3 = - r 3 1 = - 9 8, r 32 = - 9 8, R 1P = - 5 3 kn m 1 2, R 2 P = 125 3 kn m 1 2, r 33 = 35 48, R 3P = 0

6 i, : 10 Z 1 + 2Z 2-2Z 1 + 9 Z 2 - - 9 8 Z 1 - Z 1 = 0. 935, Z 2 = - 4. 932, Z 3 = - 1. 945 9 8 Z 3-5 3 = 0 1 2 Z 3 + 125 3 = 0 1 2 Z 2 + 35 48 Z 3 = 0 M = MZ 1 + M 2 Z 2 + M 3 Z 3 + M P,, M, 6. 21 ( a) F Q, 6. 21( b) F N, 6. 21( c) 6. 21 B, C, 6. 21( d), ABCD, X = 0, 2. 15-2. 15 = 0 6. 21 Y = 0, 29. 3 + 105. 5 + 48. 9-20 9-3. 7 = 0 6. 4 6. 22 ( a), M 171

, E, 6. 22 ( b) 6. 22 r 1 1 Z 1 + R 1P = 0 6. 22 ( c), ( d), Z 1 = 1 M 1 M P, ( 6. 22( c) ),, : 172 r 1 1 = 3i 1 h 2 1 + 3i 2 h 2 2 + 3i 3 h 2 3 = 3i h 2

6 1P = - P Z 1 r 11 R 1 P, 6. 22 ( e) * Z 1 = - R 1 P r 11 = - - P 3i h 2 6. 5 6. 23( a) = P 3 i h 2 6. 23 3 : Z 1, Z 2 Z 3 6. 23( b),,,, : r 11 Z 1 + r 1 2 Z 2 + r 13 Z 3 + R 1 P = 0 r 21 Z 1 + r 2 2 Z 2 + r 23 Z 3 + R 2 P = 0 r 31 Z 1 + r 3 2 Z 2 + r 33 Z 3 + R 3 P = 0, M 1, M 2 M P, 6. 24 ( a), ( b ), ( c) M 3, : M 3, C, 6. 24( d) C Z 3, AB B C AB BC BB = CC = 1 BB B = = 45 BC = B = - 1 = 1 6. 1, Z 3 = 1 M 3, AB = BB = 2 M B A = M AB = - 6i AB AB = - l AB 6 1 2 2l 2 = 3 2 l 173

M C B = M B C = - 6 i B C l BC M C D = M DC = - 6i D C l D C BC D C = - 6 2 ( - 1) = 12 l l. 24 = - 6 1 ( - 1) = 6 l l M 3 6. 24 ( e) M i M P,, : r 1 1 = 8 + 2 = 10. 83 r 12 = r 21 = 4 174

6 r 2 2 = 12 r 13 = 12-3 2 l r 2 3 = 6 l M 3 : F Q C D = 12 l 2 R 1 P = 7. 76 l = - 4 Pl 27 = - 0. 148Pl R 2P = 2P l = 0. 074Pl 27, r 33,, 6. 24 ( f), M O = 0;, R 3P = - 0. 741 F Q BA = 12i BA 12 l 2 BA = B A ( 2 l) 2 2 2 2 = 6 l 2 7. 76 l + 6 l + 3 2 l r 33 = : r 31 = r 13 = 7. 76, r 32 = r 23 = 6 l l, : 10. 83Z 1 + 4Z 2 + 7. 76 Z 3-0. 148Pl = 0 l 4 Z 1 + 12 Z 2 + 6 l Z 3 + 0. 074Pl = 0 7. 76 Z 1 + 6 l l Z 44. 48 2 + Z l 2 3-0. 741Pl = 0 + 6 l 44. 48 l 2 Z 1 = 0. 00746Pl; Z 2 = - 0. 0175 Pl; Z 3 = - 0. 01771Pl + 6 l 2 2l + 12 l 2 l - r 33 l = 0, M = Z 1 M 1 + Z 1 M 2 + Z 3 M 3 + M P,, 6. 25 ( a) 6. 25,, 6. 25 ( b) M o = ( 0. 0541P l + 0. 1763P l) + ( 0. 0839P 2l + 0. 3167 Pl) - P 2 3 l = 0 175

3 ),,,,,,,, M 6. 6 6. 26 ( a), M 6. 26 P C, C, B, 6. 26( b) r 11 Z 1 + R 1 P = 0 M 1 M P, 6. 26( c), ( d) B, r 11 = 11 2 i; R 1 P = Pl 2 Z 1 = - R 1 P r 11 = - P l 2 11 2 i = - Pl 11i M = M 1 Z 1 + M P M, 6. 26( e) 176 ( 4 ) 5,,

6,,,,, 6. 27 6. 7 6. 27 ( a) EI =,, ( 6. 27 ( b) ) ( 6. 27( c) ), ( 6. 27 ( d), ( e) ) 6. 27 ( d), B,, 6. 28 ( a) r 11 Z 1 + R 1 P = 0 M 1 M P, 6. 28( b), ( c), r 11 = 4 + 4 + 2 = 10 R 1P = ( 30-45 ) = - 15, Z 1 = - R 1 P r 11 = 1. 5 M = M 1 Z 1 + M P, 6. 28( d) 177

. 27 ( e), B, 6. 29 ( a), r 11 Z 1 + R 1 P = 0 6. 28 178 6. 29

6 M 1 M P, 6. 29( b), ( c),, Z 1 = - R 1P r 11 = - 2. 14 r 11 = 4 + 4 + 6 = 14 R 1P = 30, 6. 29( d), 6. 28 ( d ) 6. 29( d),, 6. 30 ( 5 ),,, 6. 30 ( 6. 2) R 1 P R i P R np R i C R i C R nc R i C 6. 1 M C, M C, 6. 31 179

. 8 6. 31( a), M A A = 1cm, D D = 0. 01rad B, 6. 31( b) r 1 1 Z 1 + R 1C = 0 M 1 M C, 6. 31( c), ( d),, R 1 C r 11 = 3 i + 4i + i = 8 i = 0. 75 i + 0. 02i = 0. 07ikN m Z 1 = - R 1 C r 11 = - 0. 77i 8i = 0. 0963 M = M 1 Z 1 + M C, i = EI, 6. 31 ( e) 4 ( 1 ),,,,,,,, ( 2 ),,,,, M i M P, 6. 1,,, 1.,,? 2.? 3. A? 180

6.? 5. M p, R 1 p? 6.,? 7.,?? 8.? 9.,? 8 9 10 10., B, B? 11.,? 12., 13., M A? 13 181

6. 1 6. 1 6. 2,,, ( c ), ( e ) C EI = 182

6. 2 6. 3, EI = 6. 4 EI = 6. 5 B 20mm, C 12mm, E = 2. 1 10 2 kn/ mm 2, I = 2 10 8 mm 4 183

. 3 6. 6 B 5 mm, EI = 3 10 5 kn mm 2 184

6. 4 6. 5 6. 6 185

,, 20 30, 7. 1 5 6,,,,,,,, ;,,, 7. 2, 7. 2 7. 3, 186 7. 2. 1 ( 1 ),

7. 1 AB, A ( ), A, S AB ( ), 6. 1 7. 1 : S AB = 4i : S AB = 3i : S AB = i : S AB = 0 i = EI l : AB, A? ( 2 ) 7. 2( a) M A, A A, M A B, M A C M A D 7. 2, : M AB M AC M AD = S AB A = 4i AB A = S AC A = i AC A = S AD A = 3i AD A ( 7. 2( b) ), M A = 0, M = S AB A + S AC A + S AD A A ( a) 187

= M S AB + S AC + S AD = M S A S A A A ( a), : A M AB = S AB A S M M AC = S AC A S M ( b) : M AD = S AD A S M, A A M Aj = Aj M Aj = S Aj S A Aj M, M Aj : Aj = AB + AC + AD = 1, A M, A ( 3 ) 7. 2( a), M A,, : M AB M AC M AD = 4i AB A, = i AC A, M BA = 2i AB A = 3i AD A, M DA = 0 M CA = - i AC A M BA M AB = C AB = 1 2 ( c) C AB = 1 2,, C, :, C = 1 2 ;, C = - 1;, C = 0 ( c) : M BA = C AB M AB M AB, C AB, M B A 188

7. 2. 2 7. 3 P, 7. 3( a), 3 : ( 1 ) B B, AB P, AB, 7. 3 ( b), M F BA BC M F BC = 0, B M B, 7. 3( b), M B = 0, B M B = M F BC + M F BA = M F BA K K K,,, ( 2 ) 7. 3,, M B, ( - M B ), 7. 3 ( c) B B M B A M BC, ; A M AB ( 3 ) 7. 3( b) ( c), 7. 3( a),, 7. 3( b) 7. 3 ( c ) 189

( 7. 3 ( a) ), M F BA + M BA = M B A, 3 :,, ;,, ;,, 7. 3 ( 1 ) 7. 1 7. 4( a), M,,, ( ) 0. 471 0. 529 M F - 60. 00 + 60. 00-75. 00 0 + 3. 53 + 7. 06 + 7. 94 0 M - 56. 47 + 67. 06-67. 06 0 : : 190 S B C S BA = 7. 4 = 4EI 6 3( 2EI) 8 = 2 3 EI = 3 4 EI

7 = S BA S = BC = S BC S = 2 3 EI 2 3 EI + 3 = 4 EI 3 4 EI 2 3 EI + 3 = 4 EI 8 17 9 17 = 0. 471 + 0. 529 = 1 BA B BC B = 0. 471 = 0. 529 B,, 6. 1 : M F BA = 1 12 ql 2 = 1 12 20 6 2 = 60. 00 kn m M F AB = - M F BC = - 1 12 ql 2 = - 1 12 20 6 2 = - 60. 00kN m 3 16 pl = - 3 50 8 = - 75. 00kN m 16 2 B B M B = M F BA + M F BC = 60 + ( - 75) = - 15. 00kN m M BA M BC = B A ( - M B ) = 0. 471 ( 15) = 7. 06 kn m = BC ( - M B ) = 0. 529 ( 15) = 7. 94kN m 3,, : M AB = C AB M BA = 1 2 7. 06 = 3. 53kN m M BC = 0 3,, ( ), 2 3 M AB M BA M BC = - 60 + 3. 53 = - 56. 47 kn m = + 60 + 7. 06 = 67. 06kN m = - 75 + 7. 94 = - 67. 06kN m M CB = 0 191

a) 4 B M B = 0, M B = 67. 06-67. 06 = 0, :,,,, b),, M Bi M B i = M Bi S Bi S Bi B BA = BC M AB, M AB, A, A, M B A, B, B,, M, 7. 4( c), : a) ; b) 6. 1 ; c) ( : ) ; d), ; e),, 7. 2 7. 5( a), ( 7. 5 ( b) ),, 7. 5( b), 7. 6 :,, EI l = 1, i 1 A = 1, i 1 C = EI l 2 1A = 1C = = 2, 3 i 1A 3i 1A + i 1 C = i 1 C 3i 1 A + i 1C = 3 1 3 1 + 2 = 0. 6 2 3 1 + 2 = 0. 4 1,, 6. 1 192

7. 5 0. 6 0. 4 0 + 120-80 - 40 0-24 - 16 + 16 0 + 96-96 - 24 1A 7. 6 M F 1 A = 1 8 ql 2 = 120kN m 1C, 1 : M F 1 C = - M F C1 = - M 1 : M, 7. 7 1 3 q l 2 1 6 q l 2 2 2 = - 1 12 ql2 = - 80kN m = - 40kN m = ( + 120-80) kn m = + 40 kn m 7. 3 7. 8( a), M, F Q, B,, 193

. 7 4 7-60 + 60 0 0 + 11. 43 + 22. 86 + 17. 14 0-48. 57 + 82. 86 + 17. 14 0 3 7 7. 8 194

7 F B A = + 1 8 pl = + 1 8 80 6 = + 60 kn m M F AB = - M F B C = 0 1 8 pl = - 60kN m M F C B = 0 B, M B M B = + 60 + 0-100 = - 40 kn m,, ( ), 7. 8 ( b),, BC,, M,, : F QAB = F QC B = M BC l = 2. 86kN AB,, AB 7. 8( c) F Q AB F Q BA = 34. 28kN = - 45. 72kN, B, 7. 8( d), F y ( 2 ) : R B + F Q BA - F Q BC = 0 R B + ( - 45. 72) - ( - 2. 86) = 0 R B = 42. 86kN = 0,,, ABCD 7. 9( a), 1, B, C,, 3 B, C,, BC, 7. 9( b), BC M F BC M F CB, B, C M B M C 2, B( C ), B M B B B, 7. 9( c) B, B, A, C 3, B, C, C M C C C, 7. 9 ( d) C 195

M C = M C + M C M C, C, B, D B M B, 2, 2 3, B, C,, 2,, ( ), ( ), 7. 9, 7. 4 7. 10 ( a) ( EI = ) EI = 1, B: S B A = 4i BA = 4 1 6 = 0. 667 S B C = 4i BC = 4 1. 5 6 = 1 BA = S BA S = B 0. 667 0. 667 + 1 B = 0. 4 + 0. 6 = 1 C: = 0. 4 BC = S B C S = B 1 0. 667 + 1 = 0. 6 S C B = 4i CB = 4 1. 5 6 = 1 S C D = 4i CD = 3 2 6 = 1 CB = S C B S = C 1 1 + 1 C = 0. 5 + 0. 5 = 1 = 0. 5 CD = S CD S = C 1 B, C, 1 1 + 1 = 0. 5 196

7 F BC = - 1 8 Pl = - 1 8 80 6 = - 60kN m M F CB = + 1 8 Pl = + 1 8 80 6 = + 60kN m M F CD = - 2 1 8 ql2 = - 1 8 20 6 2 = - 90 kn m 0. 4 0. 6 0. 5 0. 5-60 + 60-90 0 B C B C B C 12 24-0. 6-1. 2-0. 05-0. 09 36 18 3 6-1. 8-0. 9 0. 23 0. 45-0. 14-0. 07 0. 04 6 0. 45 0. 03 11. 35 22. 71-22. 71 83. 52-83. 52 0 7. 10 B, C - 60kN m - 30 kn m, B B( C ), B - 60kN m,, BA BC BC C AB A 0. 4 60 = 24kN m 0. 6 60 = 36kN m 1 36 = 18kN m 2 197

2 24 = 12kN m, B,,, B, C C 60-90 + 18 = - 12kN m, CB CD BC B 0. 5 12 = 6kN m 1 6 = 3kN m 2 1 B, 2 2 B C, 3 3 kn m - 0. 9kN m 0. 23kN m - 0. 07 kn m, 3,,,,, M,, 7. 10( b) 198 7. 5 7. 11 ( a), EI = ( EI = 1 ) i D C = 2EI 6 = 1 3 i D A = 2EI 4 = 1 2 i D E i ED i EF = 3EI 6 = 1 2 = 3EI 6 = 1 2 = 4EI 3 = 4 3 S D C = 3i DC = 1 S DA = 4i D A = 2 S D E = 4i DE = 2 S E D = 4i ED = 2 S EF = 3i EF = 4

7. 11 i EB = 2EI 4 = 1 2 S EB = 4i EB = 2 D: DC = S DC S = D S DC S DC + S DA + S D E = 1 1 + 2 + 1 = 0. 2 DA = S D A S = D 2 5 = 0. 4 D E = S D E S = D 2 5 = 0. 4 = 1 E E: 199

= S ED S = E S E D S ED + S ER + S E F = 2 2 + 2 + 4 = 0. 25 EB = S E B S = E 2 8 = 0. 25 EF = S E F S = E 4 8 = 0. 5 = 1 E M F D C = 1 8 ql2 = 1 8 10 6 2 = 45kN m M F D E = - 1 12 ql2 = - 1 12 10 6 2 = - 30kN m M F E D = + 1 12 ql2 = + 1 12 10 6 2 = 30kN m,,, E 7. 11 ( b) 200 7. 12 7. 12 ( a), ( b), ( c)

7. 12( d) 7. 6 7. 13 ( a) 0. 600 0. 400 0. 500 0. 500 0. 471 0. 529 0 0-80. 00 40. 0-60. 0 60. 0-25. 0 0-40. 0 B, D 24. 00 48. 00 32. 00 16. 00-8. 24-16. 49-18. 51 0 C 3. 06 6. 12 6. 12 3. 06 B, D - 0. 92-1. 84-1. 22-0. 61-0. 72-1. 44-1. 62 0 C 0. 33 0. 66 0. 67 0. 33 B, D - 0. 1-0. 20-0. 13-0. 07-0. 08-0. 16-0. 17 0 C 0. 04 0. 07 0. 08 0. 04 B, D - 0. 01-0. 02-0. 02-0. 01-0. 01-0. 02-0. 02 0 C 0. 01 0. 01 22. 97 45. 94-45. 94 62. 17-62. 17 45. 32-45. 32 0-40 7. 13 EF, : M E F = - 40kN m, Q E F = 20kN, M EF Q EF E, 7. 13( b), E, B, C, D3, D C = 4 4 4 4 + 3 6 = 0. 471 201

= 3 6 4 4 + 3 6 = 0. 529, DE,,, E E,, DE, M F DE = - 6. 1 3 16 60 4 + 1 40 = - 25kN m 2, B, C, D,,, BC, CD, DE 90 kn, 20kN /m 60kN 7. 13 ( c) 7. 4,, 7. 14 ( a),, 7. 14 7. 14 ( b),,, 7. 14 ( c), 7. 15( a) 7. 15 ( a),,,, 7. 15 ( b),, 7. 15 ( a), ij F Q j i = 2P, i, j ij, j, i 202

7. 15 ij, 7. 15 ( d) j,, 7. 15( c) 6. 1,,,,, 7. 15 ( e),,, i, - 1, j ( i ), i, j,,, i j, ( ),,,,,,,,, 7. 7 7. 16( a), B, C 7. 16 ( b), AB, BC, M F CB = M F B C = - M F BA = M F AB = - C M C B M B 1 20 6 = - 60kN m 2 1 40 6 = - 120kN m 2 = - 60kN m = - 180kN m 203

S C E = 3 18 = 54, S CB = S B C = 1 15 = 15, S BD = 3 18 = 54, S BA = 1 20 = 20 C, B, C E = C B = BC = B D = BA =. 16 54 54 + 15 15 54 + 15 15 15 + 54 + 20 54 15 + 54 + 20 = 0. 783 = 0. 217 = 0. 168 = 0. 607 20 15 + 54 + 20 = 0. 225 ( - 1 ) B, 7. 16( c) 7. 17 3, 7. 17( c) 7. 17( b) n 7. 17( c) 7. 17 ( b) n,,,,, 7. 17( a), 7. 17 ( a),,,,,, 204

7 C B A D EC CE CB BC BD BA AB DB 0. 783 0. 217 0. 168 0. 607 0. 225-60 - 60-120 - 120-30. 24 30. 24 109. 26 40. 5-40. 5 0 0 70. 66 19. 58-19. 58-3. 29 3. 29 11. 88 4. 41-4. 41 0 0 2. 58 0. 71-0. 71-0. 12 0. 12 0. 43 0. 16-0. 16 0 0. 09 0. 03 0 73. 33-73. 33-46. 64 121. 57-74. 93-165. 07 0 7. 17 1 ), 2 ),,, 3 ),, D, 1.? 2. ( ) 205

3. AB CD EI l, A S AB C S CD?,? 4. A, A?. 2 7. 3 7. 4 5. : ( ) A. ; B. ; C. ( ) ; D. 6. : 7. 6 7., 3 : ( a) K ; ( b) K ; ( c) K 8.,,? 9.? 10., n 1 n 2, n 1 n 2, : ( ) A. M A M B ; B. M A M B ; C. M A M B ; D. 7. 10 206

7 7. 1, M 7. 1 7. 2 7. 2 M, 7. 3, 7. 4 M, F Q, F N 7. 5 E = 7. 6 E 207

. 3 208

7. 4 7. 5 7. 6 9

,,,,, 8. 1 8. 1. 1,,,, ; 8. 1,,,, P, 8. 1,,, ( Z K ), 210

8 Kma x), Z K 8. 1. 2,, : P = 1, Z K,, Z K Z K, 8. 2( a), P = 1,, P = 1 A, F B Y 0 P = 1 B, F B Y = 1, 8. 2 ( b), 8. 2 F BY P = 1 A B, B, F B Y, F BY, P = 1 B, F BY, : ( P = 1), Z K ( ), Z K Z K x, ( ) y Z K,,, P = 1 Z K 8. 3,,, 8. 3 C M C P = 1 C 211

1 ) M C C M C P = 1 x, ( P = 1), x,,, M C = f( x) ( x p = 1 ) M,, ( P = 1), x,, x, M( x) = g( x) ( x ) ( 2 ) M C M, D y D M D y D P = 1 D M C, M D P = 1 C D 8. 2, Z K, : P = 1,, x ; x, ;, 8. 2. 1, ( 1 ) F AY : P = 1, A x( 8. 4 ( a) ) F AY = l - x l M B = 0, F AY l - P ( l - x) = 0 ( 0 x l) ( 8. 1) F AY, F AY A, x = 0, F AY = 1; B, x = l, F AY = 0 F AY, 8. 4( b) F BY : F BY = x l ( 0 x 1) ( 8. 2) 8. 4( c) 212

8. 4 8. 5 ( 2 ) 1 ) ( 8. 5( a) ) C M C P = 1 C, CB, M C = 0, M C = F BY b = x l b ( 0 x a ) ( 8. 3) M C, M C C x = 0, M C = 0 ; x = a, = a b l P = 1 C M C P = 1 C, AC, M C = 0, M C = R A a = l - x a ( a x l) ( 8. 4) l M C C x = a, M C = a b l ; x = l, M C = 0 P = 1 C M C,, M C 8. 5( b), M C, C ( 8. 3), ( 8. 4) :, [ ] ;,, F B Y b, F AY a, F AY F B Y M C 213

F BY b,, C, F AY a,, C, M C, 2 ),, C F QC, P = 1 C, CB, F Y = 0, P = 1 C, AC, F Q C = - F BY ( 0 x < a ) ( 8. 5) F Q C = F AY ( a x < l) ( 8. 6) ( 8. 5), ( 8. 6), F Q C F BY,, C a l, F AY, C b l F Q C 8. 5( c), F Q C, C P = 1 AC, C ; P = 1 CB, C P = 1 C,, F Q C a l + b l, a l + b l = 1 F Q C C,,, P = 1 C, F Q C 8. 1 8. 6( a) F AY, F B Y M C, F Q C, M D, F Q D ( 1 ) F AY, F BY A, x x, F AY F BY R A = l - x l R B = x l - d x l + e 8. 6 ( b), ( c) F AY, F BY, P = 1 - d x l + e ( 2 ) M C F Q C P = 1 C, M C F Q C : P = 1 C, 214 M C = F BY b ( - d x < a ) F Q C = - F BY M C = F AY a ( a < x l + e) F QC = F AY

8. 6 M C F Q C 8. 6( d), ( e) ( 3 ) M D, F Q D, D, x 1 P = 1 D, x 1 D,, P = 1 D, M D = - x 1 F Q D = - 1 P = 1 D, M D = 0 F Q D = 0 M D F QD 8. 6( f), ( g),,,, 215

( 8. 6( f), ( g) ) 8. 2. 2,,,,, 8. 7 ( a),, A, C, E, F, B ( ), 8. 7( a), ( 1 ) F AY F BY F AY F BY, ( 2 ) 1 ) M C C P = 1 C, C, F BY M C ; P = 1 C, C, F AY M C M C 8. 7( b) C 2 ) M E ab l = d 3 d 4d = 3 4 d P = 1 P = 1 D F, F BY F AY M E, M E P = 1 P = 1 DF, D X, DF d - x d x d - x, 8. 7( c), D d, F d x d E M E,, M E Y : P = 1 D, y = y D P = 1 F, y = y F P = 1 D x, D d - x d, F x d, y = d - x y d D + x d y F ( 8. 7) x, M E DF, 8. 7( d) M E, P = 1 AB, M E, 8. 7( e) E 216 ab l = 3 2 d 5 2 d 4d = 15 16 d

8 DF y D = 15 16 d 4 5 = 3 4 d y F = 15 16 d 2 3 = 5 8 d. 7 D, F, M E, 8. 7( e), ( ), :,,, 8. 7( f) F Q E,, D, F, DF,, F QD F, F Q E F QD F 217

. 2. 3,,,,, 8. 2 8. 8( a), P = 1 N a -, P = 1 -,, M 1 F N a h + F AY 4d = 0 F N a = - F AY 4d h P = 1 I-I,, M 1 = 0, F N a h + F BY 4d = 0 F N a = - F BY 4d h M 1 F N a = - M 1 h = 0, F Na 1, M 1 - F Na, 8. 8 ( b) F Nb 2,, F Nb 2, P = 1 2, F y = 0 F Nb sin + 1 = 0 F N b = - P = 1 3 4, F Nb F NC 1 sin -, P = 1 2,, = 0, F N b 8. 8( c) F y = 0, F NC sin - F AY = 0, F N C = F AY sin P = 1 3,, F y = 0, F NC sin - F BY = 0, F N C = F BY sin 1 h F NC 2 3 F AY F B Y, 2 3, F NC 8. 8( d) 218 F Nd -, P = 1 -,, M 3 = 0, F N d h - F AY 2d = 0, F N d = F Ay 2 d h

8 P = 1 -,, M 3 = 0, F N d h - F B Y 6d = 0, F Nd = F B Y 6 d h. 8 M 3 F N d = M 3 h F Nd 3 M 3 1 h F N d, 8. 8( e) 8. 3, 219

. 3. 1 8. 9( a) F B Y = Z, ( B), Z,, 8. 9, Z = 1, 8. 9( b) A ( ), Z P Z P = 1 Z Z, P = 1 P,, Z Z + ( - P P ) = 0 P = 1, Z = P ( 8. 8) Z Z Z, ; P P = 1, x, Z( x) = P ( x) ( 8. 9), Z( x) Z, P ( x) ( 8. 9 ( b) ), Z Z, Z ( 8. 9( c) ), R B, Z K, Z K, Z K, P = 1 Z K : Z, Z K Z K, ( p ), Z K Z = 1,, 8. 3 8. 10 M C, F Q C F Q C 8. 10 ( b) ; 8. 4 M C 8. 10( c) 8. 11 ( a) F BY, M 1, F Q 1, M 2, F Q2 F BY B, ABF A, FG G, B,, F BY, 8. 11( b) 220

8. 10 M 1, F Q1 8. 11 ( c), ( d) M 2, F Q2 M 2, 2 M 2, 2,, 8. 11 ( e) M 2 F Q2, 2 F Q2,,, 8. 11( f) F Q2,,,,, 8. 3. 2,, 8. 12( a), P = 1 x, F CY = Z 1 221

. 11 Z 1, Z 1, 8. 12( b) ( b) Z 1 ( a) ( C ),, 1 Z 1 x 1 = 1,,, 8. 12 ( c) p1 11 ( c) P = 1 Z 1, 2 8. 12( b) ( c),, Z 1 ( 8. 10), p1 x 1 ( - 1 p1 ) + Z 1 11 = x 1 0 Z 1 = p1 ( 8. 10) 1 1 = 1 Z 1 p1, x 11, x, ( 8. 10) Z 1 ( x) = 1 p1 ( x) ( 8. 11) 11 222

8 x 1 x, Z 1 ( x) Z 1 ; p1 ( x) = 1, : Z 1, Z 1 x 1 = 1 p1 ( x) 1, Z 1 11, 11 = 1, ( 8. 11) 11 Z 1 ( x) = p1 ( x) ( 8. 12), 11 = 1 p1 Z 1,,, 8. 12( d) 8. 12 Z K : Z K, Z K Z K,, P = 1 Z K ;, p1 ( x), p1 ( x),,, Z K, Z K,, 8. 5 8. 13 ( a) M C, M 1, M 2, F r Q C, F Q 1,, Z K,, ;, Z K,,, 223

. 13 8. 4 :, ;, ( ) 8. 4. 1 Z K 8. 14,,, 224

8 1 ) 8. 14 ( a), P 1, P 2, P 3, F Q C C F Q C, F Q C y 1, y 2, y 3,, P 1 F Q C P 1 y 1, P 2 F Q C P 2 y 2, P 3 F Q C P 3 y 3, F Q C F Q C = P 1 y 1 + P 2 y 2 + P 3 y 3, P 1, P 2, P 3,, P n, Z K y 1, y 2, y 3,, y n,, Z K = P 1 y 1 + P 2 y 2 + P 3 y 3 + + P n y n = P i y i ( 8. 13), y i ( 2 ) q, 8. 15( a), F QC ( 8. 15( b) ) F Q C q( x) q( x) dx, F QC yq( x) dx, F Q C F Q C = d yq( x) dx ( 8. 14) c, q =, F Q C = q d ydx = q ( 8. 15) c,, 8. 15, 8. 16, q 1, q 2 q 3 F Q C 1, 2 3 F Q C = - q 1 1 + q 2 2 + q 3 3 = q i i 8. 6 Z K n = q i i ( 8. 16) i = 1 F Q C 8. 17 8. 16 F Q C F Q C q : 225

, F Q C 1 = 1 2-2 = 1 2. 17 1 2 4 = - 1 1 2 + 1 4 2 = 3 4 y D = - = q( 1 + 2 ) + py D = 20-1 + 3 4 1 4 + 60-1 4 kn = - 20kN 8. 4. 2 Z K, Z Kma x,, C - 20kN, Z K ( ), Z K, Z K, Z K Z K Z K ( 1),,, Z K ( 8. 13 ), Z K, Z K, Z K, Z K 8. 18( c), 8. 18( a) M C 8. 18 P 1 P 2 (, P 1 > P 2 ),, P 1 Z K ( ), P 2, Z K = P 1 y 1 + P 2 y 2, 8. 18 ( d) Z K 226

8 : Z K ( 8. 13), Z K ;, Z K, Z K 8. 19 Z K, : 1, Z K 2, Z K Z K 8. 20( a) Z K, y 1, y 2,, y n, Z K Z K = P i y i = P 1 y 1 + P 2 y 2 + + P n y n ( a) P i, y i x, Z K x Z K x,, dz K dx ( 8. 19 ) 8. 20 ( a), dx, Z K : 8. 20 8. 20 dz K = P 1 dy 1 + P 2 dy 2 + + P i dy i + P n dy n ( b) 227

y = dxtan = dx c a dy = dxtan = - dx c b Z K dz K = ( P 1 + P 2 + + P i ) c a - ( P i + 1 + + P n ) c b dx, a, b, c,, dz K, dx,, dz K dx Z K, dz K dx, P k P k, 8. 20( b) P k R, P k R, : P k, dz K dx = ( R + P k ) P k, c a dz K dx = R c a - ( P k + R ) R + P k a - R c b 0 R b R a P k + R b c b 0 ( 8. 17) ( 8. 17), : P k, P k ( ), P k, ( 8. 17 ),, Z K, Z K ma x : Z K ; P k, Z K P k, ( 8. 17),, P k, ( 8. 13) Z K, Z K,, Z K 8. 7 AB, 16m, 8. 21 ( a ), P 1 = 4. 5 kn, P 2 = 2kN, P 3 = 7 kn, P 4 = 3kN C 228 C 8. 21 ( b) P K

8. 21 R + P K 6 R 10 R 6 P K + R 10 P 1 = 4. 5kN, P 2 = 2kN, P 3 = 7kN, P 4 = 3kN P K, R R,, 8. 1, P 1 P 3, P 1 P 3 C( 8. 21( b) ( c) ) : M C3 M C1 4 = P i y i 1 2 = P i y i 1 = 4. 5 3. 75 + 2 1. 25 = 19. 375 kn m = 4. 5 0. 38 + 2 1. 88 + 7 3. 75 + 3 1. 25 = 35. 47kN m M C3 M C, P 3 M C M C, P 3, 8. 21( c),,,, 229

. 1 P K P i R R P 1 = 4. 5 P 2 = 2 0 P 2 = 2 P 3 = 7 P 1 = 4. 5 P 3 = 7 P 4 = 3 P 2 + P 1 = 6. 5 P 4 = 3 0 P 3 + P 2 = 9 R + P K R 6 10 R 6 P + R K 10 4. 5 + 2 6 2 6 < 4. 5 10 7 + 2 6 > 0 10 > 4. 5 10 7 6 > 2 + 4. 5 10 3 + 7 6 > 6. 5 10 3 6 < 7 + 6. 5 10 3 6 < 9 10 0 6 < 3 + 9 10 P 1 P K P 2 P K P 3 P K P 4 P K ( 2 ), : 1 ) ( ), ( ), Z K Z K = q i i :, Z K Z Kma x ;, Z K Z Kmi n ( ), 8. 22,,, ;,, ; ( ),, 2 ),, ( ), Z K ( ), Z K Z K ( ),, 230

8. 22 8. 5 ( ), ( ), ( ),, 8. 5. 1,,, 8. 23 ( a), 12m, 280kN, 4. 8m, 1. 44m,,, 8. 23 ( b), ( 8. 23 1 668. 4kN m), 8. 23( c), 8. 5. 2,,,,,,, 231

. 23,,,,, : ;, ;, ; M ma x = M + M + 232

8 mi n = M + M- M+, M- 8. 24, q = 800 kn / m, P = 1 500kN / m : 233

. 24,,,, 234

8 1 ),,,, 2 ), 3 ),,,? 1.?? 2.? 3. 4.? 5.?? ( b) ( a) y D P = 1 8. 5 6. BC BC 7. 8. 5,, M - C ma x M + 8.? 9.? 1m ax M - 8. 6 1ma x 10.,? 8. 1 ( a ) : M A F AY ; ( b ) : F AY F BY F AX M C F Q C F NC ; ( c) : M D F QD M E F QE ; ( d) : F AY M D A M DB F Q D A F QD B 235

. 1 8. 2 ( a ) : M A F AY M C F l Q C F r Q C; ( b) : M G F Q G M B F l Q B F r QB F l Q E F r Q E 8. 2 8. 3 ( a ) : F BY F EY M B M E M G ; ( b) : F BY M D F Q D F l QC 8. 3 8. 4 8. 5 : M E F Q E R B F l Q C F r Q C 8. 6 C 8. 7, M C F QC, ( ) 8. 8 C 236

8. 4 8. 5 8. 6 8. 7 8. 8 237

,,, 9. 1,,,, P,, [ ] ( ma x [ ] ), 19,,,,,,,,,,,, 20,,,, ( ) 9. 1, ( Ultimate load), P u [ P ], 238

9 P ma x [ P] ),,, 9. 1 :, OA ( < s ), AB ( = s ),,,, C, - CD CD OA, = E, P, P, :, ;,,, ;,, 9. 2 9. 2,, 9. 2 M,,, 9. 2. 1, s, : M = yda s ( 9. 2 ( c) ), M s, W M, M M s M s = W s = bh2 6 s ( 9. 1), 239

s,, ( 9. 2d) : y 0 = s y y 0, : M = 2 y h / 2 0 ybdh + 0 y 0 s ybdh = b s h 2 4 - y 2 0 3 ( 9. 2) M,,, s,, ( 9. 2e),, M u M u ( 9. 3), a S 0 = s A 2 a = 2 S 0 s = bh 2 4 s ( 9. 3) ( 9. 1), ( 9. 3),, : 9. 2. 2 M u M s = 1. 5,,, k = M EI M = kei M M s k s = M s EI,, dx, = ky ( 9. 2) : ( 9. 1), ( 9. 4) :, = bh 2 6 EI s = 2 Eh s ( 9. 4) = s E = ky 0 h 2 M = b s 4-1 3 k = k s 3-2 M M s 2 s Ek - 1 2 ( 9. 5), M, k, M = M u, ( 9. 5), k, M u, M u, ( ),,,,,, 240

9. 2. 3,,,,, ( T ),, :,,,,,,, W u 9. 3 = 2 S 0, M u = s W u ( 9. 6) M u M s : = M u M s = sw u s W = W u W ( 9. 7) ( 9. 7),,, : : = 1. 5 : = 1. 7 : = 1. 1 1. 2 9. 3 9. 3. 1 P u, P u :, P u,,, 9. 4( a), C,, 241

M : 4M u = 2 9 P l P u1 = 18 l M u D, M,, D,, D, 9. 4( c),, T i k = 0, : P u l 3 - M u 3 = 0 P u2 = 9 l M u. 4 P, D, : C M M u = 2 /9Pl 4M u = 1 18 P u = P u2 = 9 l M u Pl, D M = 1 /9Pl = 1 M u M u M u 9,,, 9. 3. 2 P u,, Pl M u 9. 5 9. 5( a), 9. 5( b) P, A, : 242

9 A = M u = 3 16 P l P = 16 3l M u A,, P, M A, M C, P, M C P : M C = M u, : = M u, C, : P u = P + P 5Pl 32 + Pl = M C = M u 4 P = 4 l M u - 5 l 32 16 3 l M u = 2 3 l M u P u = 16 3 l M u + 2 3l M u = 6 l M u : ( ), P u, : 9. 1 9. 6 ( a ) 3, 3 1: P u, q u 1 2 l l 2 - M u - M u - M u 2 = 0 q u = 16 l 2 M u 2: P u A, B M, : q u l 2 8 - M u, : q u l 2 8 - M u = M u q u = 16 M l 2 u 9. 6 243

. 4,,, 9. 4. 1 3, 3 : ( 1 ), ; ( 2 ), ( 3 ),,,,,, P k, P s,,,,, 3,, 9. 4. 2 4 P s P k ( 9. 8) P k,, n P k = M ui i ( a) i = 1 M u i i i, M ui i,,,, M i M ui, n P s = M i i ( b) i = 1 n i = 1 M i i n i = 1 M ui i 244

s P k 9, 3 : ( ) : ( ) : P u = min{ P ki } ( ) : P u = max{ P si }, 3 3,, P Ki, P u, P K, P K,, P K = P S = P u,, 9. 2 9. 7( a) 9. 7, A, D, C : 3 1: A, C ( 9. 7( b) ) P k1 l 3-2M u 2 - M u 3 = 0, P k1 = 21 l M u 245

: A, D ( 9. 7 ( c) ) P k2 l 3 2-2M u - M u 3 = 0, P k2 = 7. 5 l 3: C, D ( 9. 7 ( d) ) M u P k3 l 3 - M u - M u 2 = 0, P k3 = 9 l M u, : : P u = P k2 = 7. 5 M u l ( 9. 7( b) ), 1 P k = 21 l M u ( ) A 2M u,, C M u,,, ( 9. 7 ( e) ) D 4M u,,, P K, 1 ( 9. 7 ( c) ) 2 P k = 7. 5 M u ( ) A 2M u,, D M u,, l, ( 9. 7 ( f) ),, P u = 7. 5 M u l 9. 5 9. 5. 1 9. 8( a), : 1 3 ( 9. 8( b), ( c), ( d) ) ; 2 ( 9. 8 ( e) ) 2, ( ) ( ),,,,,,, P K, P u 9. 3 9. 9( a) AB BC,, M u 3M u,, AB B BC B, M BC = 3 M u,, M B A = 3M u, 246

9. 8 9. 9 AB, 3 1: A, B, F, F AB ( 9. 9 ( b) ) :, : P a 1 2 2a a - M u 2 - M u 2 = 0 P k1 = 4 a M u 2: B, D ( 9. 9 ( c) ), P a + P 2a - M u 2-3M u 3 = 0, P k2 = 11 3a M u 3: B, E ( 9. 9( d) ), P a + P 2a - M u - 3 M u 3 = 0, P k3 = 10 3a M u, : P u = P k3 = 10 3a M u 9. 5. 2,,, 4 247

,,, 4,?,,,, n, h, h - n, h - n m, m = h - n,,,,,,,, 9. 4 9. 10 9. 10 ( a), : A, B, C, E, h = 4, n = 1, m = 3, 3 9. 10 ( b), ( c), ( d), ( e) 1: C, E, ( 9. 10( b) ) q 1 2 4 x - M u - M u + x l - x = 0, q k1 = dq dx = 0 x = 2. 343 m q k1 = 0. 73 M u 2: A, B, ( 9. 10( c) ) 2 q k2 2 - M u 2 = 0, q k2 = 1 2 M u 248 8 - x 2 x( 4 - x) M u

9 : A, C, ( 9. 10( d) ) 2 q k3 2 - M u 2 = 0, q k3 = 1 2 M u 4: A, E, ( 9. 10( e) ) 2 q k4 2 + q k4 1 2 4 x - M u - M u + x l - x = 0, 8 - x q k4 = 2( 2 + x) ( 4 - x) dq dx = 0 x = 1. 68m q k4 = 0. 37M u, : q u = q k4 = 0. 37M u 9. 5 9. 11 ( a), : A, B, C, D, E, F, G, H, F 3 9. 11 249

9. 11( a) ),,, 9. 11( b), F, FB FH F, M F H = 2M u, M F B = M u,, M F = 0, M F D = 3M u, FD 2M u 9. 11 ( c), : P k l + 3P k 1 2 l - M u 4-2M u - 2M u 2 - M u 2 = 0 P k = 24 5 M u l :, P k = 24 5 M u l, ( 9. 11 ( d) ) M ED, M F G, P K 9. 11 ( e) : P k l + 3 P k 1 2 l 2 - M u 3-2M u 2 3 - M u 2 = 0 P k = 17 4 M u l : M AD, M BF, M C H, M H C, M ED, M F D, M GF, ( 9. 11 ( f) ),,, P u = 17 4 M u l 1 ),,,,,,,?? 2 ),,, 250 1.?

9.?? 3.?? 4.?? 5.? ( 1) ; ( 2 ), 6.,? 7. 9. 7 9. 1 9. 3 s = 235N / mm 2 9. 1 9. 2 9. 3 9. 4 M u = 300kN m 9. 5 ABC, h = 10cm, s = 235N / mm 2 b 251

. 4 9. 5 9. 6 9. 6 [ ] = 157MPa 9. 7 9. 8 9. 7 9. 9 9. 12 9. 8 9. 9 9. 10 9. 11 9. 13 9. 16 9. 12 252

9. 13 9. 14 9. 15 9. 16 253

0,,,,, : 10. 1,,,,,,,,, :, ; ;,,,,,,,,,, 254

10 0. 1. 1,,,,,,, : ( 1 ) :, 10. 1 ( a), P ( t) t,, 10. 1 ( b) 10. 1 ( 2 ), ( 10. 2 ( a ) ) ( 10. 2( b) ) 10. 2 ( 3 ),,, 10. 1. 2, 255

,, 10. 3 ( a), m dx, 10. 3 ( b), mdx, mdx,,,,,,,, 10. 3 10. 4, 10. 4( a), m,, ( m ),,,,,, ( 10. 4 ( b) ),,, y 10. 4 ( a) 10. 5, x, y ( ), 10. 6,,, 10. 5 10. 6, :, ; ; 256

10 0. 1. 3,,,, ( ), 3 ( 1 ),,,,, 10. 7 ( 2 ),,, 10. 7, ( ), ( 3 ),,, ( ),,,,,,,,,,,, 257

r = - c y, c, y = y, t,,, 10. 2,,, d Alembert ( ), d Alembert,,, ; 10. 2. 1 d Alembert ( ) :, ( ) 10. 8 10. 8( a), m m,, m,, m t, y( t) y( t) 10. 8 ( b) m, k( ) ( ) 10. 2. 2,,, ( ) d Alembert,, ( ), 258 10. 1

10 0. 9 10. 9 ( a), ( ), y, 10. 9 ( c) : F I = - m y F s = - ky F r = - c y F p ( t),,, :, k = 24EI l 3 10. 2 m y + c y + ky = F p ( t) ( 10. 1) 10. 10( a) 10. 10 EI =,, 2 k 1 k 2 k 1 = 2 12EI h 3 1 = 24EI h 3 1 ( a) k 2 = 2 12 2EI h 3 2 = 48EI h 3 2 ( b) 259

0. 11 ( d) ( c), m 1 y 1, m 2 y 2, 10. 10( b) m 1, m 2 10. 11 :, F p1 ( t) + F I1 + F s1 = 0, F p2 ( t) + F I2 + F s2 + F s1 = 0 F I1 = - m 1 y 1, F s1 = - k 1 ( y 1 - y 2 ) ( d) F I2 = - m 2 y 2, F s2 = - k 2 y 2, F s1 = - F s1 m 1 m 2 y 1 + k 1 y 1 - k 1 y 2 = F p1 ( t) y 2 - k 1 y 1 + ( k 1 + k 2 ) y 2 = F p2 ( t) ( c) ( 10. 2), m 1 m 2 ( ) : i j, i k i j, 10. 10( c) : k 11 = k 1 k 12 = k 2 1 = - k 1 k 22 = k 1 + k 2 ( 10. 3) y 1 y 2, : : m 1 m 2 y 1 + k 11 y 1 + k 1 2 y 2 = F p1 ( t) y 2 + k 21 y 1 + k 2 2 y 2 = F p2 ( t) ( 10. 3) ( 10. 4), ( 10. 2) ( 10. 4), : m 1 0 y 1 + k 11 k 12 y 1 = 0 m 2 y 2 k 21 k 22 y 2 F p1 F p2 ( 10. 4) M Y + KY = F p ( 10. 5) ( 10. 4) ( 10. 5) M, K, Y, Y, F p M = m 1 0 0 m 2, K = k 11 k 1 2 k 21 k 2 2 Y = y 1, Y = y 2 y 1 y 2, F p = F p1 F p2 10. 2. 3, t,, j ( x j = 1), i( i = 1, 2, ) i j, i 260

10, i, 10. 3 10. 12( a) : : m y, : 10. 12 ( b), F p F I F r : 10. 12, : y = p + ( F I + F r ) p ; l3 = 48EI ; F I = - m y F r = - c y y = - m y - c y + F p ( t) ( 10. 6) : F p ( t) = p k = 1, ( 10. 6 ) 10. 4 m y + c y + ky = F p ( t) 10. 13( a),,, y 1 = - m 1 y 1 11 - m 2 y 2 1 2 y 2 = - m 1 y 1 21 - m 2 y 2 2 2 ( 10. 7), 1 2,, M 1 M 2 ( 10. 13( b), ( c) ), 1 2, M 1 M 2, : EI 11 = M 1 M 1 EI 22 = M 2 M 2 dx = dx = 10 l3 768EI 13l 3 1 536EI 261

: 12 = 0. 13 EI 21 = M 1 M 2 dx = - l 3 256EI, ( 10. 7), : y 1 + y 2 1 1 12 2 1 y 1 = 0 0 m 2 y 2 0 22 m 1 0 ( 10. 8) FM Y + Y = 0 ( 10. 9) ( 10. 8) ( 10. 9) F, M, Y, Y M = m 1 0 0 m 2, F = 11 12 Y = 21 22 y 1, Y = y 2,,,,,, ;,, y 1 y 2 262

10 0. 3 : = 10. 3. 1, F p ( t), ( 10. 1) m y + ky = 0 ( 10. 10) ( 10. 10) m k k m ( 10. 10) y + 2 y = 0 ( 10. 11) : :, C 1 C 2 ( t = 0) y 0 y( t) = C 1 cos t + C 2 sin t ( a) y = v = - C 1 sin t + C 2 cos t ( b) v 0, ( b), y( 0) = y 0, y ( 0 ) = v 0 C 1 = y 0, C 2 = v 0, : y 0 ( v 0 10. 14( a) v 0 ( y 0 10. 14( b) ( 10. 10) y( t) = y 0 cos t + v 0 sin t ( 10. 12) = 0),, = 0),, y( t) = Asin( t + ) ( 10. 13) ( 10. 14), 10. 14 ( c) A, ; A y 0 v 0 A = y 2 0 + v2 0 = arctan y 0 ( 10. 14) 2 v 0 263

0. 14 ( 10. 14),,, T, T = 2 ( 10. 15) T, ( s),, f f, 1 / ( 1 / s), ( Hz) f = 1 T = 2 ( 10. 16), 2,,, : T = 2 m k = 2 m = 2 W = 2 st g g ( 10. 17),,,, st = W W, ( 10. 15( a), ( b) ) 264

10 ( 10. 17),, ( 10. 17), T : 1 ),, ( ) ;,, ( ) 0. 15, 2 ) ( ), ( ) A,, 10. 5 10. 16( a), l = 2m, A 2 3 l m = 100kg I = 245 cm 4, E = 2. 06 10 7 N / cm 2, T 10. 16 m, M 10. 16 ( b), = 4l 3 243EI = 4 2 3 = 0. 261 10-6 243 2. 06 10 11 245 10-8 T = 2 m = 2 100 0. 261 10-6 = 0. 032 s 10. 17 = 1 m = 195. 7 1 / s 10. 6 m /N 10. 17, l, A, I, E, W,, 10. 17, 265

l 3 3EI T = 2 W = 2 Wl3 g 3EIg W, 10. 3. 2 st = Wl EA T = 2 Wl EAg, F sin t Fcos t F ;, F sin ( 10. 1), : ( c), ( 10. 18) : A = P( t) = Fsin t ( a) m y + ky = F sin t ( 10. 18) y( t) = C 1 cos t + C 2 sin t ( b) y * ( t) = Asin t + Bcos t ( c) F m( 2-2 ) y * ( t) = y( t) = C 1 cos t + C 2 sin t + t = 0, y 0 y 0 C 1, C 2 266 ( e), C 1 = 0, C 2 = -, B = 0 F m( 2-2 ) sin t ( d) F m( 2-2 ) sin t ( e) F m ( 2-2 )

10 m( F 2-2 ) sin t - F m ( 2-2 ) sin t ( 10. 19), :, ; 2,,,,,,, y( t) = F m( 2-2 ) sin t = F m 2 1 - sin t ( f) 2 2 F = F m 2 k = F = y st ( g) y st F,, ( g) ( f) ( ) y( t) = y s t 1 1 - [ y( t) ] ma x = y st 1 [ y( t) ] ma x y st, = [ y( t) ] ma x y st = sin t ( h) 2 2 1-1 - ( ) ( 10. 21),, 10. 18 [ y( t) ] ma x = y s t ( 10. 22),, F, 5 1 ), 0 2 ( 10. 20) 2 2 1 ( 10. 21) 2 2 10. 18 0, 1, [ y( t) ] ma x y st,, 267

+ y st - y st 2 ) 0 < < 1 > 1, 3 ) 1,,,,,,,,,, 4 ) > 1, 5 ) 1 2, 1, [ y( t) ] ma x y st,,,,,,,, ( ),,,, 10. 7 10. 19, l = 2 m, EI = 527. 4 10 6 N cm 2, m = 20kg,,, u( t) = Usin t, U = 0. 5cm, = 2 101 / s m = 1 m = 3EI ml 3 = 3 527. 4 10 2 20 2 3 = 31. 45 1 /s, 10. 19( a) u( t), y( t), u( t) + y( t), u ( t) + y ( t) 268 m ( 10. 19( b) ), ky, - m( u + y )

10, 0. 19 - m( u + y ) - ky = 0 m y + ky = - m u = mu 2 sin t - m u, mu 2 F, y( t) = u( t) + y( t) = [ u( t) + y( t) ] ma x = U 2 sin t 2-2 U sin t 2 1-2 1 - = 31. 451 / s, = 2 10 = 62. 831 /s, U = 0. 5cm, 10. 3. 3 ( 1 ) 1 U = U 2 2 [ u( t) + y( t) ] m ax = - 0. 167cm,, ( 10. 1), : : 2 = k m : C cr m y + c y + ky = 0 ( 10. 23) = c 2 m ( 10. 24) y + 2 y + 2 y = 0 ( 10. 25) = 2 m,,,, ( 10. 25), ( < 1),, ( 10. 25) : 269

e - t ( y 0 cos r t + v 0 + y 0 sin r t) ( 10. 26) r y( t) = Ae - t sin( r t + r ) ( 10. 27), r, : r = 1-2 ( 10. 28), < 0. 2,,, r, 0. 01 0. 1,, y 0, v 0, : A = y 2 0 + v 2 0 + y 0 r tan r = y 0 ( v 0 + r y 0 ) ( 10. 29) ( 10. 27),,, 10. 20, 10. 20 ( 10. 27) : y n y n + j = ( a) : e - t n = e j T ( a) e - ( t n + jt) j T = ln y n y n + j ( b) T = 2 ( b),, 0. 02 0. 2, r, : 1 2 j ln y n ( 10. 30) y n + j, y n y n + j j, j = 1, ln y n y n + 1 y n y n + j, ( 10. 30) 10. 8 10. 21, EI = 4. 5 10 6 N m 2,,, m = 5000kg, 25mm,, 5, 7. 12 mm 270, : k = 2 12EI h 3 = 6 12 4. 5 10 2 N / m = 4. 0 10 6 N /m 3 3 10. 21

10 ( 10. 29) : 1 2 j ln y n = y n + j = c 2 m = c 2 km 1 25 ln 2 5 7. 12 = 0. 04 c = 2 km = 2 0. 04 4. 0 10 6 5 000 kg / s = 11 313. 7 kg / s ( = 1) ( > 1),,, ( 2 ) P ( t) = Fsin t ( 10. 1) ( 10. 24), ( 10. 32),, C 1, C 2 m y + c y + ky = Fsin t ( 10. 31) y + 2 y + 2 y = F m sin t ( 10. 32) y = e - t ( c 1 cos r t + c 2 sin r t) + m F sin( t - ) ( 10. 33) ( 2-2 ) 2 + 4 2 2 2 ( 10. 33), r,,, 3,,, F = y m 2 st, y = m y = F sin( ( 2-2 ) 2 + 4 2 2 2 t - ) 1 - y st 2 2 + 4 sin( t - ) ( 10. 34) 2 2 2 2 [ y( t) ] ma x = y s t ( 10. 35) = 1-1 ( 10. 36) 2 2 + 4 2 2 2 2 ( 10. 21 ),,, ( 10. 36),, 271

, 10. 17 0. 22, 1) 0 1, 10. 22,,,, ;,, 1, 0. 75 < < 1. 25,,, ;,, 2 ) = 0( ), = 1, < 1,, = 1, : 10. 9 ( ) = 1 = 1 2 ( 10. 37), P 0 sin t P 0 = 20 kn, = 44. 271 / s, = 41. 891 /s, = 0. 15, k = 2 10 4 kn / m, 272 1 ) 2 ) y ma x = 1-1 = y st = p 0 k 2 = 1-1 2 = 9. 52 41. 89 44. 27 = 9. 52 20 2 10 4 41. 89 = = 0. 946,, 44. 27 = 1 2 = 1 2 0. 15 = 3. 33 = 0. 952cm

10 ma x = y st = p 0 k = 3. 33 20 2 10 4 = 0. 333cm 10. 10 10. 23( a) psin t, P = 20kN, = 80 s - 1, m = 300kg, EI = 90 10-5 N m 2, l = 4m, B k = 48EI C l 3 f c = 5l 3 192 EI, = 134. 16s - 1 : ( 1 ) ; ( 2 ) = 0. 05 = : y c, ma x 1-1 10. 23 = 80 134. 16 = 2 2 = 0. 596 1 1 - ( 0. 596) 2 = 1. 552 = pf c = 1. 552 20 10 3 5 4 3 cm = 0. 575cm 192 90 10 5 2 = 0. 05 = 0. 356 : = 1-1 = 2 2 2 2 2 + 4 2 : y c, ma x 1 ( 1-0. 356 ) 2 + 4 0. 05 2 0. 356 = pf c = 1. 546 20 10 3 5 4 3 cm = 0. 573cm 192 90 10 5, = 1. 546 P = 1. 546 20 = 30. 92kN, M 10. 23( b), : M c, ma x = 1 4 ( p) l = 1 1. 546 20 4 kn m = 30. 92kN m 4,, = 0. 596 273

. 75 1. 25,, 1 ),,, 2 ),,,,,, 3 ),,,,,, 1.?? 2.? 3. 4.? 5.,,? A. B. C. D. 6.,, A B C D, 6 7.,, EI2,? 274

10 10. 1, EI 10. 1 10. 2 ( ) 10. 2 10. 3 10. 4 EI =, 275

0. 3 10. 4 10. 5 10. 5 0. 1cm( ), W = 20kN, E = 2 10 3 kn / cm 2, I = 16 10 4 cm 4, 10. 6 W,, E, 10. 7 10. 6 10. 8 10. 8 20kN, F P = 2kN, 400 r /min, EI = 1. 06 10 4 kn m 2, l = 6m ( a) ; ( b) = 0. 05 * 10. 9 10. 8 F p ( t) = 30kN, 10. 10 10, 10% ( ) 276 * 10. 11 10. 8, t 1 = T, T

10 10. 12 m 1 = 120t m 2 = 100t, ; i 1 = 20MN m i 2 = 14MN m; 10. 11 277

2. 1 ( a) ( b) 2. 2 ( a) ( b) ( c) ( d) 5 2. 3 ( a) ( b) ( c) 1 ( d) ( e) 1 ( f) ( g) ( h) 2. 4 ( a) ( b) ( c) ( d) 2. 5 ( a) ( b) 2 ( c) ( d) ( e) ( f) 2 278

3. 2 ( a) M A = 254. 84 kn m ( ), F Q A = 101. 21kN ( b) M D = 26kN m ( ), F Q D = 9kN ( c) M D = 40kN m ( ) ( d) M D = 30kN m ( ) 3. 3 ( a) M B A = 240 kn m ( ), F Q BC = 0 ( b) M AB = - 30kN m ( ) ( c) M C B = 40kN m ( ), F Q BC = - 6kN ( d) M AB = - 3. 36kN m ( ) ( e) M C A = - 24kN m ( ) ( f) M EB = Pa ( ) ( g) M B C = 25kN m ( ), F Q BC = 0 ( h) M A = M B = 5qa 2 /8kN m ( ) 3. 4 ( a) F Q CA = - 5. 37 kn m, N CA = 2. 68kN, M C = 8kN m ( ) ( b) M D A = 30 kn m ( ), F Q DA = 8kN, N D A = - 6kN 3. 5 ( a) M E A = Pa /2 ( ) ( b) M D = 12. 5kN m ( ) ( c) M D = 1. 5 F Q a 2 ( ) ( d) M D C = 12. 5F Q ( ), F QD C = 5F Q 3. 6 ( a) M B A = - 120 kn m ( ), F Q BA = - 60kN ( b) M B = - 6. 09kN m ( ), M B = - 11 kn ( c) M A = 4. 5 kn m ( ), M B = 1kN m ( ) M C = 1. 87 kn( ) ( d) M AB = Pa( ) 3. 7 ( a) M D = 25. 5kN m ( ) ( b) M D = 2. 32kN m ( ) ( c) M D = 3. 95kN m ( ) ( d) M D C = 0. 98kN m ( ) 3. 8 ( a) M C D = 160 kn m ( ), M F G = 0 ( b) M BC = 16kN m ( ) ( c) M D C = 0 ( d) M AC = Pa( ) 3. 9 ( 1) F AY = 3 4 P, F BY = 1 4 P, F H = 1 2 P ( 2) M D = - 0. 5P ( 3) F N D = - 0. 78P, F Q D = 0. 45P ( 4) F AY, F B Y, F H, M 279

5),, M 3. 10 M K = - 29kN m, F Q K = 18. 3kN, F N K = 68. 3kN 3. 11 F ND E = 135 kn, F N F D = F N GE = 22. 5kN, M K = 7. 5kN m, F QK = 2. 152kN, F NK = 158. 199kN 3. 12 ( 1) X C = 14. 09m ( 2) H = 12. 88kN, V A = 11. 03kN, V B = 8. 97 kn ( 3) M D = 17. 54kN m ( ) 3. 13 ( a) 9 ; ( b) 6 ; ( c) 4 ; ( d) 6 ; ( e) 10 ; ( f) 8 3. 14 ( a) F N 14 = 3P, F N2 3 = - 2P ( b) F N2 4 = 42. 43kN 3. 15 ( a) V a = 10 kn; V b = 10kN; ( b) F N c = 40kN ( c) F N a = - P; F N b = 2P ( d) F N a = - 2 3 P, F N b = - 5 3 P ( e) F N a = 56. 57 kn; F N b = - 28. 28kN ( f) F N a = - 1. 18 P; F N b = 1. 67P ( g) F N a = - 16kN; V B = - 20kN; F N c = 32kN ( h) F N a = 0; F N b = 20 kn; F N c = 21. 2kN 3. 16 ( a) F N D E = 22. 5kN; ( b) F N EF = - 113. 14kN; F NC H = - 28. 28 kn; M KB = 240 kn m( ) ; ( c) F N EB = - 2P ; M AB = 2Pa( ) ; ( d) F N BD = 0; M CA = 3 Pa( ) ; ( e) F N D E = 225kN; M G B = 67. 5kN m( ) ( f) F N GE = 72. 11kN; F N CG = 50kN; F N GB = - 90kN 4 4. 1 R C = 16. 25kN( ) R F = 5 kn( ) M B = 17. 5kN m( ) M C = - 5kN m( ) 4. 2 H = 3 2 P( ) R B = P 2 ( ) 4. 3 ( a) B = qa4 8EI ( ) ( b) B = 5 Pa3 48EI ( ) 4. 4 D H = 0. 563 qa 4 EI ( ) 4. 5 BH = qa 4 24EI ( ) 280 B = qa 3 6EI ( ) B = Pa 2 8EI ( )

. 6 BH = q fa 3 15EI ( ) 4. 7 1. 42 B = EI ( ) 4. 8 CV = 1. 15 cm( ) 4. 9 D B - E B = - 0. 84 10-3 rad( ) 4. 10 ( a) CV = 3 Pl3 256 EI ( ) ( b) CV = q ( 3a 4-4ca 3 + c 4 ) ( ) 24EI 2 17 ql4 ( c) CV = 128 EI ( ) 4. 11 ( a) CH = 106 3EI ( ) ( b) A = 57 EI ( ) 4. 12 D H = 1. 73 10-2 m( ) 4. 13 C = - 0. 0201rad ( ) 4. 14 C D = 0. 493cm( ) 4. 15 AV = 4. 84 cm( ) 4. 16 D V = 14. 64 qa 4 EI ( ) 4. 17 AB = 9. 81 Pa 3 EI ( ) 4. 18 C V = qah ( ) 4EAcos 3 C = qa 3 24EI + qh EA 1-1 4cos 3 ( ) 4. 19 B V = 11q 1 a 4 120EI + q 2 a 4 30 EI ( ) 3 77 qa 4. 20 c - c = 32EI ( ) 4. 21 B V = 0. 107 cm( ) 4. 22 c - c = - 0. 02rad( ) 4. 23 C F = - 0. 36cm( ) 4. 24 C H = 6 t ( ) 4. 25 CV = 2. 0cm ( ) 4. 26 D V = 2. 75 cm ( ) 4. 27 B = qa 3 24 EI ( ) 5 5. 1 ( a) n = 2 ( b) n = 3 ( c) n = 3 ( d) n = 6 ( e) n = 7 281

f) n = 4 ( g) n = 5 ( h) n = 8 ( i) n = 10 ( j) n = 6 5. 2 ( a) ( ) ( b) ( ) ( c) ( ) ( d) M AB = 1 6 Pl ( ) 5. 3 ( a) M B A = 45kN m ( ) ( b) M D A = 1 2 Pl ( ) M CB = 1 2 Pl ( ) ( c) M E A = 33 64 qi2 ( ) ( d) M AC = 97. 5 kn m( ) 5. 4 ( a) F N CE = P ( b) N BC = - 26. 67kN N D E = - 23. 33kN 5. 5 ( a) N CD = - 10 13 P ( b) M AB = 0. 31ql 2 ( ) 5. 6 ( a) M AC = 112. 5 kn m ( ) ( b) N CD = - 1. 29kN 5. 7 M A = 5 11 Pa ( ) CV = 3 Pa3 11EI ( ) 5. 8 C = 1. 25 10-5 ( ) D H = 2. 83mm ( ) 5. 9 M B = 175. 2kN m ( ) KV = 747 EI 5. 10 M CB = 480 EI ( ) l 5. 11 ( a) ( ) ( b) ( ) 5. 12 ( ) 5. 13 ( a) M CA = Pl 2 ( ) ( b) M BA = ql 2 24 ( ) ( ) C = 157 EI ( ) ( c) M A = PR ( ) ( d) M CD = Pa 2 ( ) ( e) M AC = m 4 ( ) ( f) M EC = 1 4 qa2 ( ) ( g) M BA = 3 28 Pl M CB = - 1 7 Pl 5. 14 F H = 16. 67 kn M C = - 8. 40kN m ( ) 5. 15 F H = 0. 4519P M A = M B = 0. 1106PR ( ) 282

6. 1 ( a) 3 ( b) 1 ( c) 1 ( d) 9 ( e) 8 ( f) 7 ( g) 4 ( h) 2 ( i) 5 ( j) 4 6. 2 ( a) M D C = 14. 29 kn m M D B = 8. 57kN m M C A = - 2. 86kN m ( b) M BA = 15kN m M BD = 20kN m ( c) M B A = 20kN m M BC = 20 kn m M C B = 10kN m ( d) M A1 = M A2 = 1 3 M M A4 = 1 12 M M A3 = 1 4 M ( e) M B A = 100. 5 kn m M CD = - 118. 6kN m M DC = 43. 8 kn m 6. 3 ( a) M AC = ql 2 /104 ( b) M BE = 42. 1 kn m ( c) M AC = - 22. 5kN m M BD = - 135kN m ( d) M AC = - 150 kn m M BD = - 90kN m ( e) M AC = 59. 2kN m H A = 59. 2kN ( ) M B C = 180. 79kN m 6. 4 ( a) M E C = 2. 14kN m M EF = - 2. 74kN m ( b) M AD = - 14. 5kN m M D G = 58. 1kN m ( c) M C C = 84. 86kN m M BB = 143. 21kN m ( d) M D C = 0. 14ql 2 6. 5 M BA = - 50. 4kN m M CD = - 5. 6 kn m 6. 6 M CB = - 47. 4kN m 7 7. 1 ( a) M AB = 21. 20 kn m M BC = 17. 61kN m ( b) M AB = - 2. 67kN m M CB = 32. 67kN m ( c) M B A = 36kN m 7. 2 ( a) M B A = 42. 26 kn m M D C = 74. 61kN m ( b) M BA = 17. 4kN m M CB = 10. 6kN m ( c) M B A = 74. 38 kn m M CB = 32. 83kN m R B = 89. 49 kn( ) 7. 3 ( a) M B A = - 4. 3kN m M CD = 12. 9kN m M E C = 72. 8kN m ( b) M AB = 13. 33kN m ( c) M C A = 5kN m M D C = 10kN m 283

d) M BD = 64. 82kN m M BC = - 69. 64kN m 7. 4 ( a) M B C = - 192kN m ( b) M CB = 12. 78kN m ( c) M E F = - 41. 13kN m M F E = 75. 17kN m ( d) M D A = 7. 17kN m M D G = 14. 48kN m M GD = 9. 82 kn m 7. 5 M AB = - 179. 4kN m, M CC = 51. 7kN m 7. 6 M AC = - 33. 3kN m, M CD = 39. 8kN m 8 8. 1 5 ( ) 8. 6 M C = 164kN m, F Q C = 26kN 8. 7 M Cma x = 314kN m, F Q Cma x = 104. 5kN, F QC min = - 27. 3kN 8. 8 M Cma x = 626. 9kN m, F QC ma x = 108kN, F QC min = - 44. 3kN 9 9. 1 P u = 19. 6kN 9. 2 9. 3 P u = 41. 034kN 9. 4 q u = 16M u 3l 2 9. 5 b = 45. 5mm, b h = 5 10 cm 2 9. 6 25b 9. 7 P u = 20 kn 9. 8 q u = 18M u 7l 2 9. 9 q u = 1. 167M u a 2 9. 10 P u = 146. 875kN 9. 11 P u = 5 M u 3 9. 12 P u = 35kN 9. 13 P u = M u l 9. 14 P u = 1. 2 M u l 9. 15 P u = 1. 56M u 9. 16 P u = 0. 167M u 284

0 10. 1 ( a) 3; ( b) 2; ( c) 1; ( d) 2; ( e) 4; ( f) 3 10. 2 ( ) 10. 3 ( a) T = wl3 2EIg ( b) = 10. 4 ( a) = 3EI mh 2 l 48EI 7ml 3,, = ( b) = 16 l 8EI ml 3 6EI 23ml 10. 5 y ma x = 0. 1cm, V ma x = 4. 175cm /s, a ma x = 174. 3cm / s 2 10. 6 = 10. 7 = 12EIgn 3 wl 3 ( n + 2 ) 192EIg( 3n + 2 ) wl 3 ( 3n + 8 ) 10. 8 ( a) A = 8. 84 10-4 m, M d ma x = 6. 25 10 3 N m ( b) A = 8. 57 10-4 m, M dm ax = 6. 05 10 3 N m 10. 9 ( a) A = 0. 25 m ( b) A = 0. 24m 10. 10 = 0. 0366 10. 11 ( ) 285

.,... :, 1988 2.,... :, 1984 1998 3.,... :, 2000 4.... :, 1996 5.... :, 1986 6.,... :, 1998 7... :, 1995 8.,.. :, 1985 286