:,,,, ( CIP ) /,. :, 2001. 8 ISBN 7 5612 1363 8............. 0342 CIP ( 2001) 027392 : : 127, : 710072 : 029-8493844 : ht t p: / / www. nwpup. com : : 787mm1 092mm : 19. 75 : 480 : 2001 8 1 2001 8 1 : 017000 : 21. 00
( ) 21,,,,,,,,, *,, ;,,,,,, 2001 6
1 1 1 1 1 2 1 1 3 2 1 4 5 8 2 1 8 2 2 9 2 3 11 2 4 12 2 5 15 * 2 6 17 2 7 18 19 22 3 1 22 3 2 25 3 3 27 3 4 32 3 5 37 3 6 39 40 49 4 1 49 4 2 50 4 3 54 4 4 55
57 59 5 1 59 5 2 61 5 3 62 5 4 65 5 5 68 5 6 69 * 5 7 73 74 80 6 1 80 6 2 81 6 3 84 6 4 86 6 5 89 * 6 6 91 6 7 92 6 8 95 6 9 97 6 10 98 * 6 11 104 6 12 108 6 13 110 113 118 7 1 118 7 2 119 7 3 123 7 4 125 7 5 129 7 6 134 7 7 137 7 8 138 * 7 9 140 142
147 8 1 147 8 2 148 8 3 151 8 4 153 8 5 155 8 6 164 8 7 170 8 8 172 8 9 175 8 10 176 8 11 179 179 188 9 1 188 9 2 190 * 9 3 193 9 4 196 9 5 198 9 6 200 9 7 202 9 8 208 9 9 213 9 10 214 215 219 10 1 219 10 2 220 10 3 225 10 4 228 10 5 230 * 10 6 237 10 7 240 10 8 241 244
* 249 11 1 249 11 2 249 11 3 255 11 4 259 262 265 12 1 265 12 2 265 12 3 ( ) 272 12 4 ( ) 275 12 5 278 12 6 285 12 7 288 12 8 290 292 295 308
1 1,, : (1 ) : (2 ) :,, ;, (3 ) :, ; ; : (1 ) (2 ), (3 ) 1 2,, (1 ) :, (2 ) :,, 1
(1 ) :,, (2 ) :,,, (1 ) :, (2 ) :, (1 ) :,, (2 ) :,,, 1 3,,,,,,,,,,,, : (1 ), (2 ),,,, ;,, ;, : (1 ); (2 ); (3 ) 1.,,,, 2
,, 2.,,, (1 ):,,,,, ( 1 1 ) 1 1 1 2 (2 ):,,, ( 1 2) 3., (1 ) :, ( 1 3 ) 1 3 1 4 (2 ):, ( 1 4 ) (3 ) :, 3
, ( 1 5, 1 6) 1 5 1 6 (4 ) : ( 1 7 ) 1 7, 1 8 ( a),,,,,,,,,,, 1 8 ( b) 1 8 1 9( a) ( 1 9 ( b) ), ( 1 9( a) ),,,,, ( 1 4 9 ( b) )
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
1 10 1 11 1 12 1 13 1 14 (1 ) :,, 1 15 (2 ) :, 1 16, 6
(1 ) :, 1 10 (a), ( b ) (2 ):, 1 10 (c), ( d) 1 15 1 16 7
2 1,,,,,,, (, ), : (1 ) : 2 1 ( a),,, (2 ) : 2 1 ( b ),,, 2 1 2 1( c), ( ),, 2 1( d),,, 8
,,,,, 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
2 3 2 4 2. 2 4( 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
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) 2 6 2 1 2 7 2 2 2 7( a), 2 7 m = 8, h = 10, r = 4 W = 3 m - (2 h + r) = 3 8 - (2 10 + 4 ) = 0 7( b ), m = 9, h = 12, r = 3 W = 3 m - (2 h + r) = 3 9 - (2 12 + 3 ) = 0 7( b ), j 11
, b, r, 2 j,, ( b+ r). W = 2 j - ( b + r) (2 2) 2 7( b )( 2 2) W = 2 6 - ( 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
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
(7,10, 9),,,, ( ) ( ), 2 11 2 12,, ; 2 13 (a), O, O,, 2 13 ( b),,,,,, 2 13( c),,,,, 2 13 2 14 3, 3, C A C BC,, C, 3,,,?, 2 14 14
2 15 (a)c ( 2 15( b) ), X = 0, N1 = N2 = N Y = 0, 2 Nsin- P = 0 N = P 2sin = 0,, P0, N,,,, 2 15 2 5, W,,,, (1 ), ;, (2 ), (3 ), (4 ), 2 2 2 16 W = 3m - ( 2 h + r) = 33 - ( 22 + 5) = 0 :,, FE,, BCE, A D, A B DC,,, AB CD EF,, 2 3 2 17 15
W = 3 m - ( 2 h + r) = 33 - ( 22 + 5) = 0, AC,, A C CE, CE, EF,, E FG, CED, ABC, 2 4 2 18 W = 2 j - b - r = 212-21 - 3 = 0,,, 2 16 2 17 2 18 2 18 ( b), 9, 3 3, 6 3, AB, DC, FE,, BC, DA O1, FB, A E O2, DF, EC O3,,, 2 5 2 19 W = 2 j - b - r = 26-8 - 4 = 0, BG, DB F CH,, CE, :, BG, A D, B, A E, C H, C 2 19, ED, H F,, O B C,, 16
, A,,,, * 2 6,,, 2 20 (a), O12, O13 O23,, ;, 2 ;, 2 20 ( b ) 20 (c), O13 O2 3, 1 2, 2 20 2 21 (a), O12, O13 O23,, ;,, 2 21( b ) ; 2 21( c),,,,, 2 22 ( a), 3, 3,,, 3,, 3,, A, B, C 17
D, E, F ( 2 2 21 22( 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
,, 2 23 ( a),,,, X1 X2 ( 2 23 ( b) ),,, X1 X2, 3 H A X = 0, 4,, 2 23 2 24 ( 2 24), 3, 3 3,,, ;,,,, 2 1 2 12 20, 19
2 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2 9 20
2 10 2 11 2 12 2 13 2 14 2 15 2 16 2 17 2 18 2 19 2 20 2 1, 2 4, 2 5, 2 6, 2 7,2 8,2 9, 2 11, 2 12, 2 14, 2 15,2 18 2 2, 2 3, 2 10, 2 13, 2 19 2 20, 21
2 2 16 17, 8 22
3 1,,,, ( 3 1) 3 1, 3,, 3, 3 : N Q M N:, ( 3 2 (a) ) 3 2 Q:, ( 3 2 ( b) ) 23
( 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 ) ), 3 3 24
3 1 ( = ) ( q ) ( ) * ( = ),, 3 1 3 4( a) 3 4 (1 ) :, M A = 0 8 1 + 2 4 4 + 8 - V B 8 = 0 Y = 0 VB = 6 kn() 8 + 2 4 - V A - 5 = 0 V A = 10 kn() (2 ) :, QA = QC = V A = 10 kn 25
( 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 = 10 2-8 1 = 12 knm = 6 2-8 = 4 knm MH = 6 1-8 = - 2 knm MH = 6 1 = 6 knm 4 (c) ) DE,, 3 MD M E, D E, DE F, DE Mmax, : DE M F MF = 10 4-8 3-2 2 1 = 12 knm Q M, a = 10-8 2 = 1 m Mmax = 10 3-8 2-2 1 2 12 = 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
, 3 5 ( d ) M0 M, M, A B, 3 5 3 2 3 6( a) 3 6 B, D MD = 0 27
3 6( c) MB = - 1 2 = - 2 knm ( ) BD, AB A B P M A, MB ( 3 6 ( b ) ), A B, MA, MB ( ), 3 MC = - 4 + 2 2 6( d) A B C + 1 4 6 4 = 3 knm ( ) 3 3, ( 3 7 (a) ), 3 7 ( b) 3 7, 3 8, AC, ; CE, ;, EF,,,,,, ( 3 9 ), 3 8, :,,,,,, 28
,,,, 3 9 3 3 3 10 (a) 3 10 29
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),,, 3 4 3 11 (a)q,, C, D, 3 11 30
CD, B, E, C, D B, E x, CD Mmax = 1 8 q( 2-2 x) 2 = 1 2 q( - x) 2 3 3 11 ( b) B, E, Mmin = - q( - x) x - 1 2 q( - x) 2 = 1 2 1 2 qx2 = - x = 1 2 ( 2-2 ) 1 2 qx (2 - x) q( 2 - x) x Mmax = Mmi n = 1 2 q[ - 1 2 (2-2 ) ] 2 = 1 4 q2 3 11 (c) 3, 11 ( d),,,,,,,,,, 3 5 3 12 (a),,,,,, A C, CF F H F H, GE,, GF E, EF, ME = - 1 2 qa2, CE CB EF,, A B,, 3 12 ( b),, (), EG QEG = 1 2 qa2 + 1 2 qa2 2 a = 1 2 qa, : ( 90 ),,,, QEG BD 31
QBD = - 3 4 qa2 + 3 4 qa2 2 a = - 3 4 qa 3 12, AB, A B (A B ) 3 12 (c), MB = 0 Y = 0 32
, 3 QA = q2 aa + 3 4 qa2 2 a QB = - 2 qa + 11 8 qa = - 5 8 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
,,, (2 ),,,, MAB A B A (3 ) 3 14 ( a) 34 3 14 (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 ( )
(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 = 0 3 6 3 15 (a) (1 ) : 3 15 X = 0 HB = 8 kn() 8 2 + 50 3 + 8 MA = 0 V B = 6 = 29 kn() Y = 0 V A = 50-29 = 21 kn () (2 ): A C : MAC = 0, MCA = - 8 4 = - 32 knm ( ) MEA = 0 CD : 35
MCD = - 8 4 = - 32 knm ( ) MF = - 32 + 56 2 + 1 4 50 6 = 31 knm ( ) MDC = 21 6-8 4-50 3 = - 56 knm ( ) BD : MB D = 0 MDB = - 8 6 = - 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), 3 7 3 16 (a) (1 ) : 4 6 3 MA = 0, VB = 12 = 6 kn() Y = 0, V A = 4 6-6 = 18 kn( ) X = 0, H A = HB = H C, MC = 0 C, 6.5H - 66 = 0 H = 5.54 kn (2 )M : DC :, MDC = - 5.54 4.5 = - 24.92 knm ( ) MCD = 0 DC 1 8 4 62-1 2 24.92 = 5.54 knm ( ) 3 16 ( b) (3 )Q, N : DC,, 36
QDC = V A cos- HA sin= 18 3 10-5.54 1 10 = 15.31 kn QCD = - V B cos- HB sin= - 6 3 10-5.54 1 10 = - 7.44 kn NDC = - V A sin- H A cos= - 18 1 10-5.54 3 10 = - 10.94 kn N CD = V B sin- HB cos= 6 1 10-5.54 3 10 = - 3.36 kn 3 16 (c), ( d) 3 16 3 8 3 17 (a) G ; G,, ( 3 17 ( b) ),, G, ( 3 17 (c) ),, ( 3 17( d) ) 3 5,,,, 37
3 17, 3 9 3 18 ( a) M H D = q() A B M, BD M, BC, B, MBC = 3 2 q2 ( ) M, 3 18 ( b ) 3 10 3 19( a) M A, C, 3 18, CE A F, CE AF,, Y B = 0B F, DE,, M ( ) E, MEF = m( ) F 38
, MFE = 03 19 ( b) 3 11 3 20( a)m A B, BD, M MDC = 3 knm, MC = 0 M BC = 3 knm ; B M BA = 3 + 10 = 13 knm MAB = 5 knm, M, 3 20 ( b) 3 19 3 20 3 12 3 21( 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 = 0 3 21( b ) 39
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
3 23,,,, 3 24 ( a), P, 3 24 (a), 3 24 ( b ), M 3 24 ( b ), A C DB M, CD ( 3 24( c) ),,, 3 24 3 1 41
3 1 3 2 3 3 M, Q, N 3 2 42
3 4, M, Q 3 4 3 5, M 3 5 43
3 6 3 6 44
3 7 M 3 7 45
3 8 M 3 7 3 8 46
3 9 M, 3 9 47
3 10 3 10 3 1 ( 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= 0 3 3 ( a) Mmax = 1 8 q2 ( b) Mmax = q2 8cos ( c) Mmax = 1 8 q2 3 4 ( a) MB = - 120 knm ( ) 3 5 ( b) MC = 3 2 qa2 ( c) MC = - 1 knm ( ) ( d ) MB = - 80 3 knm( ) 3 6 ( a) MBC = 90 knm ( ), QBC = 20 kn, NBC = - 5 kn 48 ( b) MCA = 2 knm ( ), QCA = 3 kn
( 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 ( ) 3 8 3 9 3 10 : 49
4 1,,, ( 4 1( a), ( b ), ( c) ), 4 1,, 4 1( e),,,,,,, ( ),, 4 1( d ) 4 2 4 2 49
, f /, 4 2 4 3( 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, ( 4 50 4( a ) ), 4( d) ) K M 0 K,
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),, 4 1 4 5( a), y= 4f 2 x ( - x ) V A = V 0 A = 6018 + 10126 24 V B = V 0 B = 60610126 24 H = M C f = 7. 512-606 6 = 75 kn = 105 kn = 90 kn, 8,,,, = 24 m f = 6 m, 51
y = 4f 2 x ( - x ) = 46 24 2 ( 24x - x 2 ) = x - t an = y = 1 - x 12 x 2 24 4 5 6 m 2, : x 2 = 6 m y 2 = x - t an 2 = 1 - x 2 24 = 6-6 2 24 = 4. 5 m x 12 = 1-6 = 0. 5, 12 2 = 26 34 52
2, 2 sin 2 = 0. 447, cos 2 = 0. 894 M 0 2 = 7. 56 = 4. 50 kn m Q 0 2= 7. 5 k N, Q 0 2= 1. 5 kn M 2= M 0 2- H y 2= 450-904. 5= 45 kn m Q 2 = Q 0 2 cos 2- H sin 2= 750. 894-900. 447= 26. 9 kn Q 2 = Q 0 2 cos 2- H sin 2= 150. 894-900. 447= - 26. 8 kn N 2= Q 0 2sin 2+ H cos 2= 750. 447+ 900. 894= 114. 0 k N N 2= Q 0 2sin 2+ H cos 2= 150. 447+ 900. 894= 87. 2 kn, ( 4 4 1 1) M/ ( knm) x y t an 0 sin cos M 0 - Hy M 0 0 0 1 45 0. 707 0. 707 0 0 0 1 3 2. 625 0. 75 36. 87 0. 600 0. 800 225-236. 3-11. 3 2 6 4. 5 0. 5 26. 57 0. 447 0. 894 450-405 45 3 9 5. 625 0. 25 14. 04 0. 243 0. 970 495-506. 3-11. 3 4 12 6 0 0 0 1. 00 540-540 0 5 15 5. 625-0. 25-14. 04-0. 243 0. 970 540-506. 3 33. 7 6 18 4. 5-0. 5-26. 57-0. 447 0. 894 450-405 45 7 21 2. 625-0. 75-36. 87-0. 600 0. 800 270-236. 3 33. 7 8 24 0-1 - 45-0. 707 0. 707 0 0 0 Q/ ( kn) N / ( kn) Q 0 Q 0 cos - H sin Q Q 0 sin H cos N 0 75 53. 0-63. 6-10. 6 53. 0 63. 6 116. 6 1 75 60-54 6 45 72 117. 0 2 75 15 67. 1 13. 4-40. 2 26. 9-26. 8 33. 5 6. 7 80. 5 114. 0 87. 2 3 15 14. 6-21. 9-7. 3 3. 7 87. 3 91 4 15 15 0 15 0 90 90 5-15 - 14. 6 21. 9 7. 3 3. 7 87. 3 91 6-45 - 40. 2 40. 2 0 20. 1 80. 5 100. 6 7-75 - 60 54-6 45 72 117 8-105 - 74. 2 63. 6-10. 6 74. 2 63. 6 137. 8,, N, Q, M 4 5( c), ( d), ( e) 53
, 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),, 4 7 54
4 4,,,,,, ( 4 5), M = M 0 - H y = 0 y =,, y,, H, 4 2 4 8( 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, 4 3 4 9 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 8 4 9 55 ( 4 7)
, 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
, 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 = 4 1 4 1 y= 4f 2 x ( - x ), K 4 1 4 2 4 2 3/ 4 D 57
4 3 4 3 K 4 2 4 3 4 4 4 4 4 4 4 1 H = 50, MK = 103. 1 kn m, Q K = 33. 9 kn, Q K = - 41. 0 kn, N K = 66. 1 kn, N K = 38. 0 kn 4 2 M D = 1. 07q 4 3 5 kn, M K = 44 k Nm, QK = - 0. 6 kn, N K = - 5. 8 kn ( ) 4 3 58
5 1,,,,,,,,,,,,,, : ( 1) ( 2), ( 3) ( ), 5 1( a), ( 5 1( b) ), 5 1,,,,,,,,,,,,,, d h ( 59
5 2) 5 2, : 1. ( 1) :, ( 5 3( a ), ( e), ( f) ) ( 2) : ( 5 3 ( b), ( d) ) ( 3) : ( 5 3( c) ) 5 3 2. ( 1) ( 5 3( a) ) ( 2) ( 5 3( b), ( f) ) ( 3) ( 5 3( e) ) 3. ( 1) ( 5 3( a) ) ( 2) ( 5 3( d) ) 60
5 2,,,,,,,,,, N N x N y 5 4, x y, N = N x x = N y y ( 5 1),, 5 1 5 5( 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
3. X ( ), ( 5 6( c) ) 4. K (, ), ( ) ( 5 6( d) ) 5 6,, 5 7( a ), ( b) 5 7 5 3 ( ),,,,,, ( ), M = 0, 5 2 5 8( a ) 1, 2, 3 ( 1) 62
( 2) 1, 2, 3, ( 5 8( b) ) 5 8 F, 1, 2, 3 F, M F = 0, N 1 1 2 a - 3 2 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 = - 1 2 P N 2 = N 2y 2 2y N 2 = N 2y 2 2y 3 N 3, 2 = - 1 2 P a 2 + ( 1 2 a ) 2 = - 1 2 a 5 2 P ( ) MC = 0 3 2 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
Y = 0, 5 3 5 9( 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 = 0 15-10- N by= 0 N by = 5 kn N b = N by b by = 5 32 + 4 2 4 = 6. 25 k N ( ),,,,,,,,,, ( 5 10( a), ( b ) ) 5 10,, 2 ; 3,,, 64
( 5 11( a), ( b) ) 5 11 5 4,,,, 5 4 5 12 1, 2, 3 5 12 ( 1), X A = 0, YA = 12 k N( ), YB= 4 k N( ) ( 2) 1, 2, 3 : 65
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)4-42- 82- Y22. 5= 0 Y2 = 6. 4 kn N 2 = Y2 2 2y = 1. 5 2 + 2 2 6. 4 = 8 kn ( ) 2 c) D, 5 12( c), N 3 D X 3 Y3, Y = 0, Y3 + Y2 = 0 Y 3 = - Y2 = - 6. 4 kn N 3 = Y3 3 3y = 1 2 + 2 2 ( - 6. 4) = - 7. 16 kn ( ) 2 5 5 5 13( a) a, 5 13 a, ( 5 13( b ) ),, B N b = 0, Y1 = 0 N a 1 2-2 3 P 1 2 = 0 N a = 2 3 P ( ) 5 6 5 14( a) a, b 66
, a, ( 5 Y = 0 14( b) ) 3 + 6-12 - 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 2 ) ( 32 + 4 2 ) 3 = - 3 2 kn 5 2 kn ( ) N a, M D = 0 N b, b ( 5 14( c) ) MC = 0 124-34 + N b6 = 0 N b = - 6 kn ( ) 5 7 5 15( 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
N bx = N by bx by = ( - P ) ( a ) 1 2 a = - 1 2 P X = 0, N a = - 1 2 P ( ) 5 15 5 5 : 5 16( a), ( b), ( c) (,, P = 10), N = M 0 r, M 0, r,,,, r,,,,,, ( ),, M 0,,,,,,,,,, 68
5 16, : ( 1),,,,,,,,,,, ( 2),, ;, ;,, ( 3),,, ( 1830 m) ( 100150 m),, 5 6,,,,,, ; 3,,,,,, 69
5 8 5 17( a) ( 1) ( 2),, M C = 0 106-124 - 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
,, 5 18( b) 5 18 5 9 5 19( 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 - 2. 2P = 3. 8P 5 19( b), C MC = 0 = 2. 2P H B ( 0. 8d + 0. 2d ) - ( 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 - 3. 52P = 0. 28P VB = 2. 2P - 3. 52P = - 1. 32P = 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 1 4. 4P d ( 0. 2d ) 2 + d = 4. 49P 2 71
, C ( 5 19( c) ), Y = 0 N C C = 2T C E sin 1 = 24. 49P 0. 2d = 1. 76P ( 0. 2d ) 2 2 + d 5 19 72
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 ) ),,, 5 20 5 10 5 21( 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
, 5 11 5 22( 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, 5 1 5 1, 5 1 74
5 2 5 2 5 2 5 3 5 3 5 3 75
5 4 5 4 5 4 76
5 5 5 5 5 5 5 6 5 6 5 6 * 5 7 5 7 5 7 77
5 8 5 8 5 8 5 15 2 5 3 ( a ) N 1= - ( b ) N b= - 45 kn ( ) 8 3 P ( ), N 2= 5 6 P ( ), N 3= 2P ( ), N 4= - 1 2 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= - 5 2 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 = - 1. 7 kn ( ), N b= 1. 3 kn ( ), N c = - 28. 2 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
5 7 ( a ) ; ( b) 5 8 ( a ) N 2= 0; ( b) N a = 2 P ( ) 79
6 1,,,,, ( ),, A B A B ( 6 1 ( a), ( b ) ), A B ( 6 1 (c) ), RA, RB,,,, 6 1,,, P = 1,, 80
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 2 1. ( 6 3 ( ) ),,, = 1 = 1 0,, - ( - ) = 0 = - = - = 0 (0 ) 6 3 81
,, 6 3 ( ), = 1,,,, = 1, = 1,,, 2. 6 4( ) = 1,, = 1,, ( 6 = 0 = - 4( ) ) + = 0, = - (0 < ) = 1, ( 6 4 ( ) ) = 0 - = 0 = = - ( < ),, ;,,, 6 6 6 4 4 ( ), 4( ),,, = 1,, = 1, = 1, = - ; = 1, =, = 1,, 1, = 1, 82 = 1, 3. 6 5( ) = 1
,, (6, = 0 - = 0 4 ( ) ), = = (0 ) = 1, ( 6 4( ) ), = = - ( < ),, 6 5 ( ),,, = 1, 6 5 1. ( 6 6 ( ) ), = 1, = 0, = - = 0, = ( - 1 + 2 ), = 1 ( - 1 0 + 2 ) ( = 1, ),, 6 6( ), ( ) 2. 6 6( ) = 1,, = - = - 1 < - 1 = 1,, = = < + 2 83
, 6 6( )( ),, = 1,, = 1, = 1, = - ( 0 < ) 6 6 ( ), ( ) 6 6 84
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)
+= 1 = ( 6 8 ( ) ), 6 8 6 8( ),,,, 6 1 + 2 = 1 8 ( ) ( 1 + 2 ) - = 0 =, 6 8 ( ),,,, 1 2, 6 4,,,,, 6 9( ), 6 9 ( ) = 1, ;, 86
= 1,, = 1, ( 6 9 ( ) ) = -,, = 1, ; = 1, = 0 6 9 ( ) 6 9, : (1 ) = 1, (2 ) = 1, (3 ) = 1,,, 6 9( ) ( ), 87
,,,,, ;,,,, 6 1. 10 ( ),,,,,, ;, ; = 1,,,,,, 6 2. 10( ),,,,,,,, 1, 6 3. 10 ( ),,,,,,,, 6 10 ( ),, 6 5 6 11 ( ),,, (),,, = 1, ( 6,, 11 ( ) ),, = 1,,, - ( 6 11 ( ) ) = 1,,, 88
6 10 = = - +,, = 0, = ; =, =,, ( 6 11 ( ) ),, : (1 ); 89
6 11 (2 ), 6 12, 6 12, = 1,,, 6 90 13
91
6 13 * 6 6,, 6 14 ( ), (4-1) = 0 = 0 = 0, ;,, 6, ( 4 2) = 0-14( ) : 0 ;,,,, 6 6 (4 5 ) 14 ( ) = 0 - = 0 + 14 ( ), 0 ;,, 6 14( ),, 6 14 ( ), 6 14 ( ), ( ) 92
6 14 6 7,,,,, 93
,,, 6 15 ( ),, = 1 6 15 94
,, = 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
6 = + 0 ( 6 13) 15 ( ) 0 = 1, -, = 0 0, = 0, = - 0 ( 6 14),,, 6 15 ( ),,, 6 = 1, ( 6 15 ( ), ( )( ), = - 0 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 = 1 1 + 2 2 + 3 3 96
, 1, 2,,, 1, 2,,, (6 = 1 1 + 2 2 + 3 3 + = = 1 ( 6 15) 15), 6 16 6 17, 6 17,,,,, = 1 1 + 2 2 + + = ( 1 1 + 2 2 + + )= = 1,,, = = 1 = = ( 6 16) ( ) ( ), 6 6 18 ( ), ( ) 18 ( ) ;, ( ), ( ) ; = ( ) ( ), ( ) = = 97
,, ( ) = ( ) ( 6 17) = ( 6 18) 6 18 6 19 6 1 6 19 ( ),, 6 19 ( ) 1, 2, 1 = 1 2 6 3 5 = 1.8 (6 18) 2 = 1 2 4 ( - 2 5 ) = - 0.8 = ( 1 + 2 ) = 10 (1.8-0.8 ) = 10 * 6 9,,,,,,,, 10 15 20 20, 6 20 ;,, 6 20,,,, : 5080100120 98
, 021-89 99
6 20 6 10,,, (, ),, ( ),, ( ) 6 8, ; ( 6 21) 6 21 6 22 (,, ), ( 6 18 ) 100
=,, ;,, ( 6 22 ), ( ),,,, 6 23 ( ), 1, 2,,,, 6 23 ( ), 1, 2,,, 1 = 1 1 + 2 2 + + ( 6 19) 6 23,, :,, 6 24( ) 6 24 ( ), 6 24 0 ( 6 20), 2 2 = 1 ( 1 + 1 ) + 2 ( 2 + 2 ) + + ( + ) = 1 1 + 2 2 + + + 1 1 + 2 2 + + ) = 101
1 + 1 1 + 2 2 + + = 2-1 = 1 1 + 2 2 + + = = 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
,, ( ), =,,, = = 0 ( 6 25 ) 6 2 6 26 ( ), 20, 6 25 (1 ) :, 3 1 2, 6 26 ( ) 6 26 (6 1 = 1 16, 2 = - 22 ), 1 16, 3 = 3 16, 4 = - 1 16 130 1 16-70 1 16 - (120 + 180 ) 1 16 < 0 130 1 16-70 1 16, + 120 3 16-180 1 16 > 0 = 130 1 8 + 70 1 8 + 120 1 2 + 120 1 2.6 6 8 + 103
60 1 2 2.6 8 = 144.25 4 1 2, 130 1 16 130 1 16-70 1 16-70 1 16 + 120 3 16-180 1 16 > 0 + ( 120 + 120) 3 16-60 1 16 > 0, 3 1 2, 5,, = 144.25 ( 2 ) : 3, 6 26( ), - 180 1 16-120 1 16 < 0-180 1 16 + 120 3 16 > 0,,, = 60 1 4 1.4 4-120 1 4 ( 6 2.6 4-120 1 4 = - 44.25 27 ),,,,, : ( + )- 0 - ( + ) 0 = = 6 27 6 28 104
+ + ( 6 23) :, ( 6 = = 1 - = 0 = 28), = = 0 = 1 ( 6 24) 6 3 6 29 ( ), 12 82 ( 1 = 2 = 3 = 4 = 82 ), 3.5, 1.5 ( 1 ) 6 29 ( ) (2 ) 2 3, 2 6 29( ), (6 23) 2 82 + 82 3.6 > 82 + 82 8.4 82 82 + 82 + 82 < 3.6 8.4 3 6 29 ( ), (6 23), 1 3 82 + 82 3.6 > 82 8.4 82 82 + 82 > 3.6 8.4 (3 ) 2, 6 29 = 82(0.07 + 2.52 + 2.07 + 1.02) = 465.76 6 4 6 30 ( )15,, 6 30( ) (1 ), 130, 6 30( ) (6 23) 105
70 + 130 15 70 15 > 200 25 < 200 + 130 25, 130, = 706.88 + 1309.38 + 507.50 + 1006.0 + 500.38 = 2 694 (2 ), 130, 6 (6 23) 150 + 130 15 150 15 > 200 25 < 200 + 130 25 30 ( ), = 1003.75 + 506.25 + 1309.38 + 707.88 + 1002.25 + 500.75 = 2 720, 6 = 2 720 6 30 30 ( ), 6 11,, ( ),,,,,,,, =, 6 15 = = 2 720 = 14.50 / 1 2 40 9.33 4,,, 106
, 2 = 1 6 31 : 2 = 1, 2 = 1 2 = 2 2 = 1 1 = 1 1 = 1 6 16 3 : (1 ), (2 ) ( ), 6 32, 1, 2 6 31 (3 ), ( ), (4 ) ( 6 32), 00.5, 6 32 6 1-10 / ( / ) () 1/ 8 1/ 4 3/ 8 1/ 8 1/ 4 3/ 8 1 200.0 200.0 200.0 200.0 200.0 140.0 140.0 140.0 140.0 140.0 2 100.0 100.0 100.0 100.0 100.0 70.0 70.0 70.0 70.0 70.0 3 66.7 66.7 66.7 66.7 66.7 46.7 46.7 46.7 46.7 46.7 4 50.0 50.0 50.0 50.0 50.0 35.0 35.0 35.0 35.0 35.0 6 38.9 37.3 35.2 33.3 33.3 26.7 25.7 24.4 23.3 23.3 8 31.3 30.4 29.2 27.5 25.0 21.3 20.7 20.0 19.0 17.5 10 26.0 25.4 24.7 23.6 22.0 17.6 17.3 16.8 16.2 15.2 13 21.5 20.4 19.9 19.3 19.4 14.0 13.7 13.5 13.1 12.5 16 18.9 18.0 16.9 17.3 17.0 11.6 11.4 11.3 11.0 10.6 20 17.1 16.0 15.8 16.1 15.2 9.8 9.3 9.2 9.0 8.8 25 14.9 14.2 14.1 14.3 13.7 9.2 8.3 7.5 7.4 7.2 30 13.3 12.7 12.6 12.7 12.3 8.6 7.9 7.0 6.4 6.1 35 12.5 11.5 11.4 11.4 11.1 7.9 7.4 6.8 6.3 5.6 40 11.8 10.8 10.7 10.5 10.2 7.5 6.9 6.4 6.0 5.4 45 11.0 10.3 10.2 10.0 9.7 7.3 6.6 6.1 5.8 5.6 107
50 10.5 9.7 9.7 9.5 9.3 7.3 6.5 5.8 5.5 5.1 65 9.8 9.0 8.7 8.7 8.7 6.7 6.2 5.7 5.5 5.6 108
6 2-15 / ( / ) () 1/ 8 1/ 4 3/ 8 1/ 8 1/ 4 3/ 8 0 260.0 260.0 260.0 260.0 260.0 200.0 200.0 200.0 200.0 200.0 2 130.0 130.0 130.0 130.0 130.0 100.0 100.0 100.0 100.0 100.0 3 86.7 86.7 86.7 86.7 86.7 66.7 66.7 66.7 66.7 66.7 4 65.0 65.0 65.0 65.0 65.0 50.0 50.0 50.0 50.0 50.0 6 51.1 48.9 45.9 43.3 43.3 38.9 37.3 35.2 33.3 33.3 8 41.3 40.0 38.3 36.0 32.5 31.3 30.4 29.2 27.5 25.0 10 34.4 33.6 32.5 31.0 28.8 26.0 25.4 24.7 23.6 22.0 13 29.5 27.5 26.4 25.5 25.9 20.7 20.4 19.9 19.3 18.3 16 26.0 24.7 23.0 23.5 23.0 17.2 17.0 16.7 16.3 15.6 20 23.7 22.0 21.7 22.1 20.7 14.5 13.9 13.7 13.4 13.0 25 20.7 19.7 19.5 19.7 18.8 13.6 12.3 11.1 11.0 10.7 30 18.7 17.6 17.4 17.6 17.0 12.8 11.7 10.4 9.5 9.1 35 17.7 16.0 15.9 15.8 15.3 11.8 11.1 10.1 9.3 8.3 40 16.7 15.2 15.0 14.5 14.2 11.2 10.4 9.6 9.0 8.1 45 15.6 14.5 14.3 13.9 11.0 11.0 9.8 9.1 8.6 8.4 50 14.9 13.7 13.6 13.3 12.9 10.7 9.6 8.7 8.2 8.6 60 13.9 12.8 12.3 12.2 12.2 10.1 9.2 8.5 8.2 8.4 6 3-20 / ( / ) () 1/ 8 1/ 4 3/ 8 1/ 8 1/ 4 3/ 8 1 260.0 260.0 260.0 260.0 260.0 260.0 260.0 260.0 260.0 260.0 2 156.0 144.0 130.0 130.0 130.0 130.0 130.0 130.0 130.0 130.0 3 122.7 117.3 110.2 100.0 86.7 86.7 86.7 86.7 86.7 86.7 4 99.0 96.0 92.0 86.4 78.0 65.0 65.0 65.0 65.0 65.0 6 72.7 69.3 67.6 65.1 61.3 51.1 48.9 45.9 43.3 43.3 8 59.6 57.4 54.5 51.6 49.5 41.3 40.0 38.3 36.0 32.5 10 50.2 48.8 46.9 44.3 43.7 34.2 33.6 32.5 31.0 28.8 13 40.3 29.5 38.4 36.3 36.0 27.5 27.0 26.4 25.5 24.1 16 33.7 33.1 32.4 31.4 31.1 22.8 22.5 22.1 21.5 20.6 20 29.2 27.2 26.7 26.1 25.9 19.3 18.4 18.1 17.8 17.2 25 25.7 24.3 24.3 22.8 22.0 18.0 16.3 14.8 14.6 14.2 30 22.7 21.8 22.4 21.5 19.9 17.0 15.6 13.9 12.6 12.1 35 20.9 19.9 20.5 19.8 18.7 15.7 14.7 13.4 12.4 11.1 40 20.0 18.9 18.3 17.5 14.9 14.9 13.8 12.7 12.0 10.8 45 19.0 18.4 17.7 16.9 16.8 14.6 13.1 12.0 11.5 11.2 50 18.0 17.7 17.0 16.4 16.3 14.2 12.8 11.6 11.0 11.4 60 16.9 16.3 15.7 15.3 15.2 13.4 12.2 11.3 10.0 11.2 109
6 5 6 33 ( )15,, 6 6 33 33 ( ), ( ) (1 ) : = 6,= 0, = 5.11 /, = = 5.11 1 2 ( - 1 ) 6 = - 5.11 3 (2 ) : = 12,= 0,, = 10,= 0, = 13,= 0, = 0, = 12, ( 6 = 2.95 + = 3.44 / = 2.95 / 34) 13-12 (3.44-2.95) = 3.11 / 13-10 = = 3.11 1 2 2 3 12 = 12.44 (3 ): = 18, = 1 3,, 6 4 6 4 ( / ) / 0.250 0.333 0.375 16 2.3 2.33 2.35 18 2.27 20 2.17 2.20 2.21 = 16,= 1 3 = 0.333, 110 0.3 33 = 2.3 + 2.35-2.3 3 8-1 4 ( 1 3-1 4 ) = 2.33 /
= 20,= 1 3 = 0.333, 0.333 = 2.17 + 2.21-2.17 3 8-1 4 ( 1 3-1 4 = 18,= 0.333 = 2.20 + 2.33-2.20 20-16 ) = 2.20 / (20-18) = 2.27 / = = 2.27 1 2 18 4 = 81.72 6 12,,,,, : (1 )? (2 ),,,,,,,,, ( 6 34),,,,,,,,,,, 6 6 34 34,,,, = ( - - ) 111
= - = ( - - ) -,, = ( - 2 - ) = 0 = 2-2,,,, ( 6 ( 6 25) = ( 2-2 ) 2 - ( 6 26) 26 ),,,,,,,,,,,,, 6 6 6 35 ( )15, 6 35 (1 ) : 6 35 ( ), 2, = 2, = 350, 2 (6 112,, = 1 (50 5 + 100 9-70 4) = 2.486 350 25),,
= 350 20 = 2-2 = 20 2-2.486 2 = 8.757 2.486 (10 - ) 2-70 4 = 1 062 2 (2 ) : 6 35( ), 2 = 130, = 70 3 + 130 5 + 50 2.5 + 100 0.5 = 1 035, 1 062, 1 035 3 %, 6 13,,,,, 6 36 ( ), ( 6 36( ) ) (),,, ( ), 6 36 ( )( ),,, ( 6 36 ( ) ), 6, 6 37 ( )( ), 37( ), ( )( ),,, + - ( ), ( 021-89 ),, = + ( 1 + ) + = + (1 + ) - ( 6 10) 113
6 36 6 37 6 7 6, 1 : = 12.75 /, 10, = 1.82, = 0.29 8,,, 6 38 ( ),,, ( 6 38 ( ) ) 1-4 114
, 6 6 6, 6 38 5 6 38 6 5 1 +. 1 = 12.75 ( 1 + ) 2 = + = 2 / 1 6.32 0.125 1.98 25.25 3735 1.29 26.31 2 6.32 0.25 3.39 43.22 35.2 1.29 42.29 3 6.32 0.375 4.23 53.93 33.3 1.29 49.92 4 6.32 0.5 4.50 57.38 33.3 1.29 53.11 51.56 25.25 85.51 43.22 103.85 53.93 110.49 57.38 115
6 6 1 +, = 12.75 (1 + ) 2 + / 0 6 0 + 3 + 3 38.25 38.9 1.29 41.36 + 79.61 + 38.25 4 3 3 0 0 + 0.75-0.75 0 0 66.7 66.7 1.29 + 17.73-17.73 + 17.73-17.73 6 1 ( ), ( ),, 1 2 6 2,,, 6 1 6 2 6 3,,, 6 4,,, 6 3 6 4 6 5,,,, 6 6 :,,, = 1 6 7, = 1 6 8,, = 1 6 9,,,, 6 106 15 116
6 5 6 6 6 7 6 8 6 9 6 10 (,,,, ) 6 11 (,,, ) 6 12 (,,, ) 117
6 13 (,, ) 6 14 (,,,, ) 6 15 (,,,,,, ) 6 16 6 16 = 4 ( - ),,,, 6 176 18, 6 17 6 18 6 19 6 19 6 206 21, 6 226 23, 6 24,,, 118
6 20 6 21 6 22(, ) 6 23 (,, ) 6 24 6 25 15,,, 6 26 6 25 6 26 6 27 15,, 6 28 6 27 6 28 6 29 = 20, = 12 /, 10, 119
( ) 6 29 6 16 19 6 20 = 7.5 = 7.5 6 21 = 12.22 = 8.89 6 22 = - 29 = 116 6 23 = 16.38 6 24 6 25 = 237, = 149, = - 36 6 26 = 242.5 6 27 6 28 426.7 6 29 120
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 1 7 2, ( ), 7 3, 118
,, 7 3,,, : (1 ),,,,,,, (, 1/ 700, 1/ 900) (2 ),,,, (3 ),,,,,,,, : (1 ), ; (2 ), ; (3 ), ( ),,,,,,, 7 2, 119
: 7 4( a) P1,, P1, P1, 1 7 4 ( b) P1 W = 1 2 P1 1 7 4( 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
d s 7 5( a) d s 7 5 (c) 7 5( b) d s CD C D:,,, d s, 7 5( d ) 7 7 5 ( 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
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
RA = - P 0 (7 4) (7 4 ) (7 Cy = CA 0 (7 5) 5 ), Cy P, P = 1, Cy P, 7 3 7 7( 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
,,, 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
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
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) 7 1 7 9( 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 = - 1 2 qx2, N P = 0, QP = qx BC : M P = - 1 2 q2, N P = - q, QP = 0 126
(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 = 1.2 1 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 ( 1 + 16 75 ( h ) 2 + 2 15 ( h ) 2, h, h = 1 10, A y = 5 q4 8 EI 1 + 1 750 + 1 500,, 7 2 7 10( a), C E = 2.110 4 kn/ cm 2, A = 12 cm 2 7 10 ( a) ; ( b ) 127
(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, 2 7 1 ( ) N/ k N NP/ k N / cm A/ cm 2 E/ ( kn/ cm 2 ) NN P E A / cm AC A D - DE - DC 3 8 5 8 5 8 3 4 + 45 600 12 2.110 4 0.040-75 500 12 2.110 4 0.093 45 600 12 2.110 4 0.080 0 500 12 2.110 4 0 = 0.213 cm Cy = 2 0.213-0.08 = 0.346 cm () 7 3 7 11 ( 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
By = MR M P ds = E I EI 2 PR 3 0 sin2 d= 7 EI 1 2 0 PR3 EI ( - Rsin ) ( - PR sin ) Rd= 1 2-1 2 sin2 2 0 5 = 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,, 7 12 129
= 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 ), 130 3 y3 )
2. MR M P E I 7 14 d x = 1 y1 EI 1 + 2 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 + 1 3 d y2 = 1 3 c + 2 3 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 7 4 7 17 (a)c EI (1 )MP 7 17 ( b) (2 ) C P = 1, M7 17( c) ( 3) C y M P, MP, M,, 131
7 15 7 16 Cy = yc E I = 2 1 EI 7 17 2 3 1 8 q2 2 5 8 4 = 5 q4 384 EI () 7 5 7 18 (a)d Dy E I 7 18 MP M7 18 ( b), ( c), CB M 1, A B M 2, 132
1 = 1 2 1 2 1 2 = 1 8 2 y1 = 5 6 P( 1 ) D y = y C E I = 1 EI 2 = 1 2 = 1 2 2 y2 = P( 2 ) 1 8 2 5 6 P + 2 2 P = 29 P3 48 EI () 7 6 7 19 (a) C, D EI 7 19 MP M7 19 ( b), ( c) 7 19 ( b) 7 19( c) CD = - 1 EI ( 2 3 1 2 qa2 2 aa) = - 2 qa4 3 EI ( ), C, D 7 7 7 20 ( 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 ( 2 3 1 8 q2 1 2 ) + 1 EI ( 1 2 1 8 q2 2 1) + 1 EI ( 1 3 1 8 q2 2 1) = 133
3 q 3 32 EI () 134
7 8 7 21 (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 ( 2 24 2) 2 + 6 EI EA 16 4 3 4 + ( - 20) ( - 5 3 ) 5 = 96 EI + 252 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
( h1 = h2 ), t0 = t1 + t2 2 7 22 ( 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
, N, t0 M t ( M t ),,,,,, Kt = t0 N ( 7 19),,, K = N ( 7 20) 7 9 7 23( a) 20,, - 10, 0 A A y = 4 m, = 10-5,, h = 40 cm 7 23 ( a) ; ( b) ( c) t1 = - 10-20= - 30, t2 = 0-20= - 20, t0 = t1 + t2 2 = - 30-20 2 = - 25 t = t2 - t1 = - 20- ( - 30) = 10 M, N( 7 22 ( b), ( c) )( 7 18 b),, Ay = t0 N + t h M R = ( - 25) ( 2 ) + 10 h - 25 2-15 4 h 2 = - 25 2 10-5 - 0.20 cm () 1 2 1 2-1 2 ( 2 ) 2 = 400-10 - 5 15 4 40 4002 = 137
* 7 10 7 24( a), CD, 2 cm, E = N, E, E P = 1, 7 24 ( b) P = 1 CD ( 7 24( b) ) K y NCD = - 1 4 5 3 = - 5 12 kn K y = 5 12 2 = 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, :, 7 11 7 25( a), A a, B B 7 25 ( b), (c),, 7 25 ( b) V A = h (), 7 25(c) V A = 1 ()(7 21) 138
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) 7 26 7 8,,, 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
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 = 1 2 1 12 = 2 1 28, 7 28 7 29 (a) ; ( b) ( a) ; ( b ) 12 21,, 1 2 2 1, 140 12 = 2 1 ( 7 25)
, :, P1 P2, 12 2 1, 7 29 1 = 2 = 1 k12 1 = k2 1 2 k12 = k2 1 ( 7 26), : 1 2, 2 1 7 29, 7 30 7 30 (a) 2 P2 = 1, 1 k12, ; 7 30( b) 1 k12 1 = 1, 2 P2 = 1 21,, k12 1 + 1 21 = 0 k12 = - 2 1 ( 7 27), :,, * 7 9 7 31 (a), P = 1, K KP K P x,, K P K P 141
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 7 31 32 (a), A AP, AP = 1 P A ( 7 32 ( b) ) P A,, AP, MP, 7 32( c), ( d), M A 7 32 142
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? 7 1 7 2 (1 )( a), E A =, Dx CD? (2 )( b), E A =, G y? 143
7 2 7 3,?? 7 4, B y? 7 5, Cy, C? 144
7 3 7 4 7 5 7 6, B? 7 7, B y? 7 8, Ax, Ay? 7 9, A (A )? 145
7 6 7 7 7 8 7 9 7 10, Cx, D? 7 11, C C, D? 7 10 7 11 7 12 D ( E I = 7.510 5 knm 2, E A = 2.110 6 kn) 7 13 D, h = 1, 10 7 14, CD DE t, E 7 15 C 146
7 12 7 13 7 14 7 15 7 16 A 0.01 rad, B 0.01 a, D C 7 17 CD 0.5 cm, F 7 16 7 17 7 1 ( 1) By = 7 q4 24 E I () ( 2) A = M 3 E I ( ) C y = M2 16 E I ( ) 147
( 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 = 7 11 469.3 10.7 () 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 = 0.003 3 rad ( ) 7 16 D y = 0.01 a() C = 0.01 rad ( ) 7 17 Fx = 0.187 5 cm () 148
8 1,,,, 8 1 ( a),, 8 2 (a),,, 8 1 8 2,, 8 3 (a), B, 8 3( b ),,, 8 1( a), B C, 8 1 ( b), ( c), 8 2 (a),, 8 2( b),,, 149
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) ) 8 4 150
(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
, 8 8 8 ( b ), 8 8,,,, 8 8 ( c),, 8, : (1 ) 8 1 ( a), (2 ) 8 9 (a), ( 8 9 ( b ) ), ( 8 9 (c) ),, 8 9 8 6 (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) = 3 6-2 8-3 = - 1 152
8 10 8 3, 8 8 11 (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 1 8 11( b ), X1, B B 1 P ( 8 11( c) )X1 11 ( 8 11 ( d) ) 11 1 P, B, X1 Y B,, : X1 1,, 1 = 11 + 1 P = 0 (8 1) 1 X1 X1 ; 153
( d) ) ; 11 X1 X1 ( 8 11 1 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,, 8 154 11( a), 11 1 P,
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 ( 1 2 2 3 ) = 3 = - 3 X1-5 P3 3 EI 48 EI = 0 X1 = 5 16 P() 3 EI 1 EI ( 1 2 1 2 1 2 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
, ( 8 5) 1 2 1 = 1 1 + 12 + 1 P = 0 2 = 2 1 + 22 + 2 P = 0 (8 6),, 1 1 = 11 X1, 12 = 12 X2, 21 = 2 1 X1, 22 = 2 2 X2, ( 8 6) 1 1 X1 + 12 X2 + 1 P = 0 2 1 X1 + 22 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
11 X1 + 1 2 X2 + + 1 i X i + + 1 n X n + 1 P = 0 21 X1 + 2 2 X2 + + 2 i X i + + 2 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,,,, ;, ; 8 5 8 14 (a),, B, X1 X2,, 8 14( b)b, 11 X1 + 1 2 X2 + 1 P = 0 21 X1 + 2 2 X2 + 2 P = 0 157 ( 8 12)
,, X1 = 1, X2 = 1, 8 14 ( c), ( d), ( e), 11 = MR1 2 EI 22 = MR2 2 12 = EI d s = 1 EI ( 1 2 2 2 3 ) + 1 2 EI ( 2 ) = 5 2 6 EI d s = MR 1 M2 21 = EI 1 P = MR1 M P d s = EI - 1 2 EI ( 1 2 2 2 3 ) = 3 6 EI d s = - 1 2 EI ( 1 2 2 ) = - 3 4 EI 1 EI ( 1 3 1 2 q2 3 4 ) - 1 2 EI ( 1 2 q2 ) = - 3 q4 8 EI 2 P = MR2 M P d s = EI 1 2 EI ( 1 2 2 1 2 q2 ) = q4 8 EI 8 14 ( a) ; ( b) ; ( c) M 1 ; ( d) M 2 ; ( e) M P ; ( f ) M,, 158
5 6 X1-1 4 X2-3 8 q = 0-1 4 X 1 + 1 6 X 2 + 1 8 q = 0 X1 = 9 22 q, X2 = - 3 22 q(),, : M = MR1 X1 + MR2 X2 + MP M AC = 9 22 q - ( - 3 22 q) - 1 2 q2 = 1 22 q2 ( ) 8 14 (f),,, : (1 ) (2 ),, (3 ) (4 ) (5 ), (6 ), 8 1 8 15 (a)ei = (1 ), (2 ) A, B B,, 8 15 ( b ) (3 ) A, B B, 11 X1 + 12 X2 + 1 3 X3 + 1 P = 0 21 X1 + 22 X2 + 2 3 X3 + 3 P = 0 31 X1 + 32 X2 + 3 3 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 ( 1 2 1 ) 2 3 1 = 3 EI 22 = 1 EI ( 1 2 1 ) 2 3 1 = 3 EI 33 = MR2 3 EI d s + N2 3 EA d s = 0 + E A = E A 159
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 2 1 ) 1 3 1 = - 1 P = 1 EI ( 2 3 1 8 q2 ) 1 2 1 = q 3 24 EI 2 P = - 3 P = 0 6 EI 1 EI ( 2 3 1 8 q2 ) 1 2 1 = - q 3 24 EI (5 ),, 2 X1 - X2 + 1 4 q2 = 0, 160 X1 = - - X1 + 2 X2 - E A X 3 = 0 1 4 q2 = 0 1 12 q2, X2 = 1 12 q2, X3 = 0
, E I,,, E I, E I (6 ) M = M R1 X1 + M R2 X2 + M R3 X3 + MP, 8 15 ( g),, 8 15( h ) 8 2 8 16 (a), E I = (1 ) (2 ), B, C, 8 16 ( b) (3 ) B, C, 11 X1 + 1 2 X2 + 1 P = 0 21 X1 + 2 2 X2 + 2 P = 0 (4 ) ( ) X1 = 1, X2 = 1, M1, M R2 M P ( 8 16( c), ( d), ( e) ), E I = 1, 11 = 22 = 1 2 1 2 3 1 2 = 2 3 12 = 21 = 1 2 1 3 1 = 1 6 1 P = 2 3 1 1 8 q2 2 1 2 = 1 12 q3 2 P = 2 3 1 8 q2 1 2 1-1 2 q2 1 3 1 = - 1 8 q3 (5 ) 2 3 X 1 + 1 6 X 2 + 1 12 q3 = 0 1 6 X 1 + 2 3 X 2-1 8 q3 = 0 X1 = - 11 60 q2, X2 = - 14 60 q2 ( 6) M = MR1 X1 + MR2 X2 + MP 8 16 ( f), 8 16( g) 8 3 8 17 (a) E A (1 ) (2 ) CD, X1, 8 17 ( b) (3 ) CD, 11 X1 + 1 P = 0 (4 ) X1 = 1 161
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
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 = - 11 1 2 P ( ) (6 ), N = N1 X1 + N P, 8 17 (e) 8 4 8 18 (a): A B: E I = 1.510 4 knm 2 AD, BD: E A = 2.610 5 kn CD: E A = 2.010 5 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
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 ( 1 1.5 10 4 2 3 1.5 ) 2 3 1.5 2 + 1 1 1 1 + 2 10 5 1 2.6 10 5 (2 1.58 1.58 3.16) = 3.657 10-4 1 P = MR1 M P EI d s + N1 N P E A = 2 1.5 10 4 ( 1 2 1.5 0.75 2 3 180) + 1 2 1.5 (0.75 + 1.5) 180 = 495 10-4 (5 ), X1 = - 1 P = - 1 1 (6 ), m 495 10-4 3.657 10-4 = - 135.36 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 135.36 kn, 78.48 knm 180 knm, 50%, EA0, X1 0, 164
8 19 ( a ), E A, X1 165 kn, C,, 8 19 ( b ), ( ), 8 20 ( a) (),,,,, 8 20 ( b) 8 20,,, 8 5 8 21 (a), (1 ) (2 ) CD X1, 8 21( b ) (3 ) 11 X1 + 1 P = 0 (4 )M1, MP 8 21 (c), ( d) 11 = 2 EI ( 1 2 332 3 3 ) + 2 6 E I ( 1 2 63) ( 2 3 3 + 1 3 9) + ( 1 2 ( 2 3 9 + 1 3 3) = 96 E I 69) 8 19 ( a) M 0 ( k Nm ) ; ( b ) M ( kn m ) 165
8 21 (a) ; ( b ) ; (c) MR ( m ) ; ( d ) M P ( k Nm ) ; ( e) M ( kn m ) 1 P = 1 E I ( 1 2 120 )( 2 3 3 + 1 3 2 ) + 1 6 E I (5 ), ( 1 2 620)( 2 3 3 + 1 3 9) + ( 1 2 6140) ( 2 3 9 + 1 3 3 ) = 1 700 3 E I x1 = - 1 p = - 5.90 kn 11 (6 )M M = M R1 X1 + MP, 8 21( e), 8 6,, ; ( E I, E A, GA ),,,,, 8 22 (a),, ( 8 166
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 = 0 1 1 X1 + 12 X2 + 1 P = 0 2 1 X1 + 22 X2 + 2 P = 0 3 3 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
( 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 ),,,, 8 6 8 25 (a) P 168
P ( 8 25 ( b) ) ( 8 25( c) ) 8 25 ( a) ; ( b) ; (c) (1 ),, CD,,, (2 ), 8 26 (a ), ; X1 X1, 11 X1 + 1 P = 0 8 26 M1, MP ( 8 26 ( b), ( c) ),, : 1 1 = 2 EI 1 P = 2 EI ( 1 2 1 2 1 2 2 3 1 2 + 1 2 1 2 = 7 3 12 EI 1 2 1 2 P 1 2 = P3 4 EI X1 = - 1 P = - 11 3 7 P 169
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 ) 8 28 8 29 2. (1 ) : 8 30 ( a),,, 8 30 170
K ;,,,, 8 30 ( b ) (2 ) : 8 31 ( a),, I 2, ( 8 31( b ) ),,, QK, 8 31( c), QK,, QK,, 8 31( d) 171
8 31 8 7 8 32 (a)ei = 8 32 ( a) ; ( b ) ; ( c) ; ( d) M 1 ( m ) ; ( e) M P ( k Nm ) ; ( f) M ( kn m ) 172
,, 8 32 ( b ) 8 32 ( b), C 8 32 (c) M1, MP ( 8 32 ( d), ( e) ), 11 = 1 EI 1 P = - 1 EI ( 1 2 3 3 2 3 3 ) 2 + 3 6 3 = 72 EI ( 1 2 6 60 3) + ( 1 2 3 12 2 3 3 ) = - 900 EI X1 = - 1 P = - 11-900 72 = 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 X1 + 1 2 X2 + 13 X3 + 1 t = 0 21 X1 + 2 2 X2 + 23 X3 + 2 t = 0 31 X1 + 3 2 X2 + 33 X3 + 3 t = 0 1 t, 2 t, 3 t X1, X2 X3, 173
it = t0 N + t h M R,,, M = MR1 X1 + MR2 X2 + MR3 X3 ( 8 14) 8 8 8 34 (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 = 1 2 2 2 3 = 2 3 3 EI t0 N 1 10 (1 + h ) + t h M R 10 = + 5 2 + 2 = h (5 ), 174 X1 = - 1 t = - 15 E I ( 1 + 1 1 2 h )
(6 )M M = M R1 X1 8 34 ( d), E I, 8 8,,,,,,, 8 35 (a) 8 35 ( a) ; ( b ) ; ( c) 8 8 35 ( b), 11 X1 + 1 2 X2 + 1 C = 0 21 X1 + 2 2 X2 + 2 C = 0 35 (c), 11 X1 + 1 2 X2 + 1 C = C1 21 X1 + 2 2 X2 + 2 C = C3,,, 1 C, 2 C X1, X2 ic = - Ri Ci 8 9 8 36 (a), A, EI = (1 ) (2 )8 36( b ) (3 ) 11 X1 + 1 C = 0 (4 )M1 ( 8 36 ( d) ), 175
11 = 1 EI ( 1 2 2 3 ) = 3 3 EI 1 C = - Ri Ci = - ( ) = - 8 36 ( 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 ( 1 2 1 2 3 1) = 3 EI X1 = 3 EI 36( e) ) 8 10 8 37 ( a), B, k = 10 E I 3, (1 ): B, X1, 8 37 ( b) B,, B = 1 k X 1 B, 176 1 1 X1 + 1 P = - X1 k
X1, ( 11 + 1 ) X1 + k 1 P = 0, 8 11 = 1 EI ( 1 2 2 3 ) = 3 3 EI 1 P = - 1 EI 37( c), ( d) ; 1 2 P 2 1 2 2 3 + 1 3 1 2 = - 5 P3 48 EI X1 = 5 Pk 16 (3 EI + k 3 ) = 25 104 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
11 X1 + 1 P = 0, 1 1 1 P, 8, 11, 1 P 1 1 = 1 EI ( 1 2 1 2 3 1 ) - ( - 1 1 k ) = 13 30 EI 1 P = 1 EI ( 1 2 1 4 P 1 2 ) - ( - 1 P 2 k ) = 9 P2 80 EI 8 X1 = - 1 P 11 = - 27 104 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 = 1 8 14 (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 3 264 EI ( 2 3 1 8 q2 ) 1 - ( 1 2 1 11 q2 ) 1 + ( 1 2 1 22 q2 ) 1 - ( 1 2 1 11 q2 ) 1 = - q 3 88 EI = 7 q3 264 EI 38 (c), ( ) 178 B = 1 EI ( 2 3 1 8 q2 ) 1 2 - ( 1 2 1 11 q2 ) 1 3 1 =
8 38 ( a) M ; ( b ) M; ( c) M, q 3 24 EI - q 3 66 EI = 7 q3 264 EI ( ) 8 9 8 36 (a) M 8 36 (e), (1 ), 8 39 (a) M = MR M P E I 1 EI d s - Ri Ci = 1 2 1 4 3E I 2-0 = 3 () 16 8 39 (2 ), 8 39 ( b) M = MR M P EI - d s - Ri Ci = 1 EI ( 1 2 1 2 1 2 ) ( 5 6 3E I ) - ( -, 1 2 ) = 3 () 16 179
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 - 3 22 q = 0 Y = 13 13 q - 22 22 q = 0 MC = 1 11 q2-40( f) ) 1 11 q2 = 0 40 (e) ) 180
MB = 1 11 q2 + 1 2 q2-13 22 q2 = 0 X = 3 22 q - 3 22 q = 0 13 Y = q - 22 q - 9 22 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 ( 1 2 1 11 q2 2 3 ) - ( 2 3 1 8 q2 1 2 ) + ( 1 2 1 11 q2 2 3 ) - ( 1 2 1 22 q2 1 3 ) = 0 8 41 ( 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
8 42 ( a) M ; ( b ) M M EI,, M, M EI 8 11, (1 ),,,,,,, (2 ), ;,, (3 ) :,, ;,,,, (4 ) 8 43 ( a) ( b ),,, 8 1 182
8 43 8 1 8 2, 183
8 2 8 3 E A = 8 4 184
8 3 8 4 8 5, 8 5 185
8 6 8 6 8 7 8 7 186
8 8 8 8 187
8 9 ( E A = ) 8 9 8 10, E I,, h = (1 ) (2 )A A 10, 8 11, 10 C, E A, 8 10 8 11 8 12, A A,, M 8 13 28 a, I = 7114 cm 4, E = 2.110 4 kn/ cm 2, = 10 m, P = 50 kn, B? 8 12 8 13 8 14 M EI =, k = EI a 3 * 8 15 A B 0.5 cm,, 188
EA = 6 10 5 kn 8 14 8 15 8 16 K 8 17 8 12 8 18 M ( E I = ) 8 16 8 18 8 19 M 8 1 2 5 4 3 6 4 7 2 8 2 ( 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
( c) MBC = 76 P ( ) 191 ( d ) MAD = 3 p ( ) 16 8 4 ( a) NCD = 0.442 P() ( b) NDE = - 0.198 P() 8 5 ( a) NCD = 125.2 kn( ) 8 19 ( b) MDB = 1 3 p( ) 8 6 ( a) MAC = 112.5 knm ( ) ( b) MA D = 31 116 q2 ( ) 8 7 ( a) MAC = 11.1 knm( ) ( b) NDE NFG = - 17.39 kn = - 8.69 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
( f) MCA = 1 4 P ( ) ( g ) MCA = 60 knm ( ) ( h) MBA = 1 4 Ph ( ) 8 9 ( a) N2 5 = - 0.602 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 ( ) 8 13 2.32 cm ( ) A = 60 () 8 14 MAB = 5 Pa ( ), 14 11 11 P () 8 15 N AB = 62.5 kn () 8 16 K y = 13.5 E I ( ) 8 17 = 3 16 A ( ) 8 18 8 19 191
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
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) 9 1 9 2 9 1 9 2 (1 ), 9 2( b ) (2 ) m1, MP, 9 2( c), ( d) (3 ) 1 1 P1 (4 ) 1 1, P1 ( 9 1 1 = 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
(9 4 ), 11 = 1, X1 P1 X1 X1 = - P1 ( x), P1,,,,,,,,,,,,,,, 9 3 ( b), ( c), ( d), ( e) 9 3 9 2,,,,,,, ( ), 190
,, ( S = qw ),, ;,,,, 9 4, 9 4,,, 9 4,,,,, QK,,,,, 191
,,,,,,,,,, 9 2 9 5 ( 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 ) = ( - 72.0 ) + 24.0 = - 48.0 knm 192
M1 ( mi n) = ( - 72.0 ) + ( - 96.0 ) + ( - 72.0) = - 240.0 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) + ( - 136 ) + ( - 12) = - 220.0 kn,,,, 9 6 (e) 9 6 * 9 3 ( 9 7), 9 8,,,,,, 9 9 P, 193
, A, B, C, D,,, 9 9 9( b ),,, 9( c), 11 X1 + 1 P = 0 9 7 9 8 9 9 m1, MP ( 9 9( d ), (e) ), 11 = 3 1 48 EI 1 + X1 = 3 2 48 EI2, 1 P = - 3 I1 2 P I1 2 3 + I2 1 3, M 3 P2 48 EI2 9 7 9 8,,,, 194
9 3 9 10 E I,, q kn/ m 2 () 9 10 P = q 2 9 13 ( b) x, 1, 2, 3, 4, X1 ( ) : 5, 6, X2 11 X1 + 1 2 X2 + 1 P = 0 21 X1 + 2 2 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 = 2 2 2 2 3 2 + 2 + 2 2 2 2 3 2 + 2 2 = 26 3 3 195
EI 2 2 = 2 2 2 3 2 + 2 + 2 2 2 2 2 3 EI 1 2 = 2 2 2 3 2 + 2 3 4 2 = 11 3 3 EI 1 P = - 2 2 2 EI 2 P = - 2 2 2 P 3 2 P 3 2 + 2 P = - 10 3 P3 2 + 2 P = - 3 3 E I 26 X1 + 11 X2-10 P = 0 5 3 P3 2 = 13 3 3 11 X1 + 13 X2-5 P = 0 X1 = 75 P, X2 = 20 217 217 P X1 X2 G H, I J, A B(CD) E F P - X1 = 142 197 P, P - X2 = 217 217 P,, M = m1 X1 + m2 X2 + MP, 9 10 ( f) 9 4, ( 9 11( a) ) ; ( 9 11 ( b) ) ;,, ( 9 11( c) ) 9 11, 9 9 11 (f) 196 11 ( d ), (e ), ( f )
,,,,,,,,,,,,,,,, 9 12,, I = IC [ 1 - ( 1 - n) x 1 ] cos ( 9 5) Ix ; ; IC ; 1 ; 9 12 n, 0.251 (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
9 5 ( 9 13 ( a ) ),, I = ICcos (9 8) 9 13, f < 4, (9 6 ) I = IC cos (9 9 13 ( 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 0 1 1 = y2 EI d s + cos2 EA d s,, 11 1 P 1 P = - ym0 EI d s 198
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) 9 4 9 14 (a),, H I x = IC cosix = IC cos, y = 4 f x( - x), f > 2 5 (9 f > 8 ) 1 1 = y 2 0 5 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 0 9 14 ( b),, 2 M 0 = Px 0 < x 4 M 0 = P 4 1 P = - 0 - H = - 1 P = 1 1 4 < 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 2 128 EIC 8 f 2 15 EIC 2 = 0.278 P f 19 P f 2 128 EIC 9 14, H, f/,, 9 15,,, X1, 11 X1 + 1 P = 0 11 1 P,,, 9 15 199
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) 9 16 11 E1 A1 X1 11 = m2 1 11 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, 9 200 13 = 3 1 = 0 23 = 3 2 = 0 17 ( a ),
12 X1 + 2 1 X2 + 1 P = 0 21 X1 + 2 2 X2 + 2 P = 0 31 X1 + 3 P = 0 ( 9 12) 12 = 21 0, 12 = 21, 12 m1, m2, m1 m2 9 9 17 9 18 18 ( 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 + 0 + 0 = 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
, ( 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 20 9 20,,, 9 21 9 21 9 7, ( 9 15 ), 202
ii = mi 2 X1 X2 X3 EI d s + ni = - 1 P 1 1 = - 2 P 2 2 = - 3 P 3 3 2 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 11 22 33 1 P 2 P 3 P f < 1 5 f > 1 5 30 < h C < 10 h C < hc > h C < 30 10 10 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, 10 5 2 1 1 = 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)
, 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 - 1 + 1 2 Fn ) ( 9 22) 9 22 204
, n 2, 9 n b a 22 ( b ), Fd s = s 3 [ F 0 + 4 ( F1 + F3 + + Fn - 1 ) + 2 ( F2 + F4 + + Fn - 2 ) + Fn ] ( 9 23),,,, 812, 9 5 9 23 (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) : y1 9 2 2) (9 19) ys y1 y1 d x = 9 23 23( b ) 8,x = 4 f x 2 = 4 4 - x 2 = x2 2 12 2 9 = 1.5 3 [ 32.00] 12 = 1.33 m x y1 d x = [ 4.00 + 4 (2.25 + 0.25 + 0.25 + 2.25) + 3 2 ( 1.00 + 0.00 + 1.00) + 4.00] = 1.5 3 9 2 3) : 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
x m y 1 m 1.5 3 [ 34.40] + 0.6 3 1.5 [16.696] = 12 0.6 3 17.20 + 0.25 = 17.45 EIC 33 = x2 d x = 1.5 [288 ] = 144 3 9 2 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) 4-6.0 4.00 2.67-1.333-0.800 0.600 36.00 7.13 0.360-252.0 1 512-673 1 3-4.5 2.25 0.92-1.000-0.707 0.707 20.25 0.85 0.500-141.8 638-130 4 2-3.0 1.00-0.33-0.667-0.555 0.832 9.00 0.11 0.692-63.0 189 21 2 1-1.5 0.25-1.08-0.333-0.316 0.949 2.25 1.17 0.901-15.8 24 17 4 0 0.0 0.00-1.33 0.000 0.000 1.000 0.00 1.77 1.000 0 0 2 1 1.5 0.25-1.08 0.333 0.316 0.949 2.25 1.17 0.901 0 0 4 2 3.0 1.00-0.33 0.667 0.555 0.832 9.00 0.11 0.692 0 0 2 3 4.5 2.25 0.92 1.000 0.707 0.707 20.25 0.85 0.500-75.0-338 - 69 4 4 6.0 4.00 2.67 1.333 0.800 0.600 36.00 7.13 0.360-150.0-900 - 400 1 32.00 288 34.40 16.696-1 458 2 286-1 759 ym P kn f = 1 3 > 1 5, 2 2 0.25/ 17.20 = 1.45%, MP 5) : MP = - 1 2 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 [ - 1 458] = - 729 3 EI C 2 P = 1.5 ymp d x = [ - 1 759 ] = - 879.5 3 1.5 EI C 3 P = xm P d x = 3 X1 X2 = - 1 P = 729 11 12 = - 2 P = 22 (2 ) ( 9 21 ) 206 X3 879.5 17.45 = - 3 P = - 1 143 33 144 [2 286] = 1143 = 60.8 knm = 50.4 knm = - 7.9 knm
M = X1 + X2 y + X3 x + MP = 60.8 + 50.4 y - 7.9 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 ) 9 24 9 3 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 4-6.0 2.67 60.8 134.6 47.4-252.0-9.2 3-4.5 0.92 60.8 46.4 35.6-141.8 1.0 2-3.0-0.33 60.8-16.6 23.7-63.0 4.9 1-1.5-1.08 60.8-54.4 11.9-15.8 2.5 0 0.0-1.33 60.8-67.0 0-6.2 1 1.5-1.08 60.8-54.4-11.9-5.5 207
2 3.0-0.33 60.8-16.6-23.7 20.5 3 4.5 0.92 60.8 46.4-35.6-75.0-3.4 4 6.0 2.67 60.8 134.6-47.4-150.0-2.0 208
9 4 Q N x m sin cos14x Q 50.4-7.9 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 4-6.0-0.800 0.600-84.0-40.3-4.7 50.4 5.4 30.2-6.3 67.2 91.1 3-4.5-0.707 0.707-63.0-35.6-5.6 44.5 3.3 35.6-5.6 44.5 74.5 2-3.0-0.555 0.832-42.0-28.0-6.6 34.9 0.3 41.9-4.4 23.3 60.8 1-1.5-0.316 0.949-21.0-15.9 7.5 19.9-3.5 47.8-2.5 6.6 51.9 0 0 0.000 1.000 0 0-7.9 0-7.9 50.4 0 0 50.4 1 1.5 0.316 0.949 15.9-7.5 8.4 47.8 2.5 50.3 2 3.0 0.555 0.832 28.0-6.6 21.4 41.9 4.4 46.3 2 3.0 0.555 0.832 28.0-6.6-41.6-20.2 41.9 4.4 27.8 74.1 3 4.5 0.707 0.707 35.6-5.6-35.4-5.4 35.6 5.6 35.4 76.6 4 6.0 0.800 0.600 40.3-4.7-30.0 5.6 30.2 6.3 40.0 76.5 * 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 = = 2 2 4 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
3 = - 3 P 3 3 ( 9 24) f > 1 5, ( 9 22 ) EI C 1 1 = d x = EIC 22 = EIC y2 d x = 2 2 4 f 2 45 33 = x2 d x = 2 0 0 ( 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 ( 1 8-2 + 2 2 ) ymp dx = 2 P = 2 EIC 3 P = = - 3 ( 1 24-8 + 3 6 ) (9 - ( 4 f x 2-2 - f 2 ( 1 48-2 6 + 4 3 ) xm P d x = (9 X1 X2 X3 f 3 ) ( x - ) dx = 2 - x( x - ) d x 20) = - 1 P = ( 1 1 1 8-2 + 2 2 ) = - 2 P = 2 2 1 ( 1 + ) f ( 15 = - 3 P = 1 3 3 2-3 2 + 2 3 64-15 2 8 + 15 4 4 ) 9 25 ( 9 25) 25) P = 1 0 0.5, 210 X
, 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 = 4 4 12 2 ( - 3 ) 2 = 1 m ys = f 3 = 1.33 m tan K = y= 8 f x = 2 8 4 12 2 4 ( - 3) 2 = - 0.667 K = - 33 42 sin K = - 0.555 cos K = 0.832 MK = X1-0.333 X2-3 X3 + MKP QK = - 0.555 X2 + 0.832 X3 + QK P N K = - 0.555 X2-0.832 X3 + N KP 9 5, 9 6 9 26 211
9 5 MK P = 1 X1 X2 X3-0.333 X3-3 X3 M 0 K MK 4 0 0 0 0 0 0 0 3 0.094 0.135-0.043-0.045 0.129 0 0.178 2 0.375 0.396-0.156-0.132 0.468 0 0.711 1 0.844 0.618-0.316-0.206 0.948-1.500 0.086 0 1.500 0.703-0.500-0.234 1.500-3.000-0.234 0 1.500 0.703 0.500-0.234-1.500 0-0.234 1 0.844 0.618 0.316-0.206-0.948 0-0.310 2 0.375 0.396 0.156-0.132-0.468 0-0.225 3 0.094 0.135 0.043-0.045-0.129 0-0.080 4 0 0 0 0 0 0 0 9 6 QK N K P = 1-0.555 X 2 0.832 X 3 Q 0 K Q K 0.832 X 2 0.555 X 3 N 0 K N K 4 0 0 0 0 0 0 0 0 3-0.075-0.036 0-0.111 0.112-0.024 0 0.088 2-0.220-0.130 0-0.350 0.330-0.087 0 0.243 2-0.220-0.130 0.832 0.482 0.330-0.087 0.555 0.798 1-0.343-0.263 0.832 0.226 0.515-0.175 0.555 0.895 0-0.390-0.416 0.832 0.026 0.585-0.278 0.555 0.862 0-0.390-0.416 0 0.026 0.585 0.278 0 0.862 1-0.343 0.263 0-0.080 0.515 0.175 0 0.690 2-0.220 0.130 0-0.090 0.330 0.087 0 0.417 3-0.075 0.036 0-0.039 0.112 0.024 0 0.136 4 0 0 0 0 0 0 0 0 212
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 X1 + 2.67 X2-6 X3 + MP 27( d ), (e), (f) 9 9 27 7, 213
9 7 H, V A, MA P = 1 H = X2 X3 V AP V A X1 2.67 X2-6 X3 M 0 A MA 4 0 0 1.000 1.000 0 0 0 0 0 3 0.135-0.043 1.000 0.957 0.094 0.360 0.258-1.500-0.788 2 0.326-0.156 1.000 1.844 0.375 1.056 0.936-3.000-0.633 1 0.618 0.316 1.000 0.684 0.844 1.648 1.896-4.500-0.112 0 0.703-0.050 1.000 0.500 1.500 1.875 3.000-6.000 0.375 0 0.703 0.500 0 0.500 1.500 1.875-3.000 0 0.375 1 0.618 0.316 0 0.316 0.844 1.648-1.896 0 0.596 2 0.396 0.156 0 0.156 0.375 1.056-0.936 0 0.495 3 0.135 0.043 0 0.043 0.004 0.360-0.258 0 0.196 4 0 0 0 0 0 0 0 0 0 214
9 9,,, ( ) t2,, 1 1 X1 + 1 t = 0 2 2 X1 + 2 t = 0 3 3 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
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 0.000 01, = - 0.000 25, 25,,,, 1015 9 10, 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 - 2 216
X1 = - X 2 = - X 3 = - 1 11 2 22 3 33 = - 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),, 9 29 9 1 9 1 E I = 217
(1 ) MB : ; 4,, (2 ) MK, ( :, M = m1 X1 + MP M K = mk1 MB + MK P, mk1 = 1/ 2, MB (1 ), MK P ) 9 1 9 2 9 2 9 2 RB, MA, MC, MK, QK, QB, QB 9 3 9 3 q= 10 kn/ m, p = 20 kn/ m, E I = 9 3 * 9 49 5, E I, P, 9 4 9 5 9 6 y = 4 f 2 x( - x), Ix = IC cos, E IC = 5 000 knm2, E1 A1 = 210 5 kn, K 9 7 H, 0 = 2 9 8 y1 = 4 f 2 x 2, A = AC cos, I = m, f = 3 m, hc 218 IC cos, = 18 = 0.6 m,,,