材料力學(xué)第五版劉鴻文 第六章 彎曲變形

1、 Company Logo Company Logo Company Logo Company Logo 2 F F 2 F Company Logo w撓度撓度 C C A B w x B Company Logo 轉(zhuǎn)角轉(zhuǎn)角 A C C w B x w撓度（撓度（ B Company Logo 撓曲線(xiàn)撓曲線(xiàn) w A B x 轉(zhuǎn)角轉(zhuǎn)角 w撓度（撓度（ C C B ( )wf x Company Logo w AB x 轉(zhuǎn)角轉(zhuǎn)角 w撓度撓度 C C B 撓曲線(xiàn)撓曲線(xiàn) tan( )ww x Company Logo w A B x 轉(zhuǎn)角轉(zhuǎn)角 w撓度撓度 C C B 撓曲線(xiàn)撓曲線(xiàn) Company L

2、ogo 1M EI 1( ) ( ) M x xEI Company Logo 3 2 2 1| ( ) (1) w x w 3 2 2 |( ) (1) wM x EI w Company Logo O x w x O w 00 wM w M 0 0 M w 00 wM 0 0 M w M M MM Company Logo 3 2 2 ( ) (1) wM x EI w ( ) M x w EI 2 w tan( )ww x 2 w Company Logo ( )M x w EI ( )EIwM x Company Logo 1 ( )dEIwM xxC 12 ( )d dEIwM xx

3、 xC xC Company Logo A B A w B w A w A 0 A w0 B w 0 A w 0 A AB Company Logo l ABx F max w max Company Logo x l w ABx F ( )() (1)M xF lx ( ) (2)EIwM xFlFx 2 1 (3) 2 Fx EIwFlxC 23 12 (4) 26 FlxFx EIwx CC Company Logo 2 1 (3) 2 Fx EIwFlxC 23 12 (4) 26 FlxFx EIwx CC 0,0 0,0 xw xw 12 0 0CC 2 2 Fx EIwFlx 2

4、3 26 FlxFx EIw Company Logo B wmax max x l y A F （ ） 222 max | 22 x l FlFlFl EIEIEI max max w （ ） 3 max | 3 x l Pl ww EI Company Logo max max w A B q Company Logo RR 2 AB ql FF AB q FRAFRB x 2 ( ) 22 qlq M xxx 23 46 qlq EIwxxC 2 22 qlq EIwxx 34 1224 qlq EIwxxCxD Company Logo 233 (64) 24 q lxxl EI 23

5、3 (2) 24 qx wlxxl EI 0w x AB q FRAFRB A B 3 max 24 AB ql EI wmax 4 max 2 5 384 l x ql ww EI Company Logo A B F D a b Company Logo RA b FF l RB a FF l FRA FRB A B F D ab 12 x x 1R (0) A b MFxFxxa l 2 () () b MFxF xaaxl l Company Logo 11 b Fx EIwM l 2 11 2 bx EIwFC l 3 111 6 b x EIwFC xD l Company Log

6、o 22 () b FxF xa EIwM l 2 2 22 () 22 bF xa x F EIwC l 3 3 222 () 66 bF xa x Fx EIwCD l Company Logo 12 ww 12 ww 1 0w 2 0w 12 0 DD 22 12 () 6 Fb CClb l AB F D ab l 12 FRA FRB Company Logo 222 11 () 3 6 Fb wlbx lEI 2 22 1 6 Fbx lwbx lEI 2 222 22 1 ()() 23 Fbl xa wxlb lEI b 3 322 2 () () 6 Fbl xxa wxlb

7、 lEI b Company Logo 10 () | 6 Ax Fab lb lEI 2 () | 6 Bx l Fab la lEI max () 6 B Fab la lEI Company Logo 0w 1 0w 222 11 ()0 3 6 Fb wlbx lEI 22 1 (2 ) 33 lba ab x 1 2 22 3 max ()0 0642 9 3 x x FbPbl w |lb. w EIlEI Company Logo 2 22 (34)0.0625 48 C FbFbl wlb EIEI 1 2 22 3 max ()0 0642 9 3 x x FbFbl y |

8、lb. w EIlEI Company Logo Company Logo Company Logo 121122 (,)()()() nnn F FFFFF 121122 (,)()()() nnn w F FFw FwFwF Company Logo B qF A C aa F = A B + AB q 2 () 4 A F Fa EI 3 () 6 CF Fa w EI 4 5 () 24 Cq qa w EI 3 () 3 A q qa EI Company Logo 2 () 4 A F Fa EI 3 () 6 CF Fa w EI 3 () 3 A F qa EI 4 5 ()

9、24 CF qa w EI ()() AA FA q 2 (34) 12 a Fqa EI 43 5 () 246 C qaFa w EIEI qF F =+ A A A B B B C aa q Company Logo AB C Company Logo A B C q (a) BA Me (c) A q (b) B )( qA )( qB () Cq w e () BM e () M A e () CM w C e ()( CC qMC w ww e )( A qMAA 2 4 e 5 38416 M lql EIEI ( ) ( ) 3 e () 243 M lql EIEI e )(

10、 B qMBB ( ) 3 e 246 M lql EIEI Company Logo A B C q l/2 A B C q/2 C A B q/2 q/2 Company Logo A B C q/2 44 1 5(2)5 384768 C qlql w EIEI 33 11 (2) 2448 BA qlql EIEI C A B q/2 q/2 Company Logo C AB q/2 q/2 B q/2 A C q/2 3 3 22 ( )( ) 22 24384 AB ql ql EIEI 2 0 C w 4 12 5 768 CCC ql www EI ( ) 333 12 3

11、48384128 AAA qlqlql EIEIEI ( ) 333 12 7 48384384 BBB qlqlql EIEIEI ( ) Company Logo A B C D a a 2a 2q q Company Logo A B C D a a 2a 2q q B C D q 2qa 2 B Mqa 2q A B 2qa 2 B Mqa 2 B Mqa 2qa Company Logo 2qa B C D q 2 B Mqa q B C D B C D 2 B Mqa Company Logo () Dq w() B q D B C 3 )()( 3 B B qBMB qa EI

12、4 ()() 24 B DD qDM qa www EI 2qa B C D q 2 B Mqa () B BM () B D M w D B C 2 B Mqa 33 )( 243 qB qlqa EIEI 3 2 () 33 B B BM M lqa EIEI 44 55 () 38424 D q qlqa w EIEI 4 2 () 164 B B DM Mqa l w EIEI Company Logo 2 w A 2q B 2qa 2 B Mqa A B 1 w B C 2qa B D q 2 B Mqa 122 B A wwwaw 2 2 (2 ) 8 q a w EI 444 7

13、 3412 A qaqaqa w EIEIEI Company Logo max max ww w Company Logo l=400mm F2=2kN A C a=0.1m 200mm D F1=1kN B F2 B C D A = + F2 B C a F2 B C D A M = + F1=1kN ADC F2=2kN C A B B Company Logo l=400mm F2=2kN A C a=0.1m 200mm D F1=1kN B 2 1 1 16 B F l EI 2 1 11 16 CB F l a wa EI 2 0 B 3 2 2 3 C F a w EI 2 3

14、 33 B MllaF EIEI 2 2 33 3 CB F la wa EI + F2 B C 圖圖2 圖圖3 + F2 B CDA M = 圖圖1 F1=1kN DC Company Logo 2 12 163 B F lF la EIEI 232 122 1633 C F l aF aF a l w EIEIEI 44 4412 84 () 64 3.14 (8040 ) 10 64 188 10 m IDd F2=2kN =+ 圖圖1 圖圖2 l=400mm A C a=0.1m 200mm D F1=1kN B F1=1kN D B C 圖圖3 F2 B DA M AC C F2 C

15、ompany Logo 232 6 122 5.19 10 m 1633 C F l aF aF a l w EIEIEI 2 12 -4 0.4400200 () 163210 1880163 +0.423 10 B F lF la EIEI max ww ll 65 max 5.19 10 m10 mww 4 max 0.423 100.001 Company Logo F AB AB C F FRAFRB FRC Company Logo FRB AB C F F AB FRAFRC Company Logo A B q l 0 B w q A B FRB R ()() B BB qBF

16、 www R ()()0 B B qBF ww Company Logo () B q w R () B BF w q AB 4 () 8 B q ql w EI R 3 R () 3 B B BF F l w EI B A FRB q A B FRB Company Logo 43 R 0 83 B Flql EIEI R 3 8 B Fql q A B FRB FRA MA R 5 8 B Fql 2 1 8 A Mql () B q w R () B BF w q AB B A FRB Company Logo 0 A A B q l A B q l MA Company Logo a2

17、a A B C q 2q D l Company Logo C A D B q 2q A FN FN A wl A D B C q 2q A w FN FN l Company Logo B C q 2q FN A w N ()() AA qA F www N ()() A qA F wwl B C q 2q () Aq w 4 7 () 12 A q qa w EI N 3 N () AF F a w EI C FN B N () AF w Company Logo N F l l EA 43 NN 7 12 F aF lqa EIEIEA 4 N 3 7 12() Aqa F Il Aa

18、A D B C q 2q FN FN l A1 A w Company Logo 4m3m2m A B D C 30kN 20kN/m Company Logo 4m3m2m A B D C 30kN 20kN/m 4m3m2m A B D C 30kN 20kN/m MB B B BB Company Logo 3 4 20 4 243 B B M EIEI 12804 () 243 B M EIEI 3032(52)5 653 B B M EIEI 425 3 B M EIEI 4m3m2m A B D C 30kN 20kN/m D A B 30kN 20kN/m MB B B C Company Logo 12804425 2433