第六章 弯曲变形

1、 ()Chapter6 Deflection of BeamsMechanics of Materials () () () () () 2FF2F () w挠度挠度CCAB w xB ()转角转角 ACCwB xw挠度（挠度（B ()挠曲线挠曲线wAB x转角转角 w挠度（挠度（CCB( )wf x ()wAB x转角转角 w挠度挠度CCB挠曲线挠曲线( )tgww x () wAB x转角转角 w挠度挠度CCB挠曲线挠曲线 ()1MEI 1( )( )M xxEI ()3221|( )(1)wxw 322|( )(1)wM xEIw ()OxwxOw00 wM wM00Mw 00 wM 0

2、0Mw MMMM () 2 2w322( )(1)wM xEIw( )M xwEI2w( )tgww x ()( )M xwEI ( )EIwM x () 1( )EIwM x dxC 12( )EIwM x dxdxC xC ()ABAwBwAwA 0Aw0Bw0Aw0A AB () lABxFmaxwmax ()xlwABxF( )() (1)M xF lx ( ) (2)EIwM xFlFx 21 (3)2FxEIwFlxC 2312(4)26FlxFxEIwxCC ()21 (3)2FxEIwFlxC 2312(4)26FlxFxEIwxCC 0,0 0,0 xwxw120 0CC22

3、FxEIwFlx 2326FlxFxEIw ()BwmaxmaxxlyAF（ ）222max|22x lFlFlFlEIEIEI max maxw（ ）3max|3x lPlwwEI ()max maxwABq ()2ABqlRRABqRARBx2( )22qlqM xxx2346qlqEIwxxC 222qlqEIwxx 341224qlqEIwxxCxD ()233(64)24qlxxlEI 233(2)24qxwlxxlEIxl0w xABqRARB A B3max24ABqlEI wmax4max25384lxqlwwEI ()ABFDab ()AbRFlBaRFlRARBABFDab

4、12xx1(0)AbMR xFxxal2() ()bMFxF xaaxll ()111bFxEIwMl2112bxEIwFCl 31116b xEIwFC xDl ()22()bFxF xaEIwMl 2222()22bF xaxFEIwCl33222()66bF xaxFxEIwCDl2 ()12ww12ww10w 20w 120DD2212()6FbCClbl ABFDabl12RARB ()1(0)xa22211()36FbwlbxlEI 22216FbxlwbxlEI2()axl2222221()()23FblxawxlblEI b 33222() ()6FblxxawxlblEI b

5、 ()10()|6AxPab lblEI 2()|6Bx lPab lalEImax()6BPab lalEI ()0w 10w22211()036FbwlbxlEI 221(2 )33lba abx1222 3max()0 06429 3x xFbPblw |lb.wEIlEI ()222(34)0.062548CFbFblwlbEIEI1222 3max()0 06429 3x xFbFbly |lb.wEIlEI () () ()121122(,)()()()nnnF FFFFF121122(,)()()()nnnw F FFw FwFwF ()BqFACaaF=AB+ABq24PAFa

6、EI 36PCFawEI 4524qCqawEI 33qAqaEI () 24PAFaEI 36PCFawEI 33qAqaEI 4524qCqawEI APAqA2(34)12aFqaEI 435()246CqaFawEIEI qFF=+AAABBBCaaq ()ABC ()ABCq(a)BAm(c)Aq(b)BBq Aq CqwBm Am CmwCCCqCmwwwAAqAm42538416qlmlEIEI( )( )3()243mlqlEIEI BBqBm( )3246mlqlEIEI ()ABCql/2ABCq/2CABq/2q/2 ()ABCq/24415(2)5384768Cqlql

7、wEIEI 3311(2)2448BAqlqlEIEI CABq/2q/2 ()CABq/2q/2Bq/2ACq/23322( )( )2224384ABqlqlEIEI 20Cw4125768CCCqlwwwEI ( )33312348384128AAAqlqlqlEIEIEI ( )33312748384384BBBqlqlqlEIEIEI ( ) ()ABCDaa2a2qq ()ABCDaa2a2qqBCDq2qa2BqaM2qAB2qa2BqaM2BMqa2qa ()2qaBCDq2BqaMqBCDBCD2BqaM ()wDqBqDBC33MBBBqBqaEI 424BDDqDMqaw

8、wwEI 2qaBCDq2BqaMBBM BDMwDBC2BqaM33243BqqlqaEIEI 3233BBBMlqaMEIEI 445538424DqqlqawEIEI42164BBDMqalMwEIEI ()2wAB1wA2qB2qa2BqaM2qaBBCDq2BqaM122BAwwwaw 22(2 )8qawEI44473412AqaqaqawEIEIEI ()maxmax ww w ()L=400mmF2=2kNACa=0.1m200mmDF1=1kNBF2BCDA=+F2BCaF2BCDAM=+F1=1kNADCF2=2kNCABB ()L=400mmF2=2kNACa=0.1m2

9、00mmDF1=1kNB21116BF LEI 211116CBF L awaEI 20B 3223CF awEI 2333BMLLaFEIEI 22333CBF LawaEI F2BC=+图图1 1图图2 2图图3 3F1=1kNDCF2BCDAM ()212163BP LF LaEIEI 2321221633CF L aF aF a LwEIEIEI 44441284()643.14 (8040 ) 1064 188 10 mIDd F2=2kN=+图图1 1图图2 2L=400mmACa=0.1m200mmDF1=1kNBF1=1kNDBC图图3 3F2BDAMACCF2 ()23261

10、225.19 10 m1633CP L aF aF a LwEIEIEI 212-40.4400200()163210 1880163 +0.423 10BF LF LaEIEI maxwwLL 65max5.19 10 m10 mww 4max0.423 100.001 ()FABABCFRARBRC ()RBABCFFABRARC ()ABql0BwqABRBBBBqBRwww0BBqBRww () BqwBBRwqAB48BqqlwEI 33BBBRlRwEI BARBqABRB ()43083BqllREIEI38BqlRqABqABBABqwBBRwRBRBRAmA58AqlR218

11、Aqlm ()0A ABqlABqlmA ()a2aABCq2qDl ()CADBq2qANNADBCq2qwANNlA1Awl ()BCq2qNAwAAqANwwwAqANwwl BCq2qAqwBCNANwEIqawAq1274EINawAN3 ()EAlFlN EAlFEIaFEIqaNN34127)(12734AaIlAqaNADBCq2qNNlA1Aw ()4m3m2mABDC30kN20kN/m ()4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/mMBB B BB ()EIMEIB34244203B )34241280(EIMEIBEIMEIBB3556)25(2330 EIMEIB35424m3m2mABDC30kN20kN/mDAB30kN20kN/mMBB B C ()EIMEIEIMEIBB35423424128