材料力学第六章弯曲时的变形

1、 ()AB 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 xwAB 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 xEIwOxwxOw00 wMwM00Mw 00 wM 00Mw MMMM 2v322( )(1)wM xEIw( )M xwEI2w( )tgww x ( )M xwEI ( )EIwM x 1( )EIwM x dxC 12(

2、)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 0CC22FxEIwFlx 2326FlxFxEIw BwmaxmaxxlyAF（ ）222max|22x lFlFlFlEIEIEI max maxw（ ）3max|3x lPlwwEI max maxwABq2ABql

3、RRABqRARBx2( )22qlqM xxx2346qlqEIwxxC 222qlqEIwxx 341224qlqEIwxxCxD233(64)24qlxxlEI 233(2)24qxwlxxlEIxl0w xABqRARB A B3max24ABqlEI wmax4max25384lxqlwwEI ABFDabAbRFlBaRFlRARBABFDab12xx1(0)AbMR xFxxal2() ()bMFxF xaaxll111bFxEIwMl212bxEIwFCl 31116b xEIwFC xDl22()bFxF xaEIwMl 2222()22bF xaxFEIwCl33222()

4、66bF xaxFxEIwCDl212ww12ww10w 20w 120DD2212()6FbCClbl ABFDabl12RARB1(0)xa22211()36FbwlbxlEI 22216FbxlwbxlEI2()axl2222221()()23FblxawxlblEI b 33222() ()6FblxxawxlblEI b 10()|6AxPab lblEI 2()|6Bx lPab lalEImax()6BPab lalEI0w 10w22211()036FbwlbxlEI 221(2 )33lba abx1222 3max()0 06429 3x xFbPblw |lb.wEIlE

5、I 222(34)0.062548CFbFblwlbEIEI1222 3max()0 06429 3x xFbFbly |lb.wEIlEI 121122(,)()()()nnnF FFFFF 121122(,)()()()nnnw F FFw Fw FwFBqFACaaF=AB+ABq24PAFaEI 36PCFawEI 4524qCqawEI 33qAqaEI 24PAFaEI 36PCFawEI 33qAqaEI 4524qCqawEI APAqA 2(34)12aFqaEI 435()246CqaFawEIEI qFF=+AAABBBCaaqABCABCq(a)BAm(c)Aq(b)B

6、Bq Aq CqwBm Am CmwCCCqCmwwwAAqAm42538416qlmlEIEI( )( )3()243mlqlEIEI BBqBm( )3246mlqlEIEI ABCql/2ABCq/2CABq/2q/2ABCq/24415(2)5384768CqlqlwEIEI 3311(2)2448BAqlqlEIEI CABq/2q/2CABq/2q/2Bq/2ACq/23322( )( )2224384ABqlqlEIEI 20Cw4125768CCCqlwwwEI ( )33312348384128AAAqlqlqlEIEIEI ( )33312748384384BBBqlqlq

7、lEIEIEI ( )ABCDaa2a2qqABCDaa2a2qqBCDq2qa2BqaM2qAB2qa2BqaM2BMqa2qa2qaBCDq2BqaMqBCDBCD2BqaMwDqBqDBC33MBBBqBqaEI 424BDDqDMqawwwEI 2qaBCDq2BqaMBBM BDMwDBC2BqaM33243BqqlqaEIEI 3233BBBMlqaMEIEI 445538424DqqlqawEIEI42164BBDMqalMwEIEI 2wAB1wA2qB2qa2BqaM2qaBBCDq2BqaM122BAwwwaw 22(2 )8qawEI44473412AqaqaqawEIE

8、IEImaxmax ww w L=400mmF2=2kNACa=0.1m200mmDF1=1kNBF2BCDA=+F2BCaF2BCDAM=+F1=1kNADCF2=2kNCABBL=400mmF2=2kNACa=0.1m200mmDF1=1kNB21116BF LEI 211116CBF L awaEI 20B 3223CF awEI 2333BMLLaFEIEI 22333CBF LawaEI F2BC=+图图1 1图图2 2图图3 3F1=1kNDCF2BCDAM212163BP LF LaEIEI 2321221633CF L aF aF a LwEIEIEI 44441284()64

9、3.14 (8040 ) 1064 188 10 mIDd F2=2kN=+图图1 1图图2 2L=400mmACa=0.1m200mmDF1=1kNBF1=1kNDBC图图3 3F2BDAMACCF223261225.19 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 FABABCFRARBRCRBABCFFABRARCABql0BwqABRBBBBqBRwww0BBqBRww B

10、qwBBRwqAB48BqqlwEI 33BBBRlRwEI BARBqABRB43083BqllREIEI38BqlRqABqABBABqwBBRwRBRBRAmA58AqlR218Aqlm0A ABqlABqlmAa2aABCq2qDlCADBq2qANNADBCq2qwANNlA1Awl BCq2qNAwAAqANwwwAqANwwl BCq2qAqwBCNANwEIqawAq1274EINawAN3EAlFlN EAlFEIaFEIqaNN34127)(12734AaIlAqaNADBCq2qNNlA1Aw4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/mMBB B BB EIMEIB34244203B )34241280(EIMEIBEIMEIBB3556)25(2330 EIMEIB35424m3m2mABDC30kN20kN/mDAB30kN20kN/mMBB B CEIMEIEIMEIBB35423424128