第六章弯曲变形01

1、 2FF2F OB xC挠曲线挠曲线wB)(xwCCw挠度挠度AB w xB转角转角 ACCwB xw挠度（挠度（BwAB x转角转角 w挠度挠度CCB挠曲线挠曲线tan( )ww x 1MEI 1( )( )M xxEI 232)1 ()(1wwx EIxMww)()1 (232 OxwxOw00 wMwM00Mw 00 wM 00Mw MMMM 322( )(1)wM xEIw( )M xwEI2w2w ( )M xwEI ( )EIwM x 1( )dEIwM xxC 12( )d dEIwM xx xC xC ABAwBwAwA 0Aw0Bw0Aw0A ABlABxFmaxwmax x

2、lwABxF( )() (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 maxwABqRR2ABqlFFABqFRAFRBx2( )22qlqM xxx2346qlqEIwxxC 222qlqEIwxx 34

3、1224qlqEIwxxCxD233(64)24qlxxlEI 233(2)24qxwlxxlEI 0w xABqFRAFRB A B3max24ABqlEI wmax4max25384lxqlwwEI ABFDabRAbFFlRBaFFlFRAFRBABFDab12xx1R(0)AbMFxFxxal2() ()bMFxF xaaxll11bFxEIwMl2112bxEIwFCl 31116b xEIwFC xDl22()bFxF xaEIwMl 2222()22bF xaxFEIwCl33222()66bF xaxFxEIwCDl12ww12ww10w 20w 120DD2212()6FbC

4、Clbl ABFDabl12FRAFRB22211()36FbwlbxlEI 22216FbxlwbxlEI2222221()()23FblxawxlblEI b 33222() ()6FblxxawxlblEI b 10()|6AxFab lblEI 2()|6Bx lFab lalEI max()6BFab lalEI 0w 10w22211()036FbwlbxlEI 221(2 )33lba abx1222 3max()0 06429 3x xFbPblw |lb.wEIlEI 222(34)0.062548CFbFblwlbEIEI1222 3max()0 06429 3x xFbF

5、bly |lb.wEIlEI 121122(,)()()()nnnF FFFFF 121122(,)()()()nnnw F FFw Fw FwFBqFACaaF=AB+ABq 2()4A FFaEI 3()6CFFawEI 45()24CqqawEI 3()3A qqaEI 2()4A FFaEI 3()6CFFawEI 3()3A FqaEI 45()24CFqawEI()()AA FA q2(34)12aFqaEI 435()246CqaFawEIEI qFF=+AAABBBCaaqABCABCq(a)BAMe(c)Aq(b)B)(qA )(qB ()Cqwe()BM e()MA e()

6、CMwCe()(CCqMCwwwe)(AqMAA24e538416M lqlEIEI( )( )3e()243M lqlEIEI e)(BqMBB( )3e246M lqlEIEI ABCql/2ABCq/2CABq/2q/2ABCq/24415(2)5384768CqlqlwEIEI 3311(2)2448BAqlqlEIEI CABq/2q/2CABq/2q/2Bq/2ACq/23322( )( )2224384ABqlqlEIEI 20Cw 4125768CCCqlwwwEI( )33312348384128AAAqlqlqlEIEIEI ( )33312748384384BBBqlql

7、qlEIEIEI ( )ABCDaa2a2qqABCDaa2a2qqBCDq2qa2BMqa2qAB2qa2BMqa2BMqa2qa2qaBCDq2BMqaqBCDBCD2BMqa()Dqw()B q DBC 3)()(3BBqBMBqaEI 4()()24BDD qDMqawwwEI2qaBCDq2BMqa()BBM ()BD MwDBC2BMqa33)(243qBqlqaEIEI 32()33BBBMM lqaEIEI 4455()38424D qqlqawEIEI 42()164BBDMMqalwEIEI2wA2qB2qa2BMqaAB1wBC2qaBDq2BMqa122BAwwwaw

8、22(2 )8qawEI44473412AqaqaqawEIEIEImaxmax ww w l=400mmF2=2kNACa=0.1m200mmDF1=1kNBF2BCDA=+F2BCaF2BCDAM=+F1=1kNADCF2=2kNCABBl=400mmF2=2kNACa=0.1m200mmDF1=1kNB 21116BF lEI 211116CBF l awaEI 20B 3223CF awEI 2333BMllaFEIEI 22333CBF lawaEI +F2BC图图2图图3+F2BCDAM=图图1F1=1kNDC 212163BF lF laEIEI 2321221633CF l a

9、F aF a lwEIEIEI44441284()643.14 (8040 ) 1064 188 10 mIDd F2=2kN=+图图1图图2l=400mmACa=0.1m200mmDF1=1kNBF1=1kNDBC图图3F2BDAMACCF2 23261225.19 10 m1633CF 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 FABABCFFRAFRBFRCFRBABCFFABFRAFRCABq

10、l0BwqABFRBR()()BBB qB FwwwR()()0BB qBFww ()B qwR()BBFwqAB 4()8BqqlwEI R3R()3BBBFFlwEIBAFRBqABFRB43R083BFlqlEIEIR38BFqlqABFRBFRAMAR58BFql218AMql()B qwR()BBFwqABBAFRB0A ABqlABqlMAa2aABCq2qDlCADBq2qAFNFNAwl ADBCq2qAwFNFNlBCq2qFNAwN()()AA qA FwwwN()()A qA Fwwl BCq2q()Aqw47()12A qqawEI N3N()AFF awEI CFNBN()AFwNF llEA 43NN712F aF lqaEIEIEA 4N3712()AqaFIlAa ADBCq2qFNFNlA1Aw4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/mMBB B BB 3420 4243BBMEIEI 12804243BMEIEI30 3 2(52)5653BBMEIEI 4253BMEIEI 4m3m2mABDC30kN20kN/mDAB30kN20kN/mMBB B C128044252433BBMMEIEI