材料力學第六章 彎曲變形

1、 2FF2Fw撓度撓度CCAB w xB轉角轉角 ACCwB xw撓度（撓度（B撓曲線撓曲線wAB x轉角轉角 w撓度（撓度（CCB( )wf xwAB x轉角轉角 w撓度撓度CCB撓曲線撓曲線tan( )ww x wAB x轉角轉角 w撓度撓度CCB撓曲線撓曲線1MEI 1( )( )M xxEI 3221|( )(1)wxw 322|( )(1)wM xEIwOxwxOw00 wM wM00Mw 00 wM 00Mw MMMM 322( )(1)wM xEIw( )M xwEI2wtan( )ww x2w ( )M xwEI ( )EIwM x 1( )dEIwM xxC 12( )d d

2、EIwM xx xC xC ABAwBwAwA 0Aw0Bw0Aw0A ABlABxFmaxwmax 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 maxwABqRR2ABqlFF

3、ABqFRAFRBx2( )22qlqM xxx2346qlqEIwxxC 222qlqEIwxx 341224qlqEIwxxCxD233(64)24qlxxlEI 233(2)24qxwlxxlEI 0w xABqFRAFRB A B3max24ABqlEI wmax4max25384lxqlwwEI ABFDabRAbFFlRBaFFlFRAFRBABFDab12xx1R(0)AbMFxFxxal2() ()bMFxF xaaxll11bFxEIwMl2112bxEIwFCl 31116b xEIwFC xDl22()bFxF xaEIwMl 2222()22bF xaxFEIwCl33

4、222()66bF xaxFxEIwCDl12ww12ww10w 20w 120DD2212()6FbCClbl ABFDabl12FRAFRB22211()36FbwlbxlEI 22216FbxlwbxlEI2222221()()23FblxawxlblEI b 33222() ()6FblxxawxlblEI b 10()|6AxFab lblEI 2()|6Bx lFab lalEImax()6BFab lalEI0w 10w22211()036FbwlbxlEI 221(2 )33lba abx1222 3max()0 06429 3x xFbPblw |lb.wEIlEI 222(

5、34)0.062548CFbFblwlbEIEI1222 3max()0 06429 3x xFbFbly |lb.wEIlEI 121122(,)()()()nnnF FFFFF121122(,)()()()nnnw F FFw FwFwFBqFACaaF=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=+AAABBBCaaqABCAB

6、Cq(a)BAMe(c)Aq(b)B)(qA )(qB ()Cqwe()BM e()MA e()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( )333123

7、48384128AAAqlqlqlEIEIEI ( )33312748384384BBBqlqlqlEIEIEI ( )ABCDaa2a2qqABCDaa2a2qqBCDq2qa2BMqa2qAB2qa2BMqa2BMqa2qa2qaBCDq2BMqaqBCDBCD2BMqa()Dqw()B q DBC 3)()(3BBqBMBqaEI 4()()24BDD qDMqawwwEI2qaBCDq2BMqa()BBM ()BD MwDBC2BMqa33)(243qBqlqaEIEI 32()33BBBMM lqaEIEI 4455()38424D qqlqawEIEI 42()164BBDMMqa

8、lwEIEI2wA2qB2qa2BMqaAB1wBC2qaBDq2BMqa122BAwwwaw 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圖圖2圖圖3+F2BCDAM

9、=圖圖1F1=1kNDC 212163BF lF laEIEI 2321221633CF l aF aF a lwEIEIEI44441284()643.14 (8040 ) 1064 188 10 mIDd F2=2kN=+圖圖1圖圖2l=400mmACa=0.1m200mmDF1=1kNBF1=1kNDBC圖圖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

10、.423 100.001FABABCFFRAFRBFRCFRBABCFFABFRAFRCABql0BwqABFRBR()()BBB qBFwwwR()()0BB qBFww ()B qwR()BBFwqAB 4()8B qqlwEI R3R()3BBBFFlwEIBAFRBqABFRB43R083BFlqlEIEIR38BFqlqABFRBFRAMAR58BFql218AMql()B qwR()BBFwqABBAFRB0A ABqlABqlMAa2aABCq2qDlCADBq2qAFNFNAwl ADBCq2qAwFNFNlBCq2qFNAwN()()AA qA FwwwN()()A qA F

11、wwl BCq2q()Aqw47()12A qqawEI N3N()AFF awEI CFNBN()AFwNF llEA 43NN712F aF lqaEIEIEA4N3712()AqaFIlAa ADBCq2qFNFNlA1Aw4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/m4m3m2mABDC30kN20kN/mMBB B BB 3420 4243BBMEIEI 12804()243BMEIEI 3032(52)5653BBMEIEI 4253BMEIEI4m3m2mABDC30kN20kN/mDAB30kN20kN/mMBB B C128044252433BBMME