材料力学第六章 弯曲变形2013

1、 ()*szzF SI bu Sz*zyy AzyAAySd注意注意：Fs为横截面的剪力；为横截面的剪力；Iz 为整个横截为整个横截面对面对 z 轴的惯性矩；轴的惯性矩；b为所求点对应位置为所求点对应位置截面的宽度；截面的宽度； 为所求点对应位置以外为所求点对应位置以外的面积对的面积对Z轴的静矩。轴的静矩。*zS ()max31.52sFAbISFzzs maxsF(1)(1) 沿截面高度按二次抛物线规律变化；沿截面高度按二次抛物线规律变化；(2) 同一横截面上的最大切应力同一横截面上的最大切应力 max在中性轴处在中性轴处( y=0 )；(3)上下边缘处上下边缘处（y=h/2)，切应力为零切

2、应力为零。 ()ydzokokAFbISFzzS*Smax34 42dA 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 ()1MEI 1( )( )M xxEI ()3221|( )(1)wxw 322|( )(1)wM xEIw)(1x2223/2ddd1dwx

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5、EIxl0w xABqRARB A B3max24ABqlEI wmax4max25384lxqlwwEI 0 x0w ()ABFDab ()AbRFlBaRFlRARBABFDab12xx1(0)AbMR xFxxal2() ()bMFxF xaaxll ()111bFxEIwMl2112b xEIwFCl 31116b xEIwFC xDl ()22()bFxF xaEIwMl 2222()22bF xaxFEIwCl33222()66bF xaxFxEIwCDl2 ()12ww12ww10w 20w 120DD2212()6FbCClbl ABFDabl12RARB ()1(0)xa22

6、211()36FbwlbxlEI 22216FbxlwbxlEI2()axl2222221()()23FblxawxlblEI b 33222() ()6FblxxawxlblEI b ()10()|6AxPab lblEI 2()|6Bx lPab lalEImax()6BPab lalEI ()0w 10w22211()036FbwlbxlEI 221(2 )33lba abx 122 3max()9 3x xFbw |lbwlEI ()222(34)0.062548CFbFblwlbEIEI1222 3max()0 06429 3x xFbFbly |lb.wEIlEI ()作业作业：

7、6.1, 6.4(d) () 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 ()( )M xwEI () ()l l ()BqFACaaF=AB+ABq24PAFaEI 36PCFawEI 4524qCqawEI 33qAqaEI () 24PAFaEI 36PCFawEI 33qAqaEI 4524qCqawEI APAqA2(34)12aFqaEI 435()246CqaFawEIEI qFF=+AAABBBCaaq

8、()ABC ()ABCq(a)BAm(c)Aq(b)BBq Aq CqwBm Am CmwCCCqCmwwwAAqAm42538416qlmlEIEI( )( )3()243mlqlEIEI BBqBm( )3246mlqlEIEI ()ABCDaa2a2qq ()ABCDaa2a2qqBCDq2qa2BqaM2qAB2qa2BqaM2BMqa2qa ()2qaBCDq2BqaMqBCDBCD2BqaM ()wDqBqDBC33MBBBqBqaEI424BDDqDMqawwwEI2qaBCDq2BqaMBBM BDMwDBC2BqaM33-243BqqlqaEIEI 3233BBBMlqaMEIEI 4455-38424DqqlqawEIEI42164BBDMqalMwEIEI ()2wAB1wA2qB2qa2BqaM2qaBBCDq2BqaM122BAwwwaw 42(2 )-8qawEI4447-3412AqaqaqawEIEIEI ()FABABCFRARBRC ()RBABCFFABRARC ()ABql0BwqABRBBBBqBRwww0BBqBRww () BqwBBRwqAB48BqqlwEI 33BBBRlRw