材料力学课件第十三章弯曲的几个补充问题

1、 FyFzFzFj jFyFzyxz挠曲线挠曲线梁的轴线梁的轴线对称轴对称轴垂直纵向对称面垂直纵向对称面xyz梁的轴线梁的轴线对称轴对称轴水平纵向对称面水平纵向对称面挠曲线挠曲线FyFzmmzyMyxMz mmzyMyxMzzIMyy yIMzz yIMzIMzzyy C ( y,z ) e ( z0 ,y0 )000 yIMzIMzzyye yIMzIMzzyy zyxzOe (z0,y0)000 yIMzIMzzyy中性轴中性轴000 yIMzIMzzyyj j cottan00 zyzyyzIIIIMMyzzyx 中性轴中性轴z0 22zyMMM yzO M中性轴中性轴 tantan00

2、 zyzyyzIIIIMMyzyzMM tan yx 中性轴中性轴 z yO 讨讨 论：论：z tantan00zyzyyzIIIIMMyz tantan00zyzyyzIIIIMMyz 中性轴中性轴 z yOM 中性轴D2D1OD1D2zy中性轴中性轴中性轴中性轴D2D1max wzwyw 22zywww yzww tan xA B CzyF2=2kNF1=1kN 0.5m 0.5m 4080zyO xA B CzyF2=2kNF1=1kN 0.5m 0.5m xA B CzyF2=2kNF1=1kN 0.5m 0.5m 1kNmMz(x)图图1kNmMy(x)图图zyxMyzyxzzyx拉

3、拉拉拉压压D2D18040zyyyyWM max zzzWM max 2408061 yW2804061 zW22408061mkN1804061mkN1 yyzzWMWMMPa02. 7)max(1 yyzzDWMWM MPa02. 7)max(2 D zyxMyzyxz拉拉拉拉压压41101101128040124080tan3333 yzzyMMII 14 zy中性轴中性轴 8040zy中性轴中性轴 1+-拉拉压压40Fqaayzz40FqaayFyFzqaFFqaFFzy321. 040sin383. 040cos FzACBxz面面qFyACBxy面面DD0.617abcda0.45

4、6qa20.266qa20.383qa2Mz图图ac0.321qa20.642qa20.444qa2My图图3636m105 .31m10237 yzWWqWMWMyyAzzAA3max105 .21)( qWMWMyyDzzDD3max1002.16)( .)(maxmax qWMWMyyAzzAA3 310105 52121kN/m44. 75 .21101603 q AAAq(x)F1F2tyOmtyzdhbh1hbdy1y1dISFzz*S )4(22221SyhdhbdIFz tyOmtyzdhbh1hbdy1y1q(x)mmnnxdxFSMFSM+dMnmmndxxnmnmdxmn

5、Ozydxm2hDCA111dAADmCdxBF*1NF*2NIhMz21 IhMMz2d11 z*AA*IhMAAAF2dd1*1*11N hIMMFz*2N2d A*mnOzydxm2hDCAADmCdxB111dAF*1NF*2NA*FF*2N*1N ADmCdxBF*1NF*2NSdF 1 1xFdd1S 0d*2NS*1N FFF z*IhMF21N hIMMFz*2N2dzIhF2S1 ADmCdxBF*1NF*2NSdF 1 1 11zIhF2S1 mnOzydxm2hDCA 1 1mmb max1zIhF2S1 zIbhF2Smax1 yOmyzdhbh1hbdy1y1)4(22221SyhdhbdIFz 11()2R2ddhhFAdy* *A A)()4(2222221SdyyhdhbIFhhz yOmyzdhbh1hbdy1y1 1