g-弯曲应力322课件

1、2.1 弯曲正应力弯曲正应力yxzxo),(zyxzdAANAzyxxF0d),()(AyAzzyxxM0d),()(AzAyzyxxMxMd),()()(PP dd)(ynmz zmndd)d(ymnmnnmxmnd)(),(xyyx ),(),(),(),(yxyxEzyxEzyx)(),(xyEyx0zS0d),()(*1ANAzyxxFANAyxExFd)()(AAyxEd)(0)(zSxE0d),()(*2AyAzzyxxMAyAyzxExMd)()(AAyzxEd)(0)(yzIxE0yzISo :)(),(xyEyxzIyxMyx)(),(AzAyzyxxMxMd),()()(*

2、3AAyxExMd)()(2AAyxEd)(2)( xIzzIxExM)()(zEIxMx)()(1zIyxMyx)(),(zEIxMx)()(1)(xzIyxMyx)(),(oo00)(xM00)(xMzEIxMx)()(10)(xMo0)(xMo实心圆截面实心圆截面D空心圆截面空心圆截面dAzAyxId)(2123bhIz6424DIIpzDdDIz/)1(6444矩形截面矩形截面bzIMyyzx1y2yzIyxMyx)(),(zIyxMxmaxmax)()(max)()(yxIxWzzzW)()()()(maxmaxxWxMIyxMxzzmaxmax)()(xWxMzbDd261bhWz

3、3321DWz)1 (32143DWzDdmax)()(yxIxWzz.)(maxmaxconstWxMMzzWMmaxmaxWMmaxmaxzWMmaxmax1y2y1y2y1y2yzIyM2maxmaxzIyM1maxmaxzIyM1maxmaxzIyM2maxmaxmaxMmaxMmaxMmaxM),max(1max2maxmaxzzIyMIyM),max(2max1maxmaxzzIyMIyM1y2ymaxMmaxMMPa62032max.zAIyMMPa81011max.zAIyMMPa81011max.zAIyMMPa81011max.zAIyMMPa51142max.zBIyMM

4、Pa51142max.zBIyMMPa51142max.zBIyMm57. 由弯曲曲率公式由弯曲曲率公式EIM1EIM WM2EdWEIMPa320 EIM1szWMmaxzsWMEIWEIMRzs1zsWEIR)2/(dIEIssdE2mm6251085320210200233?BM EIM1BBEIMB0BM43961aICx43961aICyIyMmaxmaxmaxaaqL219632423238aqL ?mABym梁为纯弯曲梁梁为纯弯曲梁, ,有有: :mxM)()()(),(yImyIyxMyxzz因因 AB AB 为水平线段为水平线段, ,则只是简单拉伸则只是简单拉伸, ,有有:

5、:zEImyEyy)()(mm125. 0GPa,80,50,480,120,40aEyahb（拉应力）（拉应力） AB 为均匀变形为均匀变形( (与与x 坐标无关坐标无关),),则有则有: :zEImyaay)(yEIaamzaayEbhm123mm125.0GPa,80,50,480,120,40aEyahbNmm104.2480125.05012120401080633mmkN4.2。后面正应力后面正应力前面正应力前面正应力后面正应力合力后面正应力合力平衡方程平衡方程zIMyzIyMM)d(dd1SIMAyIMANzAzAd2SIMMNzxbFd21NFN前面正应力合力前面正应力合力zsbIySxFyx)()(),(ddSIMMxbSIMzzzbISxMddzsbIySxFyx)()(),()4(2)(),(22yhIxFyxzs42)(2maxhIxFzsbhxFs)(23AxFs)(23)2(yhbS)2(21yh)4(222yhbk = 3/2k = 4/3xzszxsSIdFdISF:zsbIySxFyx)()(),()()()(maxxAxFkxsmaxmax)()(xAxFksAFks maxmax最大切应力产生最大切应力产生在左端截面中性轴上在左端截面中性轴上两者之比两者之比WMmax323216322dqldlqAF