材料力学6截面的几何性质

1、2022年6月10日星期五xzymirCriiiCiiim rrmm rmiiiiCim rm rrmmmmCmrdmrdmrmdmiiCm xxmiiCmyymiiCm zzmmCxdmxmmCydmymmCzdmzmiiwgmiiCw xxwiiCw yywiiCw zzwmCxdwxwmCydwywmCzdwzwy0 xdAxyACxdAxAACydAyACyCxCyASxdAxASydAyACxdASxAAxACydASyAAyCASxdAxAxCASydAyAiixAAiicAAiiSy dy dA yiiyAAicAAiiSx dx dA xycSxAic iiiiA xAxcSy

2、Aic iiiiA yA例题例题1 1 求图示图形的形心求图示图形的形心解：解：2010010020yx0A1yC1A2yC2ic iyiciiic ixiciiA xSxAAA ySyAA0cx 11221210020 1010020 70401002010020cccA yA yyAAmmC4080例题例题2 2 求图示图形的形心求图示图形的形心101020020200A1yC1解：解：yx0A2yC2A3yC30cx 200 2010200 10 100 2200 20200 10 245mmc()y 311223123cccycAyA yAyAAAC65155y0 xdAxy2xAIy

3、 dA2yAIx dAxyAIxydA222pAAIr dAxy dApxyIIIxxIrAbhyx0dyy2xAAIy d222hhyy bd31 2b h2yAAIx d31 2h bxyAAIxyd0yx0dyyd2x2xAIy dA2222ddyxdy2222242dddyy dy464d464yxdIIyx0d2pAIr dA2202drrrd432drdrRpxyIII446464dd432dy0 xy101x1badAyxy1x111xxbyya，211xAIy dA2AyadA222AAAy dAaydAadA22xxIaSa A211yAIx dA2AxbdA22yyIbSb

4、 AAx bya dA1 11 1x yAIx ydAxyyxIaSbSabA0yxSS21211 1xxyxCyCyx yCIIa AIIb AIIabA例题例题1 1 求图示图形对其形心轴求图示图形对其形心轴Xc轴的惯性矩轴的惯性矩100yx0A1yC1A2yC2C408010020 xC解：解：IIIxcxcxcIII2113211 11 13244()()1()122110020(4010)1002012187 10 mmCCXXcIIa Ahb hyb h32441()20 100(80 50)100 20447 10 mm12CXI44418744710634 10 mmxcIy0

5、 xyxy1x1x1y111xxcosy sinyx siny cos 121xAIy dA2AxsinycosdA22222AAAsinx dAcosy dAsincosxydA2212xxyxyII cosI sinI sin1222yxyxyII sinI cosI sin11222xyx yxyIIIsinIcos12222xyxyxxyIIIIIcosIsin12222xyxyyxyIIIIIcosIsin11222xyx yxyIIIsinIcos11xyxyIIII0 02202xyx yxyIIIsinI cos022xyxyItgII 1xdId2220 xyxyIIsinI

6、 cos1ydId2220 xyxyIIsinI cos00 xmaxyminIIII221422xyxyxyII(II )I例题例题1 1 试求形心主轴的位置及形心主矩试求形心主轴的位置及形心主矩200180400204040解：解： （1 1）确定形心位置）确定形心位置CxCyCxy0（2 2）在形心位置处建立）在形心位置处建立Cxy坐标坐标, ,先先分别求出三个矩形对于分别求出三个矩形对于x、y轴的惯轴的惯性矩和惯性积性矩和惯性积 , ,得整个图形对于得整个图形对于x、y 轴的惯性矩和惯性积轴的惯性矩和惯性积32384180402(18018040)12204005 75 10 mm12xI.yI323844018021001804012400201 831 10 mm12.8402 180100401802 59210CCxyx yIIabA(.mm ）（3 3）根据上述结果确定主轴位置及形心主矩）根据上述结果确定主轴位置及形心主矩02115184arctan()arctan()265223919xyxyI.a.II.图形的形心主矩为：图形的形心主矩为：0228822841()4227 581 10103 91942 5