附录a 极惯性矩与惯性矩.doc

附录A_极惯性矩与惯性矩附录A极惯性矩与惯性矩题号页码A-1........................................................................................................................................................1A-3........................................................................................................................................................2A-4........................................................................................................................................................3A-6........................................................................................................................................................4A-7........................................................................................................................................................4A-8........................................................................................................................................................5(也可通过左侧的题号书签直接查找题目与解)A-1试确定图示截面形心C的坐标y。C题A-1图(a)解:坐标及微面积示如图A?1(a)。dA=ρdϕdρ由此得Rαρcosϕ?ρdϕdρydA2Rsinα???0?αA=y==CRαA3αρdϕdρ??0?α(b)解:坐标及微面积示如图A?1(b)。1ndA=h(y)dy=aydy由此得bnydAy?aydy?(n+1)b?=A=0=y==CbAn+2naydy?0A-3试计算图示截面对水平形心轴z的惯性矩。题A-3图(a)解:取微面积如图A?3(a)所示。dA=2zdy由于2z=acosαy=bsinα,dy=bcosαdα故有π222(bsinα)?2acosα?bcosαdαydA=I=πz??A-2π33πab2(1?cos4α)dα==π?ab-442(b)解:取微面积如图A?3(b)所示。2d2ϕdϕcosdA=2zdy=2且ϕ在α与?α之间变化,而d?2δsinα=d由此可得2αdd222I=ydA=(s