附录A 极惯性矩与惯性矩.doc

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yC。题A-1图(a)解:坐标及微面积示如图A−1(a)。由此得dA=ρdϕdρRα∫ydA∫∫ρcosϕ⋅ρdϕdρ2Rsinα=yC=AA0 −αRα∫∫=ρdϕdρ 3α0 −α(b)解:坐标及微面积示如图A−1(b)。dA=h(y)dy=ayndy由此得AyC=∫A=ydA=∫by⋅ayndy0=b n=(n+1)b∫0aydyn+2A-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z=acosα∫y=bsinα,dy=bcosαdα故有Iz=y2dA=∫Aπ2(bsinα)2⋅2acosα⋅bcosαdα-π23=abπ πab32(1−cos4α)dα=∫-π4 2 4(b)解:取微面积如图A−3(b)所示。且ϕ在α与−α之间变化,而dA=2zdy=dcos2ϕdϕ22由此可得sinα=d−2δdI=∫αdy2dA=∫(