中国石油大学工程力学课件tm4a1ma

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1、2021/7/10KylinsoftMOM-A-1附录A平面图形的几何性质AppendixAPropertiesofPlaneAreas(CentroidsandMomentsofInertia)海盗船长2021/7/10KylinsoftMOM-A-21.Centroids(形心)ofPlaneAreas(1)Area(面积)yzOyzyCzCCdA(2)Firstmoments(静矩)oftheareawithrespecttotheyandzaxes2021/7/10KylinsoftMOM-A-3Ifanareaissym

2、metricaboutanaxis,thecentroidmustlieonthataxisbecausethefirstmomentaboutanaxisofsymmetryequalszero.CzyAreawithoneaxisofsymmetryAreawithtwoaxesofsymmetryCzy2021/7/10KylinsoftMOM-A-4(3)CentroidsofCompositeAreasExampleProblemA-1DeterminethedistancestothecentroidsoftheL-sh

3、apedarea(oranglesection)showninFig.Theareaandfirstmomentsofcompositearea:Thecoordinatesofthecentroidofthecompositearea:zC1yC1yC2zC2yz8010O12010C(yC,zC)IIISolution2021/7/10KylinsoftMOM-A-5rectangleⅠ：A1=1200mm2yC1=5mm，zC1=60mmrectangleII：A2=700mm2yC2=45mm，zC1=5mmTheareac

4、anbedividedintotworectanglesofareasAland,A2withcentroidsC1andC2,respectively:yC2zC2zC1yC1yz8010O12010C(y,z)IIIthecoordinatesyCandzCofthecentroidCofthecompositearea:2021/7/10KylinsoftMOM-A-62.MomentsofInertia(惯性矩)andProductsofInertia(惯性积)ofPlaneAreasThepolarmomentofine

5、rtia(极惯性矩)ofaplaneareawithrespecttoanaxisthroughperpendiculartotheplaneisdefinedbytheintegralyzOyzrdAThemomentsofinertia(惯性矩)ofaplaneareawithrespecttotheyandzaxes,respectively,aredefinedbytheintegrals2021/7/10KylinsoftMOM-A-7theproductofinertia(惯性积)ofaplaneareawithresp

6、ecttotheyandzaxesisdefinedbytheintegraltheproductofinertiaofanareaiszerowithrespecttoanypairofaxisinwhichatleastoneaxisisanaxisofsymmetryofthearea.yzyzOyzrdAMomentsofinertiaandproductsofinertiaofcompositeareas:2021/7/10KylinsoftMOM-A-8yzDRExampleProblemA-2DetermineIy,I

7、z,IP,Iyzofacirculararea.Forsymmetry：zdzIyz=0Inasmuchasbothxandyareaxesofsymmetryofthearea,weobtainSolution2021/7/10KylinsoftMOM-A-9Iyz=0dDyzHollowcirculararea:2021/7/10KylinsoftMOM-A-10ExampleProblemA-3DetermineIy,Iz,IP,Iyzofarectangulararea.bhyzy1ydymomentofinertiawit

8、hrespecttotheaxisy1atthebaseoftherectangle:zdzSolution2021/7/10KylinsoftMOM-A-11RadiusofGyration(惯性半径)ofaplaneareaisd