中国石油大学工程力学课件tm4a1mat.ppt

2020/9/25,Kylinsoft,MOM-A-1,附录A平面图形的几何性质AppendixAPropertiesofPlaneAreasCentroidsandMomentsofInertia,海盗船长,,2020/9/25,Kylinsoft,MOM-A-2,1.Centroids形心ofPlaneAreas,1Area面积,2Firstmoments静矩oftheareawithrespecttotheyandzaxes,2020/9/25,Kylinsoft,MOM-A-3,Ifanareaissymmetricaboutanaxis,thecentroidmustlieonthataxisbecausethefirstmomentaboutanaxisofsymmetryequalszero.,2020/9/25,Kylinsoft,MOM-A-4,3CentroidsofCompositeAreas,ExampleProblemA-1,DeterminethedistancestothecentroidsoftheL-shapedareaoranglesectionshowninFig.,Theareaandfirstmomentsofcompositearea,Thecoordinatesofthecentroidofthecompositearea,,I,II,Solution,2020/9/25,Kylinsoft,MOM-A-5,rectangleⅠA11200mm2yC15mm，zC160mmrectangleIIA2700mm2yC245mm，zC15mm,TheareacanbedividedintotworectanglesofareasAland,A2withcentroidsC1andC2,respectively,thecoordinatesyCandzCofthecentroidCofthecompositearea,2020/9/25,Kylinsoft,MOM-A-6,2.MomentsofInertia惯性矩andProductsofInertia惯性积ofPlaneAreas,Thepolarmomentofinertia极惯性矩ofaplaneareawithrespecttoanaxisthroughperpendiculartotheplaneisdefinedbytheintegral,Themomentsofinertia惯性矩ofaplaneareawithrespecttotheyandzaxes,respectively,aredefinedbytheintegrals,2020/9/25,Kylinsoft,MOM-A-7,theproductofinertia惯性积ofaplaneareawithrespecttotheyandzaxesisdefinedbytheintegral,theproductofinertiaofanareaiszerowithrespecttoanypairofaxisinwhichatleastoneaxisisanaxisofsymmetryofthearea.,Momentsofinertiaandproductsofinertiaofcompositeareas,2020/9/25,Kylinsoft,MOM-A-8,ExampleProblemA-2,DetermineIy,Iz,IP,Iyzofacirculararea.,Forsymmetry,Iyz0,Inasmuchasbothxandyareaxesofsymmetryofthearea,weobtain,Solution,2020/9/25,Kylinsoft,MOM-A-9,Iyz0,Hollowcirculararea,2020/9/25,Kylinsoft,MOM-A-10,,ExampleProblemA-3DetermineIy,Iz,IP,Iyzofarectangulararea.,momentofinertiawithrespecttotheaxisy1atthebaseoftherectangle,Solution,2020/9/25,Kylinsoft,MOM-A-11,RadiusofGyration惯性半径ofaplaneareaisdefinedas,RadiusofGyrationofarectangle,RadiusofGyrationofacircle,2020/9/25,Kylinsoft,MOM-A-12,3.ParallelAxisTheorem平行移轴定理,Itgivestherelationshipbetweenthemomentproductofinertiawithrespecttoacentroidalaxisandthemomentproductofinertiawithrespecttoanyparallelaxis.,Weobtain,For,2020/9/25,Kylinsoft,MOM-A-13,ParallelaxisTheorem平行移轴定理,Forexample,2020/9/25,Kylinsoft,MOM-A-14,ExampleProblemA-4,DeterminethemomentsofinertiaIyCandIzCoftheareashowninthefigurewithrespecttothecentroidalaxes.,,ThemomentofinertiawithrespecttozC,Solution,Locationofcentroid,2020/9/25,Kylinsoft,MOM-A-15,ThemomentofinertiawithrespecttoyC,2020/9/25,Kylinsoft,MOM-A-16,1Transationequationsomentsandproductsofinertia,4.RotationofAxes,For,2020/9/25,Kylinsoft,MOM-A-17,,Transationequationsomentandproductsofinertia,,2020/9/25,Kylinsoft,MOM-A-18,2Principalaxes主惯性轴，简称为主轴,Let,,Ityields2a0and2a0p,i.e.a0anda0p/2,Weget,2020/9/25,Kylinsoft,MOM-A-19,Conclusion,principalaxesthroughanoriginOareapairoforthogonalaxesforwhichthemomentsofinertiaareamaximumandaminimum;theorientationoftheprincipalaxesisgivenbytheanglea0;theproductofinertiaiszeroforprincipalaxes;anaxisofsymmetryisalwaysaprincipalaxis.,2020/9/25,Kylinsoft,MOM-A-20,3Principalmomentsofinertia主惯性矩,,Ityields2a0and2a0p,i.e.a0anda0p/2,substitutethesuesinto,weget,,2020/9/25,Kylinsoft,MOM-A-21,ExampleProblemA-5,Solution1ThemomentsandproductofinertiawithrespecttothereferenceaxesthroughthecentroidC,Determinetheorientationsoftheprincipalcentroidalaxesandthemagnitudesoftheprincipalcentroidalmomentsofinertiaforthecross-sectionalareaoftheZ-sectionshowninthefigure.,2020/9/25,Kylinsoft,MOM-A-22,2020/9/25,Kylinsoft,MOM-A-23,2theorientationsoftheprincipalcentroidalaxes,3themagnitudesoftheprincipalcentroidalmomentsofinertia,wegeta018.5anda0108.5,2020/9/25,Kylinsoft,MOM-A-24,矩形圆形圆筒形,常见截面,Conclusionanddiscussion,,2020/9/25,Kylinsoft,MOM-A-25,怎样判断主轴,Conclusionanddiscussion,,2020/9/25,Kylinsoft,MOM-A-26,怎样判断主轴,结论与讨论,,2020/9/25,Kylinsoft,MOM-A-27,怎样判断主轴,结论与讨论,,2020/9/25,Kylinsoft,MOM-A-28,结论与讨论,,怎样判断主轴,2020/9/25,Kylinsoft,MOM-A-29,a,b,结论与讨论,,怎样判断主轴,2020/9/25,Kylinsoft,MOM-A-30,转轴公式的坐标变换,结论与讨论,,其中IyzIzy,IyzIzy,令,2020/9/25,Kylinsoft,MOM-A-31,结论与讨论,,惯性矩与惯性积的莫尔圆图解法,2020/9/25,Kylinsoft,MOM-A-32,Homework,P230-A.1a*、P230-A.6a*、P230-A.7,2020/9/25,Kylinsoft,MOM-A-33,,制作群,素材收集海盗船长多媒体制作海盗船长总编辑海盗船长审核海盗船长总策划海盗船长赞助海盗船长,本章结束,