3.1 Simplification of a point in the plane acting on a planegeneral force systemCalculation ofprincipalvectorand principal moment:magnitude:R'=R'+R',= /(zX) +(ZY)direction: cos(R',7) -ZXPrincipalRR'vector(moving effect)It has nothing to do withsimplified center:simplifying the central position)magnitude: M。= mo(F)Principa+direction:moment(rotation effect)simplified center: (It has somethingto do withsimplifyingthecentralposition)
R' (rotation effect) magnitude： MO direction: + - simplified center： ( ) MO mO Fi = Calculation of principal vector and principal moment: magnitude： direction： simplified center: 2 2 2 2 R' = R' +R' = ( X ) + (Y) x y （moving effect） R X R i cos( , ) = Principal vector (It has nothing to do with simplifying the central position) Principal moment (It has something to do with simplifying the central position) 3.1 Simplification of a point in the plane acting on a plane general force system
3.1 Simplification of a point in the plane acting on a planegeneralforce systemTo sum up: Any force in a plane is simplified to any point in theacting plane to obtain a force and a couple.The force acts onthe simplified center, whose magnitude and direction are equaltotheprincipal vector of the force system, and the moment ofthe couple is equal to the principal moment of the force systemonthesimplifiedcenter.Notice:1, R' Mo can not be called the force system of resultantforce, resultantcoupling, but called the principalvector, principalmoment.2, The principalvector has nothing to do with the location of the simplified center3,Theprincipalmomentisrelatedto thelocationofthe simplificationcenter
Notice： R' 1、 、 MO can not be called the force system of resultant force, resultant coupling, but called the principal vector, principal moment. 2、The principal vector has nothing to do with the location of the simplified center 3、The principal moment is related to the location of the simplification center. To sum up: Any force in a plane is simplified to any point in the acting plane to obtain a force and a couple . The force acts on the simplified center, whose magnitude and direction are equal to the principal vector of the force system, and the moment of the couple is equal to the principal moment of the force system on the simplified center. 3.1 Simplification of a point in the plane acting on a plane general force system
3.1 Simplification of a point in the plane acting on a planegeneral force systemExample 1 Given the plane general force system as shown in thefigure, F =100/2N, F, =100N, F, = 50N, and the angleFi to xaxis is 45 degrees , solve: The force system simplifies to O pointSolution:HyV2R',= X, = F cos45° +F2 =100/2+100 = 200 N(1,2)/3. 1) F22R',=ZF= F sin 45° -F, =100/250=50A2x(2,-1)R"2+R"? = (200) +(50)2 =50/17 NRrJ2V2M=mo(F)=×2-F,×1-F×222=-300N.mm
x y (1,2) (2,-1) (3, 1) F1 F2 F3 Solution: R' R' x R' y (200) (50) 50 17 N 2 2 2 2 = + = + = R X F F N i x 100 200 2 2 ' cos 45 100 2 = = 1 + 2 = + = R F F F N i y y 50 50 2 2 ' sin 45 100 2 = = 1 − 3 = − = Example 1 Given the plane general force system as shown in the figure， ， ， ,and the angle to axis is 45 degrees , solve: The force system simplifies to O point. F1 =100 2N F2 =100N F3 = 50N F1 x N m m MO mO Fi F F F F = − = = − − − 300 2 1 2 2 2 1 2 2 ( ) 1 1 2 3 3.1 Simplification of a point in the plane acting on a plane general force system
3.1 Simplification of a point in the plane acting on a planegeneralforce system三.Planefixed endconstraintA constraint formed by a part of an object embedded inanother object is called a planefixed end constraintMx←AARemember:Don'tloseYthe counter couple
三. Plane fixed end constraint A constraint formed by a part of an object embedded in another object is called a plane fixed end constraint A A A A X A YA M A Remember: Don't lose the counter couple 3.1 Simplification of a point in the plane acting on a plane general force system
3.1 Simplification of a point in the plane acting on a planegeneralforce systemCommon fixed end constraints in engineering头YuDa
Common fixed end constraints in engineering YuDa 3.1 Simplification of a point in the plane acting on a plane general force system