《理论力学》课程教学资源（PPT课件，英文）Chapter 03 Plane General Force System

THEORYMECHANICS1902Electronic teaching planChapter3Plane GeneraForce SystemCollege of Mechanical andVehicle Engineering王晓君

THEORY MECHANICS Electronic teaching plan Chapter3 Plane General Force System College of Mechanical and Vehicle Engineering 王晓君

Chapter3 Plane General Force System> 3.1 Simplification of a point in the plane actingon a plane general force system> 3.2 Simplified results for plane general forcesystem> 3.3 Equilibrium conditions and equations of planegeneral force system> 3.4 Plane parallel force system> 3.5 Equilibrium, statically indeterminate andstatically indeterminate problems of object systems> 3.6 Calculation of internal forces of planestatically determinate truss

➢ 3.1 Simplification of a point in the plane acting on a plane general force system ➢ 3.2 Simplified results for plane general force system ➢ 3.3 Equilibrium conditions and equations of plane general force system ➢ 3.4 Plane parallel force system ➢ 3.5 Equilibrium, statically indeterminate and statically indeterminate problems of object systems ➢ 3.6 Calculation of internal forces of plane statically determinate truss Chapter3 Plane General Force System

3.1 Simplification of a point in the plane acting on a planegeneralforcesystemStringersFloorbeamsPlanegeneral force system:Anyforce systemin which the lines ofaction ofallforces are in the same plane and neither converge to a point nor paralleltoeach otheris calledaplanegeneral force system

3.1 Simplification of a point in the plane acting on a plane general force system Plane general force system：Any force system in which the lines of action of all forces are in the same plane and neither converge to a point nor parallel to each other is called a plane general force system

3.1 Simplification of a point in the plane acting on a planegeneral force system一.Translation theorem oflines offorceFF'mB。BBEF=F=AAAoF=F=-FUInstructions:Theoursan pnle translatn an tha same rigidbody parallelly fromit2. pount efartiorpiegsaybspecifiedepaint ioutbrerigid body, but acouple of forces must be attached to the plane determined by theCompositefo.Oanlethonpeaified p fintcewhose sonaerbupltheacforde of forcesis egual to the moment of the force at the specified point4.But a force + a couple

一. Translation theorem of lines of force Theorem: a force acting on a rigid body may move parallelly from its point of action to any specified point in the rigid body, but a couple of forces must be attached to the plane determined by the force and the specified point, whose moment of the couple of forces is equal to the moment of the force at the specified point. A B F  B A F  F   F   = A B m F   = F F' F''    = = − Instructions: 3.On the contrary，a force a couple+a force Composite 4.But a force ≠ a couple Disassemble 2. One force a force + a couple 1.You can only translate on the same rigid body。 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 system二. Plane general force system simplifies to a point.VytFFmIR'Am2Mo二O0xmnx(b)(c)(a)F'= F(i=1.2..n), m, =mo(F)(i =1.2...n)

O A1 A2 An F1  F2  Fn  (a) F F (i 1.2 n) , m m (F )(i 1.2 n) i i i O i  = =  = =     二. Plane general force system simplifies to a point. O F1   m1 F2   m2 Fn   mn x y (b) = O R   MO x y (c) = 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 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