<> Chapter II : Plane intersection force system

<> one : Concept of plane intersection force system :

The action lines of all forces are in the same plane , And converge at one point , It is called plane intersection force system .

<> two : Synthesis of multiple converging forces —— Polygon rule of force

The request must be remitted at one point ,FR1 And FR2 Is the initial force , Because of the intersection with a point, the force can be synthesized .

Select two forces as their resultant force , Then use this resultant force and the third force to make the next resultant force .

The polygon formed by each force vector and resultant force is called force polygon
The drawing rule of force polygon to calculate the resultant force is called the polygon rule of force
The edge representing the resultant force vector in the force polygon is called the closed edge of the force polygon .( The resultant force is the closed edge )

conclusion : The plane intersection force system can be simplified as a resultant force , The magnitude and direction of the resultant force are equal to the vector sum of all component forces .

If : There is a force in the plane intersection force system that coincides with the resultant force , Then we call this force the resultant force of this force system .

<> three : Equilibrium condition of plane intersection force system

condition : The vector sum of all components is 0
That is, the polygon of force is self closed .( The end point of the last force coincides with the starting point .)

Firstly, the stress analysis is carried out : There are four forces in total
By the meaning of the title : The plane system of converging forces is balanced .
utilize R also h You can find the angle
A series of equations can solve the first question .

Second question : Force is support 0 Time

Third question : Only gravity is considered , And the support given by the left wall .
Vertical is the shortest .

equation :
FcSin45°=F+FaSinθ
FcCos45°=FaCosθ
Tanθ=1/2

①: Three force equilibrium intersection theorem for whole ,D Support force ,A To solve the three force equilibrium intersection theorem .
②:CD It is a two force component ,AB Convergence theorem of three force equilibrium at the end
③:C Vertical force at AB, yes AB Using the intersection theorem of three force equilibrium

<> four : Analytical method for synthesis and equilibrium of plane intersection force system

Projection of force on orthogonal coordinate axis and analytical expression of force

special : If the force is not within this axis , Then the force is equal to the magnitude of the force multiplied by the direction cosine of the angle between the force and the coordinate axis . The projection of force can only determine the force vector ( size , direction ), Its location cannot be determined

Resultant projection theorem : The projection of the resultant force of a plane intersection force system on an axis is equal to the algebraic sum of the projections of each component force in the force system on that axis .

Magnitude of resultant force :

Direction of resultant force :

Action point of resultant force : Intersection of forces

<> five : Equilibrium equation of plane intersection force system :

** The vector sum of the components is 0, From the expression of resultant force X,Y The resultant force in both directions is 0. **

Necessary and sufficient conditions for the equilibrium equation of plane intersection force system : The algebraic sum of the projections of each force on any two coordinate axes in the action plane is 0; Such an expression is called the equilibrium equation of the plane intersection force system .

The question passed B Force on point , Connect all the forces . stay B If the force direction of the point is uncertain, assumptions can be made .

This topic , Respectively A,B Two point analysis , Calculate the tension of the rope .

stay AB The coordinate system is established at two points respectively , The formula can be listed according to the equilibrium equation of the plane intersection force system .

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