Diagram of forces

In mechanical statics, and more particularly that of the solid, the diagram of forces is a graphic method to determine the intensity of forces acting on a system in balance.

It is also called dynamic forces .

This method, very fast and specifies when it is carried out carefully, can apply only in the case of the plane problems (with two dimensions), i.e. with the cases of the all systems sousmis to more the three forces, and certain cases beyond three forces.

Recall basic principle of statics

The article Statique points out the conditions for application of the basic principle of statics. In a problem, certain mechanical actions are known (they are often loads), and others partially or completely unknown factors: they are the unknown factors of the system whose determination must be able to lead to an adequate dimensioning of the studied device.

Its statement provides, within the framework of the statics of the solid, two vectorial equations:

  • the sum of the forces is null: graphically that results in a closed vectorial chain, that is to say actually a closed traverse of which all with dimensions ones are directed in the same direction.
  • the sum of the moments of the forces is null: interpretations can differed according to the cases, but they result in provisions particular of the right-hand sides of actions, which makes it possible to determine the direction of it.

Limits of employment

The polygon being a plane figure, the whole of the vectors force must be coplanar. If it is not the case, the recourse to other methods is necessary. The recourse to the exclusively graphic resolution, functions only in the case of mechanical actions modélisable by slide blocks (forces applied in a point). The too complex actions of connections or the couples cannot be taken into account differently than by a calculation.

Academic cases

Mechanical system has forces different one from the other sousmis with 2 forces

A solid sousmis with two forces (i.e. 2 slide block) remains in balance if:
  • the two forces have even intensity, even direction and but are opposite directions. This relation comes from the equation known as of the resultant resulting from the basic principle of statics. Media:
  • the two slide blocks have even central axis (the points of application of the forces are on a line colinéaire with the direction of the forces). This relation comes from the equation known as of the moments exit of the same principle.

Mechanical system sousmis with 3 forces

A solid subjected to the action of three slide blocks (forces) remains in balance if and only if:

  • first case (at least two of the forces are not parallel):

    • the central axes of the three slide blocks are convergent in same a point^; that translated the equation of the moments resulting from the basic principle of dynamics.

    • the forces are coplanar, and forms a polygon (triangle) closed; that translated the equation of the resultant. Indeed the null sum makes it possible to write one of the three forces according to the two others, which imposes the membership on the same vectorial plan.

  • second case: two forces are parallel:

    • the central axes all are parallel and in the same plan.
    • the intensities check the principle of the lever.

Mechanical system sousmis with at least 4 forces

Determination of the sum of several slide blocks

(the funicular)

Resolution of a problem

See Too

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