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Basic Concept in Statics and Static Equilibrium

Concept of Particles and Free Body Diagram
Each of the bodies considered in our study are treated as a single particle, that all the forces acting on a given body will be assumed to be applied at the same point. The bodies under study in statics are rigid bodies i.e. they don’t deform when external force is applied on it.

  • Free Body Diagram
    A enormous number of problems concerning actual structures, however, can be reduced to problems concerning the equilibrium of a particle or a body. This is prepared by taking a significant particle and drawing a separate diagram showing this particle and also showing all the forces and reactions acting on that particle. Then this diagram is called a free-body diagram. This is a diagram showing reaction forces, body forces and moment on the body.
  • Steps to Draw Free Body Diagram
    • A clear decision should be made regarding the choice of the free body to be used for our analysis or study.
    • This body is then separated from the ground and is separated from all other bodies which touches it in actual condition.
    • The contour or the profile of the body thus isolated from ground is sketched which is the center of our study.
    • All external forces acting on isolated body should be indicated on the free-body diagram. These forces represent the actions that is employed on the free body by the ground and by the bodies which have been detached.
    • They should be applied at the different points where the free body was reinforced by the ground or was attached to the other bodies.
    • The weight of the free body should also be involved among the different external forces that are acted on the isolated body.
    • The weight should be applied or acted at the center of gravity of the isolated body vertically.
    • Sometime the free body is made of several different parts, these various parts exert certain amount of force on each other. This force should not be included among the external forces that are shown in free body diagram. These forces are internal forces as far as the free body is concerned.
    • The magnitudes as well as the directions of the known external forces should be evidently noticeable on the free-body diagram.
    • When indicating the directions of these forces, it must be remembered that the forces shown on the free-body diagram must be those forces which are applied on, and not applied by the free body.
    • The free-body diagram should be composed of different dimensions of that structure, since these may be needed in the calculation of moments of forces and other different parameters.
      • Any other detail, however, should be omitted or discarded.
        Fig. Free-body diagram
        Free-body Diagram

Physical Meaning of Equilibrium and its Essence in Structural Application
When the several forces act on the body and the net effect of the different forces that are applied on a body is zero, and the particle is in the state of equilibrium. A particle will be in equilibrium if it is stationary or move with a uniform velocity relative to certain reference.
A safe structure is always in a static equilibrium. For the case of the beam the applied external force, moment and couple are balanced by the reaction which keep the beam in an equilibrium position.

Fig. Beam in Equilibrium
Beam in Equilibrium

Equation of Equilibrium in Two Dimension
For the analysis or calculation of the equation of equilibrium in two dimension. The equilibrium of structure which is comprised of the two dimension is considered; i.e., it is supposed that the structure or a body being analyzed or studied and the forces applied to it are contained in the same plane. If the stationary body is subjected to the co-planar forces to be the body in equilibrium the algebraic sum of all the external force and their moments must be zero.
\(\sum{F}\) = 0 and \(\sum{M}\) = 0
These are generally resolved in two horizontal and vertical component.
Where, F represent forces and M represent moments, suffix x and y represent horizontal and vertical component respectively.


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