Short Answer:

The principle of transmissibility of forces states that the condition of equilibrium or motion of a rigid body does not change if a force acting on it is moved along its line of action. In simple words, the external effect of a force on a body remains the same as long as the line of action is not changed. This means that a force can be applied anywhere along its direction without affecting the overall motion or equilibrium of the body. This principle is widely used in Engineering Mechanics to simplify force systems in structures and machines.

Detailed Explanation :

Principle of Transmissibility of Forces

The principle of transmissibility of forces is one of the most important basic principles in Engineering Mechanics. It is used to simplify the analysis of forces acting on rigid bodies. According to this principle, the effect of a force on a rigid body remains unchanged if it is applied at any point along its line of action, provided that the magnitude, direction, and sense of the force remain the same.

In simple terms, this means that a force can be “transmitted” anywhere along its line of action without changing the external mechanical effect (like motion or equilibrium) on the body. However, it is important to remember that this principle is valid only for rigid bodies, which do not deform under the action of forces.

For example, imagine a beam subjected to a horizontal pulling force at one end. If the same force is applied at another point on the beam along the same line of action, the external effect of the force remains the same — the beam will move or resist in the same way. However, if the force is applied at a different angle or line of action, the effect on the beam will change.

Explanation of the Principle

To understand this principle more clearly, let’s consider a rigid body acted upon by a force F at point A. The line of action of this force passes through several points along its direction. If the same force F is applied at another point B along this line, then the external effect on the body (its tendency to move or stay in equilibrium) remains the same.

This is because a rigid body transmits the force internally without changing its overall condition of equilibrium or motion. The reason behind this is that in a rigid body, internal forces adjust themselves in such a way that the net effect of the external force remains unchanged.

However, if we consider a deformable body, this principle does not apply completely. When the point of application of a force changes in such a body, it can cause different internal deformations, even if the line of action remains the same. Hence, the principle of transmissibility is valid only for rigid bodies where deformation is negligible.

Mathematical and Graphical Representation

Let’s assume that a force F acts on a rigid body at point A, and it is transmitted to another point B along the same line of action.

At point A, the force can be replaced by:

• A force F acting at point B, and
• A couple whose moment is equal to F × distance between A and B, acting in the opposite direction.

However, since the body is rigid and we are only considering external effects, the moment caused internally does not affect the equilibrium condition. Therefore, the external effect remains the same, and we can consider the force to be acting at any point along its line of action.

Graphically, when we draw the force vector along a straight line (its line of action), shifting the force along this line without changing its direction or magnitude does not alter the system’s behavior.

Applications in Engineering Mechanics

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