A given force ‘F’ applied to a body at any point A can always is replaced by an equal force applied at another point B together with a couple which will be equivalent to the original force. Let us given force F is acting at point ‘A’ as shown in fig. (a).
This force is to be replaced at the point ‘B’. Introduce two equal and opposite forces at B, each of magnitude F and acting parallel to the force at A as shown in fig.(b). The force system of fig. (b) is equivalent to the single force acting at A of fig. (a). In fig. (b) three equal forces are acting. The two forces i.e. force F at A and the oppositely directed force F at B (i.e. vertically downwards force at B) from a couple. The moment of this couple is F × x clockwise where x is the perpendicular distance between the lines of action of forces at A and B. The third force is acting at B in the same direction in which the force at A is acting.
In fig. (c), the couple is shown by curved arrow with symbol M. The force system of fig. (b) is equivalent to fig. (b). Or in other words the Fig. (c) is equivalent to Fig. (a). Hence the given force F acting at A has been replaced by an equal and parallel force applied at point B in the same direction together with a couple of moment F × x. Thus force acting at a point in a rigid body can be replaced by an equal and parallel force at any other point in the body, and a couple.
Equivalent force System
An equivalent system for a given system of coplanar forces is a combination of a force passing through a given point and a moment about that point. The force is the resultant of all forces acting on the body. And the moment is the sum of all the moments about that point. Hence equivalent system consists of:
1. A single force R passing through the given point, and
2. A single moment (∑M) Where,
R = the resultant of all force acting on the body
∑M = Sum of all moments of all the forces about point P.
