Forces and Moments: Part 5

Equivalent system:

An equivalent system is:

A system in which forces and couple moments acting on a body are simplified to a single resultant force and couple moment acting at a specified point O.

Consider the figure below in which point O is on the line of action of the force:

F is applied at A (Fig. a). It is needed to move the force F to point O (keeping the external effects on the body constant). Imagine we apply +F and –F at O (Fig. b). As +F at A and –F at O are cancelled out, hence +F is applied at O (Fig. c).

Now if point O is not on the line of action of the force:

Force F is applied at A (Fig. a) and OA does not pass through the line of action of F. It is needed to move force F to O (keeping the external effects on the body constant).

In this case: Apply +F and –F at O (Fig. b), then +F at A and –F at O create a couple moment (M = r x F). M is a free vector, so remember that it can be applied on any point P (Fig. c)

So, F is applied at O and also a moment M is produced (Fig. c).