When two equal and opposite parallel non collinear forces act on a body, they form a couple.
Let d is the arm of the couple. F and – F forces can not be combined into a single force (since the sum is zero). The body in which the forces act, will have a tendency of rotation.
The couple moment M about o has a magnitude
|M|=|Fa –F (a+d)
=| Fa –Fa –Fd
=| -Fd | =Fd .
Thus the magnitude of the couple moment M is equal to the product of either one of the forces and perpendicular distance (arm of the couple) between the forces.
In Fig. 3.9, the couple moment is clockwise. It is taken as negative
Let us use the vector algebra for calculating couple moment.
Again we have
It is to be noted that in the vector expression of the couple moment M does not contain the reference point 0 and therefore, it is same for all moment centres. So the couple moment is a free vector and always be the perpendicular to the plane of the forces which contain the forces.