Couples

Couple is a system of forces whose magnitude of the resultant is zero and yet has a moment sum. Geometrically, couple is composed of two equal forces that are parallel to each other and acting in opposite direction. The magnitude of the couple is given by
 

 
Where $F$ are the two forces and $d$ is the moment arm, or the perpendicular distance between the forces.
 

Couple is independent of the moment center, thus, the effect is unchanged in the following conditions.

• The couple is rotated through any angle in its plane.
• The couple is shifted to any other position in its plane.
• The couple is shifted to a parallel plane.

In a case where a system is composed entirely of couples in the same plane or parallel planes, the resultant is a couple whose magnitude is the algebraic sum of the original couples.