ES-90 Couples and Equivalent Systems

ES-90 Couples and Equivalent Systems

A couple is defined by two forces of equal magnitude, parallel lines of action and opposite directions. A diagram showing a couple is shown.

The moment of a couple is defined by
M = F d
where d - perpendicular distance between forces

The moment of a couple is perpendicular to the plane defined by the forces.

Note: The moment due to a couple is a vector.

The moment's point of application may be moved as long as its magnitude and direction are kept invariant.
Note: The configuration shown in the two previous figures are identical. The moment may then be resolved into three orthogonal components.

Note: Couples are said to be equivalent if they cause equal moments. Moments are equal if they have the same magnitude, direction and sense.

Any force may be resolved into an equal force at another point and a moment. If the force is given as shown and it is desired to move the force to a point A, two equal and opposite forces may be placed at A.

Note: Since the same force has been added and subtracted, no net change exists.

The vectors labeled F₁ and F₂ form a couple and may be replaced by a moment perpendicular to the plane formed by vectors F₁ and F₂ and of magnitude F(d).