|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).|