Engr210 – Spring 2005 Instructor: Ahmed Abdel-Rahim
Lesson # 11: Couples/Force Couple Systems Page 1 of 2
Today’s Objectives:
1. Define a couple and determine
the moment of a couple
2. Determine the effect of moving a
force.
3. Find an equivalent force-couple
system for a system of forces
and couples.
Concept
A couple is two parallel forces with the same
magnitude but opposite in direction separated
by a perpendicular distance d.
MO = F d (using a scalar analysis)
MO = r x F (using a vector analysis).
Here r is any position vector from the line of
action of –F to the line of action of F.
The net external effect of a couple is that the
net force equals zero and the magnitude of
the net moment equals F d
Since the moment of a couple depends only
on the distance between the forces, the
moment of a couple is a free vector. It can be
moved anywhere on the body and have the
same external effect on the body.
Moments due to couples can be added using
the same rules as adding any vectors.
AN EQUIVALENT SYSTEM
Two force and couple systems are called
equivalent systems if they have the same
external effect on the body.
MOVING A FORCE ON ITS LINE OF
ACTION
Moving a force from A to O, when both
points are on the vectors’ line of action,
does not change the external effect.
Hence, a force vector is called a sliding
vector.
MOVING A FORCE OFF ITS LINE OF
ACTION
Moving a force from point A to O (as shown
above) requires creating an additional
couple moment.
Since this new couple moment is a “free”
vector, it can be applied at any point P on
the body.
