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Force-Couple Systems
Force – Couple Systems = Reduction of a Force to an Equivalent
Force and Moment (Moving a Force to Another Point)
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The force F acting on a body has two effects:
The first one is the tendency to push or pull the body in the
direction of the force, and the second one is to rotate the body
about any fixed axis which does not intersect nor is parallel to the
line of the force.
This dual effect can more easily be represented by replacing the
given force by an equal parallel force and a couple to compensate
for the change in the moment of the force.
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Let us consider for F acting at point A in a rigid body. It is

possible to slide force F along its line of action, but it is not
possible to directly move it to point B without changing the
external effect on the rigid body.
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In order to do this, two equal and opposite forces F and  F are added
to point B without introducing any net external effects on the body. It is
seen that, the original force at A and the equal and opposite one at B
constitute the couple M=Fd, which is counterclockwise for this case.
Therefore, we have replaced the original force at A by the same
force acting at a different point B and a couple, without altering

the external effects of the original force on the body. Since M is
a free vector, its location is of no concern. The combination of
the force and couple is referred to as a force-couple system.
By reversing this process, we can combine a given couple and a
force which lies in the plane of the couple (normal to the couple

vector) to produce a single, equivalent force. Force F can be moved
to a point by constructing a moment equal in magnitude and
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opposite in direction M
. The magnitude and direction of
M
remains the same, but its new line of action will be d 
distance
F
away from point B.
1. A force F of magnitude 50 N is exerted on the automobile
parking-brake lever at the position x=250 mm. Replace the force by
an equivalent force-couple system at the pivot point O.
2. The device shown is part of an automobile seat-back-release
mechanism. The part is subjected to the 4 N force exerted at A and a
300 Nmm restoring moment exerted by a hidden torsional spring.
Determine the y-intercept of the line of action of the single equivalent
force.
3. A 50 N horizontal force is applied to the handle of the industrial
water valve as shown. The force is perpendicular to the vertical plane
containing line OA of the handle. Determine the equivalent forcecouple system at point O.