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CE 2010 Handout #11 Sections 4.7-4.8 (Exam #2)

Learning Objectives:

 Replace forces with an equivalent force-couple system.

 Reduce a force-couple system to a single force.

 Explain a wrench.

Relocating a Force

 Relocating (a.k.a., sliding) a force along its line of action has no (external) affect on a rigid body.

This is called the __________________ _____ ________________.

 Relocating a force in another direction results in the force and a couple acting on the body.

Relocating Numerous Forces

 A rigid body having numerous forces acting at different locations can have the external effects

of these forces reduced to a resultant force and couple system.

Ex #1 Replace the force and couple system by an

equivalent force and couple moment at point P.

CE 2010 Handout #11 Sections 4.7-4.8 (Exam #2)

Reduction of a Force Couple System

 When a force-couple system is reduced to a force and couple that are perpendicular to each

other, the system can be further simplified to just a force by relocating the force a distance d =

M/F away from that point.

Ex. #1:

 This can be done whenever forces are concurrent, coplanar or parallel.

 Otherwise, when the resultant force and couple are not perpendicular, which is common, they

can be reduced to a resultant force parallel couple acting at the same point. This is called a

________________.

Ex #2 (a) Replace the force system acting on the

frame an equivalent resultant force and couple

moment acting at point A.

(b) Replace the equivalent resultant force and couple

moment found in part (a) with an equivalent force

acting along line AB.