8/20/2019 5. Forces System - Couple

1/11

COUPLE

By Rani Rumita

8/20/2019 5. Forces System - Couple

2/11

• Is the moment produced by twoequal, opposite and noncollinearforces

8/20/2019 5. Forces System - Couple

3/11

• Consider the action of two equal andopposite forces F and –F a distance d apart

•  These two forces cannot be combined into

a single force because their sum in everydirection is ero! Their only e"ect is toproduce a tendency of rotation

•  The combined moment of the two forcesabout an a#is normal to their plane andpassing through any point such as $ intheir plane is the couple %

8/20/2019 5. Forces System - Couple

4/11

•  This couple has a magnitude

% & F!'a(d) – F!aor

% & F!d

8/20/2019 5. Forces System - Couple

5/11

•  The magnitude of the couple isindependent of the distance a whichlocates the forces with respect to the

moment center $

•  The moment of a couple has thesame value for all moment centers

8/20/2019 5. Forces System - Couple

6/11

*ector +lgebra %ethod

% & 'r+ # F) ( 'rB # 'F))

& 'r+ – rB)!F

8/20/2019 5. Forces System - Couple

7/11

•  The moment e#pressioncontains no reference to themoment center $ and,

therefore, is the same for allmoment centers

• -e may represent % by a freevector

• The direction of % is normal tothe plane of the couple andthe sense of % is establishedby the righthand rule

8/20/2019 5. Forces System - Couple

8/11

.quivalent Couples

8/20/2019 5. Forces System - Couple

9/11

ForceCouple /ystems

8/20/2019 5. Forces System - Couple

10/11

8/20/2019 5. Forces System - Couple

11/11