Couples

1
Couples

• A system of 2 forces of equal magnitude
  parallel lines of action and opposite sense.
• The Couple

2
Moment of a Couple

• ?MO rA?F rB?(-F) (rA- rB) ?F r?F
• Moment of a couple
• M r?F

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more

• M r?F , M rF sinq Fd
• Magnitude Fd
• Sense right hand rule

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• Strength of a couple is independent of point
  about which moment is taken! Depends only on F
  and d.

strength equal to Fd
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Force Systems

• Definition. Two force systems are equivalent
  (have the same effect on a rigid body) if they
  can be transformed into one another by (i)
  resolving vectors, (ii) canceling equal and
  opposite vectors, (iii) sliding vectors
  (transmissibility).

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• Theorem. Two couples that have the same moment
  are equivalent.
• It does not matter where couple acts on a
  rigid body, or what the forces or directions are.
  The effect is the same if moment of the couple is
  the same.

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• The sum of two couples is a couple with a moment
  which is the resultant of its components.

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Moving a Force Off its Line of Action

• Problem. Move force F to point O.
• Note. F can always be moved along its
• line of action (transmissibility).

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Procedure

• Step 1.

• Step 2.

• When moving a force off its line of action
  we must add a couple with moment equal to moment
  of F about O.

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Relation of Moments at Different Points

• Move F to another point O.
• MO MO s?F
• MO r?F MO r?F
• r r s

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DISMISSED !