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ENGI 1313 Mechanics I

ENGI 1313 Mechanics I . Lecture 20: Couple Moment. Lecture 20 Objective. to define a couple and determine the couple moment. What is a couple?. Two parallel forces Equal magnitude Opposite sense and direction Separated by a perpendicular distance d. Couple Moment – Scalar. Magnitude

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ENGI 1313 Mechanics I

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  1. ENGI 1313 Mechanics I Lecture 20: Couple Moment

  2. Lecture 20 Objective • to define a couple and determine the couple moment

  3. What is a couple? • Two parallel forces • Equal magnitude • Opposite sense and direction • Separated by a perpendicular distance d.

  4. Couple Moment – Scalar • Magnitude • Direction and sense • Right-hand rule • Moment axis perpendicularto the couple force and moment arm plane

  5. Couple Moment – Vector • Determine couple moment by taking moment about a point on the line action of one of the forces • Position vector between couple

  6. Couple Moment – Characteristics • Net Force on System is Zero • Only Tendency for Rotation • Free Vector • Depends only on distance between couple force line of action • Same external effect on a body regardless of position

  7. Couple Moment – Characteristics (cont.) Two couples ondifferent planes • Rules for vector addition apply Couples replaced bycorresponding momentof a couple As a free vector moment couplesmoved to any Point P and resultantcouple moment determined

  8. Comprehension Quiz 20-01 • 1. F1 and F2 form a couple. The couple moment is given by ____ . • A) r1F1 • B) r2F1 • C) F2r1 • D) r2F2 • Answer: B F1 r1 r2 F2

  9. 50 N 5 1m 2m 3 4 50 N Comprehension Quiz 20-02 • A couple is applied to the beam. The couple moment is _____. • A) 50 N·m • B) 60 N·m • C) 80 N·m • D) 100 N·m • Answer: B

  10. Example 20-01 • Two couples act on the beam. The resultant couple is zero. Find the force magnitudes of P and F and the moment arm distance d.

  11. Example 20-02 • Determine the resultant couple moment acting on the beam. Solve the problem two ways: (a) sum moments about point O; and (b) sum moments about point A.

  12. Example 20-03 • Determine the couple moment. Express the result as a Cartesian vector.

  13. References • Hibbeler (2007) • http://wps.prenhall.com/esm_hibbeler_engmech_1

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