1. Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr.mun.ca ENGI 1313 Mechanics I Lecture 20:Couple Moment

2. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 2 Lecture 20 Objective to define a couple and determine the couple moment

3. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 3 What is a couple? Two parallel forces  Equal magnitude  Opposite sense and direction Separated by a perpendicular distance d.

4. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 4 Couple Moment – Scalar Magnitude Direction and sense  Right-hand rule Moment axis perpendicular to the couple force and moment arm plane

5. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 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. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 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. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 7 Couple Moment – Characteristics (cont.) Rules for vector addition apply Two couples on different planes Couples replaced by corresponding moment of a couple As a free vector moment couples moved to any Point P and resultant couple moment determined

8. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 8 Comprehension Quiz 20-01 1. F 1 and F 2 form a couple. The couple moment is given by ____.  A) r 1  F 1  B) r 2  F 1  C) F 2  r 1  D) r 2  F 2 Answer: B F1F1 F2F2 r1r1 r2r2

9. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 9 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 3 4 5 50 N 1m2m

10. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 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. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 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. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 12 Example 20-03 Determine the couple moment. Express the result as a Cartesian vector.

13. ENGI 1313 Statics I – Lecture 20© 2007 S. Kenny, Ph.D., P.Eng. 13 References Hibbeler (2007) http://wps.prenhall.com/esm_hibbeler_eng mech_1