Download presentation
Presentation is loading. Please wait.
Published byAmber Russell Modified over 9 years ago
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
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.