ENGI 1313 Mechanics I Lecture 20: Couple Moment Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected] Lecture 20 Objective  to.

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Transcript ENGI 1313 Mechanics I Lecture 20: Couple Moment Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland [email protected] Lecture 20 Objective  to. 

ENGI 1313 Mechanics I
Lecture 20:
Couple Moment
Shawn Kenny, Ph.D., P.Eng.
Assistant Professor
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
[email protected]
Lecture 20 Objective

2
to define a couple and determine the
couple moment
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
What is a couple?

Two parallel forces
Equal magnitude
 Opposite sense and direction


3
Separated by a perpendicular
distance d.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
Couple Moment – Scalar

Magnitude


M Fd

Direction and sense


4
Right-hand rule
Moment axis perpendicular
to the couple force and
moment arm plane
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
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
 
  
M  rA  F  rB  F


 
M  rB  rA  F
 

M  rAB  F
5
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
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

6
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
Couple Moment – Characteristics (cont.)

Rules for vector
addition apply

N 


MR   ri  Fi
i 1
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
7
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
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
F1


8
r1
F2
Answer: B
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
r2
Comprehension Quiz 20-02

A couple is applied to the beam. The
couple moment is _____.
50 N
A) 50 N·m
 B) 60 N·m
 C) 80 N·m
 D) 100 N·m

1m
9
Answer: B
© 2007 S. Kenny, Ph.D., P.Eng.
5
3
4 50 N
  
M  r F 

2m
i
j
k
2
0
0  60N  m
4 50  3 50 0
5
5
 
 
ENGI 1313 Statics I – Lecture 20
Example 20-01

10
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.
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
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.
Given:
F1  2 kN
 1  30 deg
F2  8 kN
 2  45 deg
a  0.3 m
b  1.5 m
c  1.8 m
11
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
Example 20-03

Determine the
couple moment.
Express the result
as a Cartesian
vector.
a  5m
b  3m
c  4m
 8 
F   4  N
 
 10 
d  2m
e  3m
12
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20
References
Hibbeler (2007)
 http://wps.prenhall.com/esm_hibbeler_eng
mech_1

13
© 2007 S. Kenny, Ph.D., P.Eng.
ENGI 1313 Statics I – Lecture 20