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) r1F1
B) r2F1
C) F2r1
D) r2F2
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