Steps to Solve Moment of Force about an Axis
12
1.
Identify knows and unknowns.
2.
Select the X-Y-Z coordinates system (use the problem default system).
3.
Identify three vectors in terms of rectangular components: force vector
F
,
position vector
r
, and unit direction vector
λ
for the axis.
4.
Calculate the moment.

Sample Problem
x
y
z
C(0,0.9,-0.4)
D(0,0.7,0)
B(1.2,0.35,0)
T
CF
=33N
The triangular plate
ABC
is supported by ball-
and-socket joints at
B
and
D
and is held in the
position shown by cables
AE
and
CF
. If the force
exerted by cable
CF
at
C
is 33 N, determine the
moment of that force about the line joining Points
D
and
B
.
F(0.6,0,-0.6)
r

Sample Problem
The triangular plate
ABC
is supported by ball-
and-socket joints at
B
and
D
and is held in the
position shown by cables
AE
and
CF
. If the force
exerted by cable
CF
at
C
is 33 N, determine the
moment of that force about the line joining Points
D
and
B
.
x
y
z
C(0,0.9,-0.4)
D(0,0.7,0)
B(1.2,0.35,0)
T
CF
=33N
F(0.6,0,-0.6)
r

Fundamental Concepts
•
A Couple
15
A
couple
is an interaction involving multiple forces that produce no
translation, but only rotation; in other words, the couple produces net
moment, but zero force.

Fundamental Concepts
•
A Couple
16
The net moment of a couple formed by two equal and opposite forces is the
same about all points.
∑M|
O
=F(0)+F(d)=Fd
∑M|
P
=F(d)+F(0)=Fd
∑M|
Q
=F(d
Q
)−F(d
Q
−d)=F(d
Q
)−F(d
Q
)+Fd=Fd
Fd
rF
M
F
r
M
sin
r

Fundamental Concepts
•
Equivalent Forces system
17
To preserve static equivalency when changing the point of application of a
force to a new line of action, one must also apply a couple. The couple
restores the original tendency to rotate, the moment, without altering the
sum of forces. The additional couple must be equal to the moment of the
original force about the point to which the force has been moved.

Fundamental Concepts
•
Equivalent Forces System
18
A system of forces may be replaced by a collection of force-couple systems acting at a
given point O. The force and couple vectors may be combined into a resultant force
vector and a resultant couple vector,
R
O
R
F
M
r
F

Sample Problem