Handout for TAM 210/211 BL1
posted 19 September, 2004
Things to keep in mind for finding special equipollent systems and resultants for a system of forces and couples
I.
Finding the “force couple resultant” (at point P) of a system of forces and couples
a.
Resultant Force
i.
The resultant force is found by simply adding all the forces, regardless of point P
∑
=
=
F
N
n
n
r
1
F
F
v
v
, where
F
N
refers to the number of applied forces
ii.
For finding the resultant force, I recommend the following steps:
1.
Express all forces in terms of their components in an appropriate coordinate system.
For this
class, this will usually be the Cartesian coordinate system, e.g.
k
j
i
F
z
y
x
n
n
n
n
F
F
F
+
+
=
v
2.
Add all forces by summing the components
(
)
(
)
(
)
k
j
i
k
j
i
F
F
...
...
...
2
1
2
1
2
1
1
1
+
+
+
+
+
+
+
+
=
+
+
=
=
∑
∑
=
=
z
z
y
y
x
x
F
z
y
x
F
F
F
F
F
F
F
F
F
F
N
n
n
n
n
N
n
n
r
v
v
b.
Resultant Moment at point P
i.
This is the
sum of the moments
with respect to point P of all forces and couples
∑
∑
∑
=
=
+
=
+
=
=
C
m
F
n
C
F
n
N
m
P
N
n
P
N
N
n
P
P
r
1
1
1
,
M
M
M
M
v
v
v
v
, where
F
N
refers to the number of applied forces, and
C
N
refers to
the number of applied couples
ii.
For finding the moments with respect to point P due to force
n,
n
P
M
v
1.
Express all forces in terms of their components in an appropriate coordinate system.
For this
class, this will usually be the Cartesian coordinate system, e.g.
k
j
i
F
z
y
x
n
n
n
n
F
F
F
+
+
=
v
2.
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 Fall '05
 Downing
 Cartesian Coordinate System, Force, resultant, couple resultant

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