For 3D moments I will use r cross F
[
]
[
]
[
] [
]
[
]
N
i
k
j
k
M
Nm
k
j
i
x
j
i
M
N
k
j
i
F
m
k
j
i
r
xF
r
M
P
P
AB
AB
A
720
720
)
120
(
60
)
(
600
300
600
2
.
1
2
.
0
600
300
600
0
2
.
1
2
.
0


+


=

+
+
=

+
=
+
+
=
=
Combining Similar terms
[
]
Nm
k
j
i
M
P
660
120
720

+

=
Want to find moment about xaxis
Convert to meters
[
]
[
]
[
] [
]
[
]
Nm
i
j
i
k
M
Nm
k
j
i
x
k
j
M
N
k
j
i
F
m
k
j
i
r
xF
r
M
P
P
AB
AB
A
)
6
.
3
(
)
2
.
1
(
15
.
0
)
3
.
0
(
)
(
2
12
4
3
.
0
075
.
0
2
12
4
3
.
0
075
.
0
0


+
+

=
+

+
=
+

=
+
+
=
=
Combining Similar terms
[
]
Nm
k
j
i
M
P
3
.
0
2
.
1
75
.
3

+
=
Need only i term or dot with unit vector i.
Nm
M
P
75
.
3
=
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Sum the moments about point A
They have to be equal to zero so there is
no couple
[
]
[
]
[
] [
]
[
]
Nmm
k
Nk
Nmm
Nj
i
x
j
i
M
N
Nj
i
F
mm
j
j
j
i
r
xF
r
M
P
AB
AB
A
1125
3
.
43
0
)
(
15
75
3
.
43
0
15
30
sin
50
25
25
30
cos
50
0

=
+


=
=
+
=




=
=
=
o
o
All Similar terms drop k and equate
N
N
Nmm
N
mm
0
.
26
)
(
1125
)
(
3
.
43
=
=
Sum the moments about point A
Goes to zero, neglect force at B
0
=
∑
A
M