Problem 3.152
y
0.35 m
0.875 m
G
H
O
0.925 m
0.75 m
A
z
0.5
B
0.5
D
x
0.75 m
C
m
m
The frame ACD is hinged at A
and D and is supported by a
cable which passes through a
ring at B and is attached to
hooks at G and H. Knowing
that the tension in the cable is
450 N, determine the moment
about the diagonal AD of the
force exerted on the frame by
portion BH of the cable.
P
Problem 3.152
y
0.35 m
Solving Problems on Your Own
0.875 m
G
H
O
0.925 m
0.75 m
A
z
0.5
B
m
0.5
D
x
0.75 m
C
m
P
The frame ACD is hinged at A
and D and is supported by a
cable which passes through a
ring at B and is attached to
hooks at G and H. Knowing
that the tension in the cable is
450 N, determine the moment
about the diagonal AD of the
force exerted on the frame by
portion BH of the cable.
1. Determine the moment MOL of a force about a given axis OL.
MOL is defined as
MOL = λ . MO = λ . ( r x F )
where λ is the unit vector along OL and r is a position vector from
any point on the line OL to any point on the line of action of F.
Problem 3.152 Solution
y
0.35 m
Determine the moment MAD of a
force about line AD.
0.875 m
G
H
O
0.925 m
0.75 m
TBH
A λ
AD
z
B
rB/A
0.5
m
0.5
MAD
m
AD
.(r
B/A
x TBH )
Where
λ AD =
D
x
0.75 m
C
MAD = λ
1
(4 i _ 3 k)
5
rB/A = (0.5 m ) i
P
( 0.375 ) 2 + ( 0.75 ) 2 + ( _ 0.75 ) 2
dBH =
= 1.125 m
450 N
( 0.375 i + 0.75 j _ 0.75 k )
1.125
TBH =
= ( 150 N) i + ( 300 N) j _ ( 300 N) k
Problem 3.152 Solution
y
0.35 m
0.875 m
G
Finally:
H
MAD = λ AD . ( rB/A x TBH )
O
0.925 m
0.75 m
TBH
A λ
AD
z
rB/A
0.5
m
B
0.5
MAD
D
x
0.75 m
C
m
P
MAD =
=
1
5
_
4
0
3
1
0.5 0
0
5
_
150 300 300
[(_3)(0.5)(300)]
MAD = _ 90 N. m