Download PROBLEM 3.55

PROBLEM 3.55
The 23-in. vertical rod CD is welded to the midpoint C of
the 50-in. rod AB. Determine the moment about AB of the
235-lb force P.
SOLUTION
AB
(32 in.)i (30 in.) j (24 in.)k
(32) 2
AB
AB
AB
AB
( 30) 2
( 24) 2
50 in.
0.64i 0.60 0.48k
We shall apply the force P at Point G:
rG /B
(5 in.)i (30 in.)k
DG
(21 in.)i (38 in.) j (18 in.)k
DG
(21) 2
( 38) 2
DG
DG
(235 lb)
(18) 2
47 in.
21i 38 j 18k
47
P
P
P
(105 lb)i (190 lb) j (90 lb)k
The moment of P about AB is given by Eq. (3.46):
MAB
M AB
AB
(rG /B P)
0.64
5 in.
105 lb
0.60
0.48
0
30 in.
190 lb 90 lb
0.64[0 (30 in.)( 190 lb)]
0.60[(30 in.)(105 lb) (5 in.)(90 lb)]
0.48[(5 in.)( 190 lb) 0]
2484 lb in.
M AB
207 lb ft
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PROBLEM 3.59
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 AE at A is
55 N, determine the moment of that force about the line
joining Points D and B.
SOLUTION
First note:
TAE
AE
Then
TAE
Also,
DB
TAE
AE
AE
(0.9) 2
( 0.6) 2
(0.2) 2
1.1 m
55 N
(0.9i 0.6 j 0.2k )
1.1
5[(9 N)i (6 N) j (2 N)k ]
(1.2)2
( 0.35)2
(0)2
1.25 m
Then
DB
Now
M DB
where
rA /D
Then
M DB
DB
DB
1
(1.2i 0.35 j)
1.25
1
(24i 7 j)
25
DB
(rA/D TAE )
(0.1 m) j (0.2 m)k
24
1
(5) 0
25
9
7
0
0.1 0.2
6
2
1
( 4.8 12.6 28.8)
5
or M DB
2.28 N m
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 3.60
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.
SOLUTION
First note:
TCF
CF
Then
TCF
Also,
DB
TCF
CF
CF
(0.6) 2
( 0.9) 2
( 0.2) 2
1.1 m
33 N
(0.6i 0.9 j 0.2k )
1.1
3[(6 N)i (9 N) j (2 N)k ]
(1.2)2
( 0.35)2
(0)2
1.25 m
DB
DB
1
(1.2i 0.35 j)
1.25
1
(24i 7 j)
25
Then
DB
Now
M DB
where
rC/D
(0.2 m) j (0.4 m)k
M DB
24
7
1
(3) 0 0.2
25
6
9
Then
DB
(rC/D TCF )
0
0.4
2
3
( 9.6 16.8 86.4)
25
or M DB
9.50 N m
Copyright © McGraw-Hill Education. Permission required for reproduction or display.