PROBLEM 4.21
The 40-ft boom AB weighs 2 kips; the distance from the
axle A to the center of gravity G of the boom is 20 ft. For
the position shown, determine (a) the tension T in the cable,
(b) the reaction at A.
SOLUTION
AD
( AB )sin10
AD
6.9459 ft
MA
0: T ( AD )
T
29.924 kips
(40 ft)sin10
2(20 cos 30 ) 5(40 cos 30 )
0
T
Fx
Fy
0:
Ax
(29.924) cos 20
Ax
28.119 kips
0: Ay
Ay
A
(29.924) sin 20
29.9 kips
0
2 5
0
17.2346 kips
28.119 2 17.2346 2
tan
1
31.5
32.980 kips
17.2346
28.119
A
33.0 kips
31.5°
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PROBLEM 4.47
Determine the range of allowable values of the tension in wire
BD if the magnitude of the couple at the fixed support C is not
to exceed 100 N · m.
SOLUTION
MC
0: (750 N)(0.5 m) (450 N)(0.4 m)
12
T (0.15 m) M C
13
375 N m 180 N m
T
5
T (0.6 m)
13
0
4.8
m T
13
MC
0
13
(555 M C )
4.8
For
MC
100 N m: T
13
(555 100) 1232 N
4.8
For
MC
100 N m: T
13
(555 100) 1774 N
4.8
For
|M C | 100 N m:
1.232 kN T
1.774 kN
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PROBLEM 4.59
Eight identical 500 750-mm rectangular plates, each of mass m 40 kg, are held in a vertical plane as
shown. All connections consist of frictionless pins, rollers, or short links. In each case, determine whether
(a) the plate is completely, partially, or improperly constrained, (b) the reactions are statically determinate
or indeterminate, (c) the equilibrium of the plate is maintained in the position shown. Also, wherever
possible, compute the reactions.
SOLUTION
1.
Three non-concurrent, non-parallel reactions:
(a)
Plate: completely constrained
(b)
Reactions: determinate
(c)
Equilibrium maintained
A
2.
Three non-concurrent, non-parallel reactions:
(a)
Plate: completely constrained
(b)
Reactions: determinate
(c)
Equilibrium maintained
B
3.
0, C
D 196.2 N
Four non-concurrent, non-parallel reactions:
(a)
Plate: completely constrained
(b)
Reactions: indeterminate
(c)
Equilibrium maintained
(A y
4.
C 196.2 N
Ax
294 N
Dy
392 N )
,
Dx
294 N
Three concurrent reactions (through D):
(a)
Plate: improperly constrained
(b)
Reactions: indeterminate
(c)
No equilibrium
( MD
0)
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PROBLEM 4.59 (Continued)
5.
Two reactions:
(a)
Plate: partial constraint
(b)
Reactions: determinate
(c)
Equilibrium maintained
C D 196.2 N
6.
Three non-concurrent, non-parallel reactions:
(a)
Plate: completely constrained
(b)
Reactions: determinate
(c)
Equilibrium maintained
B
7.
8.
, D 491 N
294 N
53.1°
Two reactions:
(a)
Plate: improperly constrained
(b)
Reactions determined by dynamics
(c)
No equilibrium
( Fy
0)
Four non-concurrent, non-parallel reactions:
(a)
Plate: completely constrained
(b)
Reactions: indeterminate
(c)
Equilibrium maintained
B
Dy
(C D x
0)
196.2 N
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