457
SOLUTION
Force And Position Vectors. The coordinates of points A, B, and C are
A(6, 0, 0) m,
B(0, –3, 2) m
and
C(0, 0, 2) m
respectively.
Referring to the FBD of the rod shown in Fig. a, the force equation of equilibrium
gives
5–69.
Determine the tension in each cable and the components of
reaction at D needed to support the load.
C
z
B
x
y
3 m
2 m
6 m
30
A
D
458
Equating i, j and k components,
Moment equation of equilibrium gives
Equating j and k Components,
Solving Eqs. (1) to (5)
5–69. Continued
Ans:
459
5–70.
The stiff-leg derrick used on ships is supported by a ball-and-
socket joint at D and two cables BA and BC. The cables are
attached to a smooth collar ring at B, which allows rotation
of the derrick about z axis. If the derrick supports a crate
having a mass of 200 kg, determine the tension in the cables
and the x, y, z components of reaction at D.
z
y
B
D
7.5 m
6 m
6 m
2 m
C
1 m
SOLUTION
Ans:
460
SOLUTION
Force And Position Vectors. The coordinates of points A, B, C, D and E are
A(0, 0, 0),
B(6, 0, 0),
C(0, –2, 3) m,
D(0, 2, 3) m
and
E(3, 0, 0) m
respectively.
Equations of Equilibrium. Referring to the FBD of the rod shown in Fig. a, the force
5–71.
Determine the components of reaction at the ball-and-socket
joint A and the tension in each cable necessary for
equilibrium of the rod.
z
x
y
A
D
E
C
3 m
600 N
3 m
3 m
2 m
2 m
B
461
Equating i, j and k components,
The moment equation of equilibrium gives
Equating j and k components,
5–71. Continued
Ans:
462
*5–72.
Determine the components of reaction at the ball-and-
socket joint A and the tension in the supporting cables DB
and DC.
SOLUTION
Force And Position Vectors. The coordinates of points A, B, C, and D
800 N/m
1 m
1.5 m
1.5 m
1.5 m
3 m
B
z
C
A
D
463
*5–72. Continued
Equations of Equilibrium. Referring to the FBD of the assembly shown in Fig. a.
Force equation of equilibrium gives
Equating i, j and k components,
Moment equation of equilibrium gives
Equating i, j and k Components
Solving Eqs. (1) to (6)
464
5–73.
The bent rod is supported at A, B, and C by smooth journal
bearings. Determine the components of reaction at the bearings
if the rod is subjected to the force F = 800 N. The bearings are
in proper alignment and exert only force reactions on the rod.
z
y
2 m
2 m
0.75 m
1 m
30
60
C
A
B
x
SOLUTION
Equations of Equilibrium. The x, y and z components of force F are
Referring to the FBD of the bent rod shown in Fig. a,
Solving Eqs. (1) to (6)
465
5–74.
The bent rod is supported at A, B, and C by smooth journal
bearings. Determine the magnitude of F which will cause the
positive x component of reaction at the bearing C to be Cx
=
50N.
The bearings are in proper alignment and exert only force
reactions on the rod.
z
y
2 m
2 m
0.75 m
1 m
30
60
C
A
B
x
SOLUTION
Equations of Equilibrium. The x, y and z components of force F are
Here, it is required that
Cx=50
. Thus, by referring to the FBD of the beat rod
shown in Fig. a,
Solving Eqs. (1) to (4)
466
5–75.
Member AB is supported by a cable BC and at A by a
square rod which fits loosely through the square hole in the
collar fixed to the member as shown. Determine the
components of reaction at A and the tension in the cable
needed to hold the rod in equilibrium.
B
1.5 m
400 N
200 N
1 m
3 m
C
z
x
y
A
SOLUTION
Force And Position Vectors. The coordinates of points B and C are
B(3, 0, –1) m
C(0, 1.5, 0) m,
respectively.
Equations of Equilibrium. Referring to the FBD of member AB shown in Fig. a, the
force equation of equilibrium gives
Equating i, j and k components
467
Ans:
TBC =1.40 kN
5–75. Continued
The moment equation of equilibrium gives
Equating i, j, and k components,
Solving Eqs. (1) to (6),
TBC =1400 N =1.40 kN
Ax=1200 N =1.20 kN
468
*5–76.
The member is supported by a pin at A and cable BC.
Determine the components of reaction at these supports if
the cylinder has a mass of 40 kg.
SOLUTION
Force And Position Vectors. The coordinates of points B, C and D are
B(0, –0.5, 1) m
,
C(3, 1, 0) m
and
D(3, –1, 0) m
, respectively.
Equations of Equilibrium. Referring to the FBD of the assembly shown in Fig. a. the
force equation of equilibrium gives
Equating i, j and k components
The moment equation of equilibrium gives
C
0.5 m
z
A
B
D
x
3 m
1 m
1 m
1 m
y