deals with the effect of forces on three-dimensional rigid bodies. approach is the similar to 2-d...
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Deals with the effect of forces
on three-dimensional
rigid bodies.
Approach is the similar to 2-D Forces will be resolved into 3 components Moments are computed relative to an axis.
Spatial MechanicsSection 3
Components given the line of action.
Use proportions
where:
Force Components
z
z
y
y
x
x
d
F
d
F
d
F
d
F
F
dz
x
y
z
dy
dx
d
222zyx dddd
Problem 3-1
Determine the x, y and z components of the 300 lb force.
300 lbs
4 ft
5 ft
6 ftx
y
z
Components given directional angles.
Resolve into vertical (y) and horizontal components Resolve horizontal component into x & z component
Force Components
x
y
z
F
1 2
Problem 3-4
Determine the x, y and z components of the 50 lb force.
x
y
z
50 lb.
550400
Static Equilibrium
Machine component is in static equilibrium when the combination of all forces, in all three directions, is zero.
Fx = 0 Fy = 0 Fz = 0
Static Equilibrium
In addition, the net effect of all moments, about all axes (with any arbitrary origin), must also result in zero.
x = 0 y = 0 z = 0
Problem 3-7
The 400 lb plate is supported by the three cables. Determine the tension in each cable.
B
A
C
2’
4’
3’3’1’
Problem 3-10
Determine the forces at A and B to keep the bracket in equilibrium.
x
y
z
150 lbs
250
400
4 in
2 in
1 in
1 in
A
B
2 in
Problem 3-12
Determine the torque required from the flexible coupling to drive the following shaft. Also, determine the bearing reactions.
X
Y
Z
3
8 in10 in
5 in
600 lb
A
B
2
7
7
200 lb
T
Problem 3-13
Determine the required force P and the bearing reactions at A and B, to keep the winch in equilibrium.
X
Y
Z
12 in
8 in
10 in
6 in
5 in
600 lb
P
A
B
Problem
Determine the required force P and the bearing reactions at A and B, to keep the winch in equilibrium.
P
12 in
8 in
10 in
6 in
5 in
600 lbA
B
750650