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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 Mechanics Section 3

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Page 1: 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

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

Page 2: 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

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

Page 3: 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

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

Page 4: 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

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

Page 5: 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

Problem 3-4

Determine the x, y and z components of the 50 lb force.

x

y

z

50 lb.

550400

Page 6: 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

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

Page 7: 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

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

Page 8: 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

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’

Page 9: 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

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

Page 10: 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

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

Page 11: 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

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

Page 12: 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

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