Rigid Bodies:

1
Lecture 9

• Rigid Bodies
• Equivalent Force/Moment Systems

2
Forces and Moments

• The magnitude of a moment is defined as the
  product of the magnitude of the force and the
  perpendicular distance from the line of action of
  the force to the axis about which the moment is
  acting.

x
Counterclockwise rotation is positive.
3
Example 1

• Problem
• Determine the moment of F1 about B F2 about A
  F3 about C and E.

4
Example 1

• Solution
• (a) F1 about B

Ans.
(b) F2 about A
Ans.
5
Example 1

• (c) F3 about C

Ans.
6
Example 1

• (d) F3 about E

Ans.
Aside
7
Example 1

• The moment of a resultant about a point is equal
  to the sum of the moments of its components about
  the same point.

8
Example 1
Alternatively, to find the moment of F3 about E
Ans.
9
Example 2
F3 150 N
B
30º
F2 120 N
120 mm
A
E
D
160 mm
Ey
C
F1 90 N
350 mm
200 mm
140 mm

• Problem
• Determine the force Ey.

10
Example 2

• Equilibrium must apply, therefore the sum of the
  moments about a point must equal zero.

Ans.
11
Example 3

• Problem
• Determine the moment of F1 about point O and F2
  about point A.

12
Example 3

• Solution
• (a) F1 about point O

Ans.
13
Example 3

• (b) F2 about point A

Ans.
14
Example 4

• Problem
• Determine the moment of F1 and F2 about point A.

15
Example 4

• Solution
• (a) Find the rectangular components of F1 and F2

16
Example 4

• (b) Calculate the moment about point A.

Ans.
17
Additional Material

• Read Sections 3.4, 4.1-4.2
• Problems 3-42, 47, 50, 59, 70
• 4-5, 7, 9, 14, 19, 21