ME 201 Engineering Mechanics: Statics

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ME 201Engineering Mechanics Statics

• Chapter 4 Part C
• 4.7 Equivalent System
• 4.8 Resultants of a Force and Couple System
• 4.9 Further Reduction of a Force Couple System

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Movement of a Force on a Rigid Body

• What happens when a Force is moved on rigid body?
• Two effects to consider
• Translation
• Rotation

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Movement of a Force on a Rigid Body

• Case 1
• Point is on the line of action of the force

F
F
A
A
F
F


O
O
O
-F
Principle of Transmissibility The external
effects on a rigid body remain unchanged when a
force, acting at a given point on the body, is
applied to another point lying on the line of
action of the force. Internal effects may change.
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Movement of a Force on a Rigid Body

• Case 2
• Point is NOT on the line of action of the force

Mr x F
F
F
F
F
A
A
P


O
O
O
r
-F
Result is the introduction of a couple moment
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Resultants of a Force Couple System

• When a rigid body is subjected to a system of
  forces and couple moments, often simpler to work
  with resultant than individual forces or moments
• Simply Stated

2D Scalar Analysis
Vector Analysis
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Example Problem

• Given
• F1 600 N
• F2 100 N
• F3 400 N
• ? 40º
• Find
• FR, ?R, MA

F1
F3
.4m
F2
A
.3m
?
.4m
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Example Problem Solution
F1
F3
F2
.4m
A
.3m
?
.4m

• Given
• F1 600 N
• F2 100 N
• F3 400 N
• ? 40º
• Find
• FR, ?R, MA

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Example ProblemText Example 4.15, Page 170

• Given
• M, F1, F2
• Find
• FR, MRo

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Example Problem SolutionText Example 4.15, Page
170

• Given
• M, F1, F2
• Find
• FR, MRo
• Solution

O(0,0,0) B(-.15,.1,1) C(0,0,1)
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Further Reduction of a Force Couple System

• If a system of forces is
• Concurrent
• Coplanar
• Or
• Parallel
• It can always be reduced to a single resultant
  force FR acting through a unique point P

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Example Problem

• Given
• F1 100 N
• F2 200 N
• F3 400 N
• Find
• FR, d

FR
F1
F2
d

A
A
3m
2m
3m
F3
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Example ProblemSolution
FR
F1
F2
d

A
A
3m
2m
3m
F3

• Given
• F1 100 N
• F2 200 N
• F3 400 N
• Find
• FR, d

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Example Problem

• Given
• F1 500 N
• F2 600 N
• F3 100 N
• F4 400 N
• Find
• FR, dx, dy

z
z
F4
F1

FR
5m
D
5m
D
A
y
y
F3
F2
6m
dx
8m
dy
C
B
x
x
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Example Problem Solutions
z
z
F4
F1

FR
5m
D
5m
D
A
y
y
F3
F2
6m
dx
8m
dy
C
B
x
x

• Given
• F1 500 N
• F2 600 N
• F3 100 N
• F4 400 N
• Find
• FR, dx, dy

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Alternate Solution
z
z
F4
F1

FR
5m
D
5m
D
A
y
y
F3
F2
6m
dx
8m
dy
C
B
x
x

• Given
• F1 500 N
• F2 600 N
• F3 100 N
• F4 400 N
• Find
• FR, dx, dy