ME 201 Engineering Mechanics: Statics

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ME 201Engineering Mechanics Statics

• Chapter 5 Part B
• 5.3 Equations of Equilibrium
• 5.4 Two- and Three-Force Members

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Solving Problems

• Begin with FBD (Free Body Diagram)
• Use Equations of Equilibrium to formulate
  equations containing unknown forces, reactions,
  moments
• ? Fx 0 ? Fy 0 ? Mo 0
• Solve simultaneous equations (or look for
  equation with single unknown)

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Example Problem

• Given
• F1 600 N
• ? 45º
• F2 200 N
• F3 100 N
• Find
• Reactions at A, B

F2
F1
D
?
A
B
2m
3m
2m
F3
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Example Problem Solution
F2

• Given
• F1 600 N
• ? 45º
• F2 200 N
• F3 100 N
• Find
• Reactions at A, B
• Solution
• 1-FBD

F1
D
?
A
B
2m
3m
2m
F3
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Example Problem Solution

• Solution
• 1-FBD
• 2-Equilibrium Equations
• Can you find an equation with only 1 unknown?

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Example Problem Solution

• Solution
• 1-FBD
• 2-Equilibrium Equations

How can we check the results?
?Fy0
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Example Problem

• Given
• F1 100 N
• ? 30º
• Find
• T, A

A
?
T
F1
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Example Problem Solution

• Given
• F1 100 N
• ? 30º
• Find
• T, A
• Solution
• 1-FBD
• 2-Equilibrium Eqn

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Class Exercise Problems
2

• Given
• FC 60 N
• ? 30º
• MD 200 Nm
• Find
• Reactions at A, B

1
3
Given F1 400 N F2 200 N Find Reactions
at A
Given F 6 kN ? 60º mbeam 100 kg Tmax
800 N Find Reactions at A, d
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Class Exercise Problem 1

• Given
• F1 400 N
• F2 200 N
• Find
• Reactions at A
• Solution

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Class Exercise Problem 2

• Given
• FC 60 N
• ? 30º
• MD 200 Nm
• Find
• Reactions at A, B
• Solution

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Class Exercise Problem 3

• Given
• F 6 kN
• ? 60º
• mbeam 100 kg
• Tmax 800 N
• Find
• Reactions at A, d
• Solution

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2-Force Members

• If the following conditions exist
• Force applied at only 2 points on member
• No couples
• Called a 2-force member
• Then
• The line of action passes through points A B
• FA is equal and opposite in magnitude and
  direction to FB
• Rotational or moment equilibrium

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2-Force Members
B
B
A
B
A
A
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3-Force Members

• If a member is subjected to 3 coplanar forces,
  then it is necessary that the forces either be
  concurrent or parallel if the member is to be in
  equilibrium
• In other words, if not parallel, then the lines
  of action of the 3 forces must intersect at a
  single point
• The point of intersection may or may not be at
  the point of application of one of the forces

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3-Force Members
Given Simple Support _at_ B Pin Support _at_ A
B
P
W
A
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Example Problem

• Given
• F 8 kN
• Find
• A, BD

C
1m
B
D
F
.5m
A
30o
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Example Problem Solution

• Given
• F 8 kN
• Find
• A, BD
• Solution
• 1-FBD

Several possible FBDs
Most practical FBD
4 Unknowns
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Example Problem Solution

• Given
• F 8 kN
• Find
• A, BD
• Solution
• 1-FBD
• 2-Equil Eqn

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Class Exercise Problem 4

• Given
• F 400 N
• Find
• A, D

C
F
.5m
.2m
B
.2m
D
A
.1m
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Class Exercise Problem 4

• Given
• F 400 N
• Find
• A, D
• Solution