ME 201 Engineering Mechanics: Statics

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ME 201Engineering Mechanics Statics

• Chapter 5 Part A
• 5.1 Conditions for Rigid-Body Equilibrium
• 5.2 Free-Body Diagrams

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Equilibrium

• For equilibrium
• Balance of forces
• Prevents translation
• Balance of moments
• Prevents rotation

? F 0
? M 0
We will use both scalar (2D) and vector (3D)
analysis methods
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Free Body Diagrams

• Sketch shape free from constraints connections
• Include external forces and couples
• Applied loadings
• Reactions at supports
• Weight of the body
• Include dimensions

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Support Reactions

• General conditions
• If a support prevents translation in a given
  direction, then a force is developed on the
  member in that direction
• If rotation is prevented, a couple moment is
  exerted on the member

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Common Support Reactions

• Simple Support
• Pin or Hinge Support
• Fixed Support

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Common Support Reactions

• Simple support (roller, smooth)
• 1 unknown
• Reaction normal to surface
• No moment

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Common Support Reactions

• Pin or Hinge Support
• 2 unknowns
• Components along X Y
• No moment

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Common Support Reactions

• Fixed Support
• 3 unknowns
• Components along X Y
• Moment

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More Support Reactions

• See Text, pages 205-206

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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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Freebody DiagramExample 1

• The beam has as mass of 100 kg.
• Draw FBD of beam

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Freebody DiagramExample 1
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Freebody DiagramExample 2

• Vertical force applied to pedal
• Force in link at B is 20 lb.
• Spring is stretched 1.5 in.
• Draw FBD of pedal

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Freebody DiagramExample 2
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Freebody DiagramExample 3

• Pipes have a mass of 300 kg each.
• Draw FBD of each pipe and both pipes together

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Freebody DiagramExample 3
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Freebody DiagramExample 4

• Platform has a mass of 200 kg
• Draw FBD of platform

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Freebody DiagramExample 4
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Freebody DiagramExample 5

• Draw the FBD of member AB

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Freebody DiagramExample 5
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Freebody DiagramExample 6

• Draw the FBD of member AB

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Freebody DiagramExample 6
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Freebody DiagramExample 7

• Draw the FBD of member AB

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Freebody DiagramExample 7
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Freebody DiagramExample 8

• Draw the FBD of the truss

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Freebody DiagramExample 8