ENGR-1100 Introduction to Engineering Analysis

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ENGR-1100 Introduction to Engineering Analysis
Lecture 12
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Lecture Outline

• Rigid body equilibrium.
• FBD- Free Body Diagram.

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Rigid Bodies

• A rigid body is an ideal object that has
  dimensions and mass but does not deform under
  loading.
• The size and shape does significantly affect the
  response (reaction at supports) to applied
  force/s
• - A force applied to a rigid body may be
  translated along its line of action without
  altering its effects (principle of
  transmissibility)

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Necessary and Sufficient Conditions of
Equilibrium of a Rigid Body
The necessary AND sufficient condition for a
rigid body to be in equilibrium is that the
resultant force and couple acting on the rigid
body must be zero.
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3 independent equations in 2 D
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Isolation of bodies Free Body Diagram

• -In a system of interacting bodies, to be able to
  apply Newtons laws properly, a systematic
  technique is to
• isolate each of the bodies or a collection of
  bodies
• identify the forces acting on each of the
  bodies, and then
• apply the equilibrium equations to each.
• -The sketch of the isolated body or system of
  bodies considered as a single body, with all the
  external forces acting on it
• by mechanical contact with other bodies
• by gravitational attraction (weight)
• when the rest of the bodies are imagined to be
  replaced by their actions, it is known as a free
  body diagram.

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Isolation of bodies Free Body Diagram
The free body diagram is the most important
single step in the solution of problems in
mechanics.

• Remember
• The forces on the isolated body (or system of
  bodies) are to be considered.
• 2. Apply Newtons Third Law (every action has an
  equal, opposite and collinear reaction) carefully

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Steps of Drawing a FBD

• Clearly identify the body (or system of bodies)
  to be isolated (the FREE body).
• Draw a diagram of this free body completely
  isolated from the rest of the bodies.
• Traverse the boundary of this free body and
  indicate ALL forces acting ON the free body
  (contact forces with other bodies forces)
• Known forces Show vector arrows with proper
  magnitude (UNITS!!), direction and sense.
• Unknown magnitude but known direction of force
  Show vector arrows with magnitude assumed as
  positive (if calculations show that the magnitude
  is negative, the minus sign indicates that the
  sense is opposite to the one assumed)
• Unknown magnitude and direction of force Show
  x- and y- components of the vector with unknown
  magnitudes.
• 4. Show coordinate directions on the diagram

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Two-dimensional reaction at supports and
connections
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Three-dimensional reaction at supports and
connections
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Example P6-2
Draw complete free-body diagram of the beam shown
in Fig. P6-2, which has a mass m.
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Solution
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Class Assignment Exercise set 6-1, 6-3, 6-4,
6-10 please submit to TA at the end of the lecture
p
6-1
6-3
p
6-4
6-10
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Example P6-25
Draw complete free-body diagram of the bent bar
shown in Fig. P6-25. The support at A is a
journal bearing and the supports at B and C are
ball bearings.
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Solution
Known forces
Unknown forces
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Class Assignment Exercise set 6-22 6-24 please
submit to TA at the end of the lecture
p1
p2
p1
p2