ME 221 Statics
Lecture #21
Sections 5.1 – 5.4
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Homework #8
• Chapter 9 problems:
– 42, 43, 50 & 55
• Chapter 5 problems:
– 11, 13, 16, 20, 24 & 25
– See Angel for additional information
• Due Friday, October 24
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Quiz #5
Friday, October 24
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Note:
No office hours on Tuesday, October 21
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Chapter 5
Equilibrium of Rigid Bodies
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Equilibrium of Rigid Bodies
• Equilibrium equations
• Free body diagrams
• Modeling supports
• Example
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Equilibrium of Rigid Bodies
• Newton’s Second law states that if there is a
net force acting on a body, then this will cause
motion of the rigid body.
• If there is no motion, then the object is said to
be in equilibrium.
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Equilibrium Equations
When the force system is replaced by a resultant force and
moment that are zero, the rigid body is in equilibrium.
F  0
~
and
M  0
~
The moment equation is new and differentiates particle from
rigid body equilibrium.
F
F
F
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x
0
y
0
z
0
M
M
M
Lecture 21
x
0
y
0
z
0
8
Supports for Rigid Bodies
If a rigid object is subjected to some set of forces
but does not move, then its motion could be
restrained by a normal force exerted by the ground,
a wall or from fixing the object with some support.
Examples of supports:
• rollers
• cables
• smooth surfaces • links
• rockers
• fixed
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• clamps
• slots
• collars
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Support Reactions
• If the support prevents translation in a given
direction, then a force is developed on the member
in that direction. Likewise, if a rotation is
prevented, then a couple moment is exerted on the
member.
• See Figures 5.3, 5.9 and 5.10 (supports for
rigid bodies subjected to 2-D and 3-D force
systems)
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Free Body Diagram
• Draw the body separate from all other bodies
(including ground).
• Draw the magnitudes and directions of all external
forces acting on the body.
– Include: applied loads, reactions due to supports, and
the weight of the object.
– No need to scale arrow size
• Include necessary dimensions of the body
– Dimensions are needed for summing moments
• Draw the positive sense of the coordinate system
used to write out equilibrium equations
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Importance of FBD
• The FBD is at least half of an
equilibrium problem.
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Chapter 5 Equilibrium Examples
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