ME 221 Statics
Lecture #11
Sections 5.1 – 5.5
ME221
Lecture 11
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Homework #4
• Due Today
ME221
Lecture 11
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Homework #5
• Chapter 9 problem:
– 43
• Chapter 5 problems
– 11, 20, 56 & 69
– Due Monday, June 21
• MatLab Group Problems
– 5.22, 5.37 & 5.58
– Due Monday, June 21
ME221
Lecture 11
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Quiz #5
Wednesday, June 16
ME221
Lecture 11
4
Chapter 5
Equilibrium of Rigid Bodies
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Lecture 11
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Equilibrium of Rigid Bodies
• Equilibrium equations
• Free body diagrams
• Modeling supports
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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 11
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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Lecture 11
• clamps
• slots
• collars
9
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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Special Cases
•Equilibrium of Rigid Bodies
- 2D & 3D
Two- and Three-Force Members
Special Supports
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Two- and Three-Force Members
F2
F1
Two-Force Members
F3
When the member is not subjected to
a couple and the forces are applied
only at two points, the member is
said to be two-force member.
A
B
F6
Let:

 


 

FA  F1  F2  F3 and FB  F4  F5  F6
F4
F5
FA
These forces will maintain equilibrium if:
A


FA   FB
B
(FA and FB must be collinear)
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FB
Lecture 11
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Two- and Three-Force Members
Three-Force Members
If the member is subjected to three coplanar forces, then it is
necessary that the forces are either concurrent or parallel if the
member is to be in equilibrium.
F2
O

F3
F1
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Lecture 11
F3
F2
F1
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Note:
• It should be noted that single bearing, single
pin and single hinge supports can support
both forces and couples. Most often,
however, these supports are used in
conjunction with other bearings, pins or
hinges to hold the body in equilibrium. In
this case, the force reaction at the support
may be adequate.
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Chapter 5 Equilibrium Examples
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