ME 221 Statics
Lecture #13
Sections 5.1 – 5.7
Exam #2 Review
ME221
Lecture 13
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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 Wednesday, June 23
ME221
Lecture 13
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Homework #6
• Chapter 7 problems:
– 6, 19 & 26
• Chapter 6 problems
– 3&6
– Due Monday, June 28
• MatLab Group Problems
– 7.19, 7.26 & 6.15
– Due Monday, June 28
ME221
Lecture 13
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Exam #2
Monday, June 21
Details at end of lecture
ME221
Lecture 13
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Chapter 5
Equilibrium of Rigid Bodies
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Lecture 13
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Last Lecture
• Equilibrium in 3 Dimensions
• Statically Indeterminate Reactions
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Lecture 13
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Equilibrium Equations
We have examined 2-dimensional systems and analyzed their
equilibrium conditions using the following:
F  0
~
and
M  0
~
The equilibrium conditions we used may be expressed as:
F
F
F
ME221
x
0
y
0
z
0
M
M
M
Lecture 13
x
0
y
0
z
0
7
Equilibrium Equations
For 3-dimensional systems, we use the same equilibrium
equations, except we write them in vector form:
The moment equation may also be written as:
Where the couple C is the sum of all applied couples on the body
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Lecture 13
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Equilibrium Equations
If there are more than 6 unknown forces or couples,
the problem is statically indeterminate.
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Lecture 13
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Solving Equilibrium Equations
Draw a proper free body diagram
Write each force and couple as a vector
Draw position vectors from the origin to the
line of action of each force
Write the vector equations of static
equilibrium – 6 equations, 6 unknowns
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Lecture 13
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Statically Indeterminate Reactions
Underconstrained system
Cannot maintain equilibrium
Overconstrained systems
More unknown forces than equations
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Equilibrium Example Problems
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Exam #2
• Chapter 4
Center of mass
Centroids of areas and volumes
Centroids of composite bodies
Distributed loads on beams
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Exam #2
Chapter 9: Moments of Inertia
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Second Moment of Area; Ixx & Iyy
Polar Moments; J0z
Parallel Axis Theorem
Composite Areas
Principal Second Moments
Product Moments; Ixy
Mohr’s Circle – Imax & Imin
Lecture 13
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Exam #2
Chapter 5: Equilibrium of Rigid Bodies
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Equilibrium Equations
Supports
Free Body Diagrams
Two-Force Members
3D Equilibrium
Lecture 13
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