ME 221 Statics
Lecture #24
Sections 5.1 – 5.7
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Homework #9
Chapter 5 problems:
– 53, 54, 56, 62, 64, 69, 71 & 73
• Due Friday, October 31
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Last Lecture
• Equilibrium in 3 Dimensions
• Statically Indeterminate Reactions
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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
ME 221
x
0
y
0
z
0
M
M
M
Lecture 24
x
0
y
0
z
0
4
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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Equilibrium Equations
If there are more than 6 unknown forces or couples,
the problem is statically indeterminate.
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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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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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