ENGR 34
Chapter 10, Day 1
Moment of Inertia for Area
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a)
b)
c)
d)
e)
Integral definition
Parallel axis theorem
Composite body approach
Subtracting areas
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Moment of Inertia for Area
• Integration:
• Units: length4 (in4 or mm4)
• Used in beam deflection
and failure analysis
Parallel Axis Theorem
Axis
A
Which axis has
the smallest I?
d3
d2
d1
C
•
4
3
2
1
Composite Body Approach
• Each Ielement must share an axis
• Use parallel axis theorem
Subtracting regions
• Composite bodies also work in subtraction
• Element I’s must share an axis
=
Moment of Inertia for Area
Key Concepts
• Use composite body approach
• Use a table & subscripts
• Parallel axis theorem to bring to common point