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Find the moment of inertia
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Answer to Problem 9.44P
The moment of inertia
Explanation of Solution
Calculation:
Show the area with parts of the section as Figure 1.
Calculate the centroid of the area as in Table 1.
Section | Area, A |
|
| ||
1 | 3.24 | 0.45 | |||
2 | 0.475 | 4.56 | |||
3 | 0.845 | 6.24 | |||
Total | 5.0 | 4.560 | 11.25 |
Calculate the centroid of the area with respect to x axis
Substitute
Calculate the centroid of the area with respect to y axis
Substitute
Consider the x axis.
Consider the section 1.
Calculate the moment of inertia of section 1
Calculate the centroid of section 1
Substitute 2.25 in. for
Calculate the moment of inertia of section 1
Substitute
Consider the section 2.
Calculate the moment of inertia of section 2
Calculate the centroid of section 2
Substitute 2.25 in. for
Calculate the moment of inertia of section 2
Substitute
Consider the section 3.
Calculate the moment of inertia of section 3
Calculate the centroid of section 3
Substitute 2.25 in. for
Calculate the moment of inertia of section 3
Substitute
Calculate the moment of inertia of entire section
Substitute
Consider the y axis.
Consider the section 1.
Calculate the moment of inertia of section 1
Calculate the centroid of section 1
Substitute 0.912 in. for
Calculate the moment of inertia of section 1
Substitute
Consider the section 2.
Calculate the moment of inertia of section 2
Calculate the centroid of section 2
Substitute 0.912 in. for
Calculate the moment of inertia of section 2
Substitute
Consider the section 3.
Calculate the moment of inertia of section 3
Calculate the centroid of section 3
Substitute 0.912 in. for
Calculate the moment of inertia of section 3
Substitute
Calculate the moment of inertia of entire section
Substitute
Therefore, the moment of inertia
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Chapter 9 Solutions
Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
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