Concept explainers
9.41 through 9.44 Determine the moments of inertia
Fig. P9.43
Find the moment of inertia about x and y axis of the area with respect to centroid axes.
Answer to Problem 9.43P
The moment of inertia about x axis is
The moment of inertia about y axis is
Explanation of Solution
Calculation:
Sketch the cross section as shown in Figure 1.
Refer to Figure 1.
Find the area
Substitute
Find the area
Substitute
Find the total area (A) using the relation as follows:
Here,
Substitute
Refer to Figure 1.
Find the centroid
Find the centroid
Find the centroid
Find the centroid
Find the centroid
Substitute
Find the centroid
Substitute
Find the moment of inertia
Substitute
Find the moment of inertia
Substitute
Find the total moment of inertia
Substitute
Thus, the moment of inertia
Find the moment of inertia
Substitute
Find the moment of inertia
Substitute
Find the total moment of inertia
Substitute
Thus, the moment of inertia
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Chapter 9 Solutions
Vector Mechanics for Engineers: Statics
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