Concept explainers
9.135 and 9.136 A 2-mm thick piece of sheet steel is cut and bent into the machine component shown. Knowing that the density of steel is 7850 kg/m3, determine the mass moment of inertia of the component with respect to each of the coordinate axes.
Fig. P9.135
Find the mass moment of inertia of the component with respect to
Answer to Problem 9.135P
The mass moment of inertia of the component with respect to
The mass moment of inertia of the component with respect to
The mass moment of inertia of the component with respect to
Explanation of Solution
Given information:
The thickness (t) of sheet steel is
The density
Calculation:
Sketch the sheet steel as shown in Figure 1.
Find the mass of rectangular section 1 as shown in below:
Here,
Express the volume of rectangular section 1 as follows:
Substitute
Find the mass of rectangular section 2 as shown in below:
Here,
Express the volume of rectangular section 2 as follows:
Substitute
Panel 1:
Find the moment of inertia about x axis for panel 1 as shown below:
Substitute
Find the moment of inertia about y axis for panel 1 as shown below:
Substitute
Find the moment of inertia about z axis for panel 1 as shown below:
Substitute
Panel 2:
Find the moment of inertia about x axis for panel 2 as shown below:
Substitute
Find the moment of inertia about y axis for panel 2 as shown below:
Substitute
Find the moment of inertia about z axis for panel 2 as shown below:
Substitute
Find the total mass of inertia
Here,
Substitute
Thus, the mass moment of inertia of the component with respect to
Find the total mass of inertia
Here,
Substitute
Thus, the mass moment of inertia of the component with respect to
Find the total mass of inertia
Here,
Substitute
Thus, the mass moment of inertia of the component with respect to
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Chapter 9 Solutions
Vector Mechanics for Engineers: Statics
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