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Determine the moment of inertia of the area about the x-axis shown on the figure. -3 in. -3 2 in. y in.3 in.- B A 1 in. 2 in. 2 in. 4 in. x

Determine the moment of inertia of the area about the x-axis shown on the figure. -3 in. -3 2 in. y in.3 in.- B A 1 in. 2 in. 2 in. 4 in. x

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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9. What’s the inertia of the area at X-axis? Show your work.
### Calculation of Moment of Inertia for a T-Section This exercise involves determining the moment of inertia of a T-shaped area about the x-axis. The given figure illustrates a T-section with specific dimensions, and the coordinate axes are marked. #### Figure Analysis: - **T-Section Dimensions:** - The top flange of the T-section is 6 inches wide and 2 inches deep. - The web of the T-section extends 4 inches below the flange and is 1 inch wide. - **Points A and B:** - Point A is located at the bottom center of the T-section. - Point B is located at the junction of the flange and web, also along the vertical centerline. - **Coordinate Axes:** - The y-axis vertically bisects the T-section. - The x-axis intersects the bottom of the section (at point A). #### Detailed Dimensions: - Top flange horizontal dimension: 6 inches (3 inches to either side of the y-axis). - Thickness of top flange: 2 inches. - Web vertical dimension: 4 inches. - Web horizontal dimension: 1 inch (aligned centrally). The aim is to calculate the moment of inertia (I_x) of this T-section about the x-axis using these provided dimensions. ##### Graphical Explanation: The accompanying graph illustrates the T-shaped section with labeled dimensions, showcasing the symmetry and precise alignment with the coordinate axes. By using standard formulas for moments of inertia and leveraging the method of composite areas, the moment of inertia of the complete T-section about the x-axis can be determined accurately. This involves individual calculations for the flange and web sections, followed by combining the results to account for the placement of each segment relative to the x-axis.
Transcribed Image Text:### Calculation of Moment of Inertia for a T-Section This exercise involves determining the moment of inertia of a T-shaped area about the x-axis. The given figure illustrates a T-section with specific dimensions, and the coordinate axes are marked. #### Figure Analysis: - **T-Section Dimensions:** - The top flange of the T-section is 6 inches wide and 2 inches deep. - The web of the T-section extends 4 inches below the flange and is 1 inch wide. - **Points A and B:** - Point A is located at the bottom center of the T-section. - Point B is located at the junction of the flange and web, also along the vertical centerline. - **Coordinate Axes:** - The y-axis vertically bisects the T-section. - The x-axis intersects the bottom of the section (at point A). #### Detailed Dimensions: - Top flange horizontal dimension: 6 inches (3 inches to either side of the y-axis). - Thickness of top flange: 2 inches. - Web vertical dimension: 4 inches. - Web horizontal dimension: 1 inch (aligned centrally). The aim is to calculate the moment of inertia (I_x) of this T-section about the x-axis using these provided dimensions. ##### Graphical Explanation: The accompanying graph illustrates the T-shaped section with labeled dimensions, showcasing the symmetry and precise alignment with the coordinate axes. By using standard formulas for moments of inertia and leveraging the method of composite areas, the moment of inertia of the complete T-section about the x-axis can be determined accurately. This involves individual calculations for the flange and web sections, followed by combining the results to account for the placement of each segment relative to the x-axis.
### Calculation of Moment of Inertia Below is a diagram followed by a list of possible values for the moment of inertia, \( I \), in \( \text{in}^4 \). #### Diagram Explanation A horizontal line indicates the axis, \( x \). Centered above this line is a section labeled \( A \). This section is located between two distances, both labeled as 2 inches, with an additional section in the middle labeled as 1 inch. All the distances are evenly distributed along the axis. #### Options for Moment of Inertia, \( I \) 1. \( 62.7 \, \text{in}^4 \) 2. \( 58.7 \, \text{in}^4 \) 3. \( 347 \, \text{in}^4 \) 4. \( 14.7 \, \text{in}^4 \) 5. \( 359 \, \text{in}^4 \) 6. \( 26.7 \, \text{in}^4 \) Each option provides a potential value for the moment of inertia based on the given geometry in the diagram.
Transcribed Image Text:### Calculation of Moment of Inertia Below is a diagram followed by a list of possible values for the moment of inertia, \( I \), in \( \text{in}^4 \). #### Diagram Explanation A horizontal line indicates the axis, \( x \). Centered above this line is a section labeled \( A \). This section is located between two distances, both labeled as 2 inches, with an additional section in the middle labeled as 1 inch. All the distances are evenly distributed along the axis. #### Options for Moment of Inertia, \( I \) 1. \( 62.7 \, \text{in}^4 \) 2. \( 58.7 \, \text{in}^4 \) 3. \( 347 \, \text{in}^4 \) 4. \( 14.7 \, \text{in}^4 \) 5. \( 359 \, \text{in}^4 \) 6. \( 26.7 \, \text{in}^4 \) Each option provides a potential value for the moment of inertia based on the given geometry in the diagram.
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