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Determine the moment of inertia I, of the cross-sectional area shown with respect to the centroidal z-axis when t = 27 mm. The y-coordinate of the centroid is y = 54 mm.

Determine the moment of inertia I, of the cross-sectional area shown with respect to the centroidal z-axis when t = 27 mm. The y-coordinate of the centroid is y = 54 mm.

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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**Determining the Moment of Inertia** The problem involves calculating the moment of inertia \( I_z \) of a given cross-sectional area, measured with respect to the centroidal z-axis, when \( t = 27 \, \text{mm} \). The y-coordinate of the centroid is provided as \( \bar{y} = 54 \, \text{mm} \). ### Diagram Description: The diagram illustrates a T-shaped cross-section consisting of two rectangular components: 1. **Vertical Rectangle (Flange):** - Width: \( t \) - Height: \( 5t \) 2. **Horizontal Rectangle (Web):** - Width: \( 5t \) - Height: \( t \) The centroid location is marked by a black dot along the vertical axis at \( \bar{y} \). ### Calculations: The moment of inertia \( I_z \) has been calculated as: \[ I_z = 34421078.8 \times 10^6 \, \text{mm}^4 \] This value quantifies the resistance of the cross-section to bending or rotation about the z-axis.
Transcribed Image Text:**Determining the Moment of Inertia** The problem involves calculating the moment of inertia \( I_z \) of a given cross-sectional area, measured with respect to the centroidal z-axis, when \( t = 27 \, \text{mm} \). The y-coordinate of the centroid is provided as \( \bar{y} = 54 \, \text{mm} \). ### Diagram Description: The diagram illustrates a T-shaped cross-section consisting of two rectangular components: 1. **Vertical Rectangle (Flange):** - Width: \( t \) - Height: \( 5t \) 2. **Horizontal Rectangle (Web):** - Width: \( 5t \) - Height: \( t \) The centroid location is marked by a black dot along the vertical axis at \( \bar{y} \). ### Calculations: The moment of inertia \( I_z \) has been calculated as: \[ I_z = 34421078.8 \times 10^6 \, \text{mm}^4 \] This value quantifies the resistance of the cross-section to bending or rotation about the z-axis.
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