-7 Determine Ix and Iy for the cross- sections 6" 2" 12'

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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### Transcription and Explanation

**6.7 Determine \( I_x \) and \( I_y \) for the cross-sections**

**Description:**

The hand-drawn diagram depicts a cross-section resembling an I-shaped beam. The dimensions of the beam are marked throughout.

- **Top Flange:**
  - Width: 6 inches
  - Thickness: 2 inches
  
- **Bottom Flange:**
  - Total width: 12 inches
  - Thickness: 2 inches

- **Web:**
  - Height: 6 inches
  - Width: 2 inches

- **Note on Widths:**
  - The top flange divides into three equal segments, each 2 inches wide.
  - The bottom flange consists of two outer segments, each 5 inches, and a central segment of 2 inches, totaling a width of 12 inches.

**Task:**
The objective is to calculate the moment of inertia about the x-axis (\( I_x \)) and y-axis (\( I_y \)) for the given cross-sectional area.

### Explanation:

To determine \( I_x \) and \( I_y \), one would generally use the formulas for the moment of inertia of composite areas. This involves dividing the section into simpler shapes, calculating the moment of inertia for each, and then using the parallel axis theorem as needed to find the total inertia for the whole section.
Transcribed Image Text:### Transcription and Explanation **6.7 Determine \( I_x \) and \( I_y \) for the cross-sections** **Description:** The hand-drawn diagram depicts a cross-section resembling an I-shaped beam. The dimensions of the beam are marked throughout. - **Top Flange:** - Width: 6 inches - Thickness: 2 inches - **Bottom Flange:** - Total width: 12 inches - Thickness: 2 inches - **Web:** - Height: 6 inches - Width: 2 inches - **Note on Widths:** - The top flange divides into three equal segments, each 2 inches wide. - The bottom flange consists of two outer segments, each 5 inches, and a central segment of 2 inches, totaling a width of 12 inches. **Task:** The objective is to calculate the moment of inertia about the x-axis (\( I_x \)) and y-axis (\( I_y \)) for the given cross-sectional area. ### Explanation: To determine \( I_x \) and \( I_y \), one would generally use the formulas for the moment of inertia of composite areas. This involves dividing the section into simpler shapes, calculating the moment of inertia for each, and then using the parallel axis theorem as needed to find the total inertia for the whole section.
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