### 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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Answered: -7 Determine Ix and Iy for the cross-…

Engineering

Civil Engineering

-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

Problem 1P

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Concept explainers

Connections

In steel structures, connections are the members that join two or more steel members. The connections are the most important members of any steel structure, and hence, they are designed more carefully. The majority of the construction cost of steel structures is incurred due to the connections. The design of connections is done as per the recommendations and specifications of the American Institute of Steel Construction (AISC).

Question

### 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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