### Moment of Inertia Calculation**Problem 10-42:****Objective:** Determine the moment of inertia of the beam's cross-sectional area about the x-axis.**Diagram Explanation:** The diagram illustrates the cross-section of a beam resembling a channel shape. The beam sections are dimensioned as follows:- Top flange: 30 mm height- Web height: 140 mm- Bottom flange: 30 mm height- Web width: 70 mm- Overall width including flanges: 170 mm- Each flange (top and bottom) extends 30 mm beyond the web.**Coordinate System:**- The origin is positioned at the centroid (C) of the cross-section.- x-x' axis runs horizontally through the centroid (C).- y-y' axis runs vertically through the centroid (C).To solve for the moment of inertia about the x-axis, decompose the cross-section into simpler geometric shapes and calculate their individual moments of inertia, applying the parallel axis theorem if necessary. Add these to obtain the total moment of inertia about the x-axis.

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Engineering

Mechanical Engineering

10-42. Determine the moment of inertia of the beam's cross- sectional area about the x axis. 30 mm

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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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

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### Moment of Inertia Calculation

**Problem 10-42:**

**Objective:**
Determine the moment of inertia of the beam's cross-sectional area about the x-axis.

**Diagram Explanation:**
The diagram illustrates the cross-section of a beam resembling a channel shape. The beam sections are dimensioned as follows:

- Top flange: 30 mm height
- Web height: 140 mm
- Bottom flange: 30 mm height
- Web width: 70 mm
- Overall width including flanges: 170 mm
- Each flange (top and bottom) extends 30 mm beyond the web.

**Coordinate System:**

- The origin is positioned at the centroid (C) of the cross-section.
- x-x' axis runs horizontally through the centroid (C).
- y-y' axis runs vertically through the centroid (C).

To solve for the moment of inertia about the x-axis, decompose the cross-section into simpler geometric shapes and calculate their individual moments of inertia, applying the parallel axis theorem if necessary. Add these to obtain the total moment of inertia about the x-axis.

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