To form a reinforced box section, two rolled \( W \) sections and two plates are welded together. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal axes shown. Consider \( w = 6.25 \, \text{mm} \).### Diagram DescriptionThe diagram shows a reinforced box section comprising two rolled \( W \) sections with a notation of \( W200 \times 46.1 \). A vertical axis \( y \) and a horizontal axis \( x \) are shown intersecting at the centroid \( C \). The width of the section is labeled as \( 203 \, \text{mm} \). The thickness \( w \) of the welded plates is noted to be \( 6.25 \, \text{mm} \).### Calculations#### Moment of Inertia- The moment of inertia \( \bar{I}_x \) with respect to the \( x \)-axis: \[ \bar{I}_x = \boxed{} \times 10^6 \, \text{mm}^4 \]- The moment of inertia \( \bar{I}_y \) with respect to the \( y \)-axis: \[ \bar{I}_y = \boxed{} \times 10^6 \, \text{mm}^4 \]#### Radii of Gyration- The radii of gyration \( \bar{k}_x \) with respect to the \( x \)-axis: \[ \bar{k}_x = \boxed{} \, \text{mm} \]- The radii of gyration \( \bar{k}_y \) with respect to the \( y \)-axis: \[ \bar{k}_y = \boxed{} \, \text{mm} \]

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To form a reinforced box section, two rolled W sections and two plates are welded together. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal axes shown. Consider w= 6.25 mm. W200 × 46.1 203 mm- The moment of inertia I, is 106 mm4. The radii of gyration kx is mm. The moment of inertia I, is 106 mmª. The radii of gyration ky is mm.

To form a reinforced box section, two rolled W sections and two plates are welded together. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal axes shown. Consider w= 6.25 mm. W200 × 46.1 203 mm- The moment of inertia I, is 106 mm4. The radii of gyration kx is mm. The moment of inertia I, is 106 mmª. The radii of gyration ky is 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.

Question

To form a reinforced box section, two rolled \( W \) sections and two plates are welded together. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal axes shown. Consider \( w = 6.25 \, \text{mm} \).

### Diagram Description

The diagram shows a reinforced box section comprising two rolled \( W \) sections with a notation of \( W200 \times 46.1 \). A vertical axis \( y \) and a horizontal axis \( x \) are shown intersecting at the centroid \( C \). The width of the section is labeled as \( 203 \, \text{mm} \). The thickness \( w \) of the welded plates is noted to be \( 6.25 \, \text{mm} \).

### Calculations

#### Moment of Inertia
- The moment of inertia \( \bar{I}_x \) with respect to the \( x \)-axis:
\[
\bar{I}_x = \boxed{} \times 10^6 \, \text{mm}^4
\]

- The moment of inertia \( \bar{I}_y \) with respect to the \( y \)-axis:
\[
\bar{I}_y = \boxed{} \times 10^6 \, \text{mm}^4
\]

#### Radii of Gyration
- The radii of gyration \( \bar{k}_x \) with respect to the \( x \)-axis:
\[
\bar{k}_x = \boxed{} \, \text{mm}
\]

- The radii of gyration \( \bar{k}_y \) with respect to the \( y \)-axis:
\[
\bar{k}_y = \boxed{} \, \text{mm}
\]

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