**Learning Goal:**To be able to use the parallel-axis theorem to calculate the moment of inertia for an area.The parallel-axis theorem can be used to find an area's moment of inertia about any axis that is parallel to an axis that passes through the centroid and whose moment of inertia is known. If \( x' \) and \( y' \) are the axes that pass through an area's centroid, the parallel-axis theorem for the moment about the x-axis, moment about the y-axis, and the polar moment of inertia is expressed by the following equation:\[ I_x = \bar{I}_{x'} + Ad_y^2 \]**Figure Explanation:**The figure illustrates a rectangle with a centroid labeled \( C \). The rectangle is placed in a coordinate system with axes \( x \) and \( y \). The following details are provided:- The rectangle has a width \( b \) and height \( h \).- The distance from the origin \( O \) to the centroid \( C \) horizontally is \( x_1 \).- The distance from the origin \( O \) to the centroid \( C \) vertically is \( y_1 \).This figure is used to demonstrate how to apply the parallel-axis theorem to calculate the moment of inertia for the given rectangular area. **Part B**As shown, a rectangle has a base of \( b = 5.80 \, \text{ft} \) and a height of \( h = 2.70 \, \text{ft} \). *(Figure 2)* The rectangle's bottom is located at a distance \( y_1 = 1.60 \, \text{ft} \) from the x-axis, and the rectangle's left edge is located at a distance \( x_1 = 2.50 \, \text{ft} \) from the y-axis. What are \( I_x \) and \( I_y \), the area’s moments of inertia, about the x and y axes, respectively?Express your answers numerically in biquadratic feet (feet to the fourth power) to three significant figures separated by a comma.[View Available Hint(s)]\[ I_x, I_y = \, \_\_\_ \, \text{ft}^4 \]

Answered: Image /qna-images/answer/0c25fa41-d16f-4842-9820-994ec769d403.jpg

Learning Goal: To be able to use the parallel-axis theorem to calculate the moment of inertia for an area. The parallel-axis theorem can be used to find an area's moment of inertia about any axis that is parallel to an axis that passes through the centroid and whose moment of inertia is known. If x' and y' are the axes that pass through an area's centroid, the parallel-axis theorem for the moment about the x axis, moment about the y axis, and the polar moment of inertia is expressed by the following equations: I₂ = Īr + Ad² Figure 151 'C < 2 of 3 >

Learning Goal: To be able to use the parallel-axis theorem to calculate the moment of inertia for an area. The parallel-axis theorem can be used to find an area's moment of inertia about any axis that is parallel to an axis that passes through the centroid and whose moment of inertia is known. If x' and y' are the axes that pass through an area's centroid, the parallel-axis theorem for the moment about the x axis, moment about the y axis, and the polar moment of inertia is expressed by the following equations: I₂ = Īr + Ad² Figure 151 'C < 2 of 3 >

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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Question

**Learning Goal:**

To be able to use the parallel-axis theorem to calculate the moment of inertia for an area.

The parallel-axis theorem can be used to find an area's moment of inertia about any axis that is parallel to an axis that passes through the centroid and whose moment of inertia is known. If \( x' \) and \( y' \) are the axes that pass through an area's centroid, the parallel-axis theorem for the moment about the x-axis, moment about the y-axis, and the polar moment of inertia is expressed by the following equation:

\[ I_x = \bar{I}_{x'} + Ad_y^2 \]

**Figure Explanation:**

The figure illustrates a rectangle with a centroid labeled \( C \). The rectangle is placed in a coordinate system with axes \( x \) and \( y \). The following details are provided:

- The rectangle has a width \( b \) and height \( h \).
- The distance from the origin \( O \) to the centroid \( C \) horizontally is \( x_1 \).
- The distance from the origin \( O \) to the centroid \( C \) vertically is \( y_1 \).

This figure is used to demonstrate how to apply the parallel-axis theorem to calculate the moment of inertia for the given rectangular area.

**Part B**

As shown, a rectangle has a base of \( b = 5.80 \, \text{ft} \) and a height of \( h = 2.70 \, \text{ft} \). *(Figure 2)* The rectangle's bottom is located at a distance \( y_1 = 1.60 \, \text{ft} \) from the x-axis, and the rectangle's left edge is located at a distance \( x_1 = 2.50 \, \text{ft} \) from the y-axis. What are \( I_x \) and \( I_y \), the area’s moments of inertia, about the x and y axes, respectively?

Express your answers numerically in biquadratic feet (feet to the fourth power) to three significant figures separated by a comma.

[View Available Hint(s)]

\[ I_x, I_y = \, \_\_\_ \, \text{ft}^4 \]

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