3. The beam is made of steel that has an allowable stress of oallow = 40 ksi. Determine the largest internal moment the beam can resist if the moment is applied (a) about the z axis, (b) about the y axis. -3 in + 0.25 in. 0.25 in. 3 in. 3 in. 3 in. 10.25 in.
3. The beam is made of steel that has an allowable stress of oallow = 40 ksi. Determine the largest internal moment the beam can resist if the moment is applied (a) about the z axis, (b) about the y axis. -3 in + 0.25 in. 0.25 in. 3 in. 3 in. 3 in. 10.25 in.
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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![### Problem Statement:
The beam is made of steel that has an allowable stress of \(\sigma_{\text{allow}} = 40 \text{ ksi}\). Determine the largest internal moment the beam can resist if the moment is applied
(a) about the z axis,
(b) about the y axis.
### Diagram Details:
The image displays a cross-sectional view of the beam with labeled dimensions:
- **Top and Bottom Flanges:**
- Width: \(3 \text{ in.}\)
- Thickness: \(0.25 \text{ in.}\)
- **Web:**
- Height: \(3 \text{ in.}\)
- Thickness: \(0.25 \text{ in.}\)
### Analysis:
To solve the problem, one would typically use the following steps:
1. **Calculate the Moment of Inertia:**
- For axis z, calculate the moment of inertia considering the contribution from both the flanges and the web.
- For axis y, calculate similarly, but typically the web contributes more prominently.
2. **Use the Bending Stress Formula:**
\[
\sigma = \frac{M \cdot c}{I}
\]
Where:
- \(\sigma\) is the bending stress.
- \(M\) is the moment.
- \(c\) is the distance from the neutral axis to the outermost fiber.
- \(I\) is the moment of inertia.
3. **Determine Maximum Moment:**
- Rearrange the above formula to solve for \(M\), given \(\sigma_{\text{allow}}\).
This calculation will provide the largest moment that the beam can resist without exceeding the allowable stress of 40 ksi for each axis orientation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9496fb66-15f0-4d2e-bc7e-ca3bb9b70577%2Fe1e4cc9d-b63f-482b-9a8a-f6efb989e723%2Fz5no1e_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
The beam is made of steel that has an allowable stress of \(\sigma_{\text{allow}} = 40 \text{ ksi}\). Determine the largest internal moment the beam can resist if the moment is applied
(a) about the z axis,
(b) about the y axis.
### Diagram Details:
The image displays a cross-sectional view of the beam with labeled dimensions:
- **Top and Bottom Flanges:**
- Width: \(3 \text{ in.}\)
- Thickness: \(0.25 \text{ in.}\)
- **Web:**
- Height: \(3 \text{ in.}\)
- Thickness: \(0.25 \text{ in.}\)
### Analysis:
To solve the problem, one would typically use the following steps:
1. **Calculate the Moment of Inertia:**
- For axis z, calculate the moment of inertia considering the contribution from both the flanges and the web.
- For axis y, calculate similarly, but typically the web contributes more prominently.
2. **Use the Bending Stress Formula:**
\[
\sigma = \frac{M \cdot c}{I}
\]
Where:
- \(\sigma\) is the bending stress.
- \(M\) is the moment.
- \(c\) is the distance from the neutral axis to the outermost fiber.
- \(I\) is the moment of inertia.
3. **Determine Maximum Moment:**
- Rearrange the above formula to solve for \(M\), given \(\sigma_{\text{allow}}\).
This calculation will provide the largest moment that the beam can resist without exceeding the allowable stress of 40 ksi for each axis orientation.
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