### 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.

GIVEN- ALLOWABLE STRESS=40KSIDETERMINE- LARGEST INTERNAL BENDING MOMENT( A)-ABOUT Z AXIS…

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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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

### 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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