**Problem Statement:**A 1020 CD steel shaft (\(S_y=390 \text{ MPa}\)) is used to transmit 20 kW of power at 1200 rpm. There are no bending or axial loads on the shaft. It is desired to have a static factor of safety of 2 based on the Distortion Energy theory. Determine the minimum diameter needed for the shaft.- Power, \( P = T \omega \)- Pure torsion, relationship between \( T \) and \( \tau \)- Torsional stress**Instructions:**To solve this problem, calculate using the following steps:1. **Power and Torque Relationship:** Use the expression \( P = T \omega \) to find the torque \( T \) in the shaft.2. **Torsional Shear Stress:** Calculate the torsional shear stress (\( \tau \)) using the pure torsion relationship.3. **Factor of Safety and Diameter:** Apply the static factor of safety to ensure the shaft's diameter is sufficient to handle the stress without failure, using the Distortion Energy theory.Make sure to review the relevant mechanical properties of steel and the equations involved in calculating torsional stress and factor of safety.

Answered: Image /qna-images/answer/e81a9592-5c30-40ce-9841-3ef1208751fd.jpg

ling or axial loads on the shaft. It is desired to have a static factor of safety of 2 based on the ortion Energy theory. Determine the minimum diameter needed for the shaft. Power, P=To Pure torsion, relationship between T and T

ling or axial loads on the shaft. It is desired to have a static factor of safety of 2 based on the ortion Energy theory. Determine the minimum diameter needed for the shaft. Power, P=To Pure torsion, relationship between T and T

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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Engineering Drawing

Technical drawing has been around since ancient times. As in the ancient Renaissance, complicated drawings were created, including Leonardo da Vinci's drawing. Modern engineering drawing, including its specific orthographic projection with scale conventions, began in Europe (France) during the early stages of Industrialization. L.T. C. Rolt also made some of Marc's drawings for its block-making machinery (in 1799) that also may have contributed significantly to British engineering technology. Since he learned the art of presenting three-dimensional(3D) items in a two-dimensional(2D) plane, as we now term mechanical drawing. 

Question

**Problem Statement:**

A 1020 CD steel shaft (\(S_y=390 \text{ MPa}\)) is used to transmit 20 kW of power at 1200 rpm. There are no bending or axial loads on the shaft. It is desired to have a static factor of safety of 2 based on the Distortion Energy theory. Determine the minimum diameter needed for the shaft.

- Power, \( P = T \omega \)
- Pure torsion, relationship between \( T \) and \( \tau \)
- Torsional stress

**Instructions:**

To solve this problem, calculate using the following steps:

1. **Power and Torque Relationship:** Use the expression \( P = T \omega \) to find the torque \( T \) in the shaft.

2. **Torsional Shear Stress:** Calculate the torsional shear stress (\( \tau \)) using the pure torsion relationship.

3. **Factor of Safety and Diameter:** Apply the static factor of safety to ensure the shaft's diameter is sufficient to handle the stress without failure, using the Distortion Energy theory.

Make sure to review the relevant mechanical properties of steel and the equations involved in calculating torsional stress and factor of safety.

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