A link in a mechanism is made from round bar. Due to the loading condition, the link is subject to a maximum stress of 67-MPa and a minimum stress of -27-MPa. Determine the mean stress the link is experiencing?
A link in a mechanism is made from round bar. Due to the loading condition, the link is subject to a maximum stress of 67-MPa and a minimum stress of -27-MPa. Determine the mean stress the link is experiencing?
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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![### Determining Mean Stress in a Mechanism Link
In mechanical engineering, it is essential to understand the stress conditions experienced by a component, particularly under varying loading conditions. Here, we examine the stress experienced by a link in a mechanism made from a round bar. This link is subjected to a maximum stress of 67 MPa and a minimum stress of -27 MPa.
The objective is to determine the mean stress that the link is experiencing.
#### Calculation of Mean Stress
The mean stress (\( \sigma_{mean} \)) can be calculated using the following formula:
\[ \sigma_{mean} = \frac{\sigma_{max} + \sigma_{min}}{2} \]
Where:
- \( \sigma_{max} = 67 \text{ MPa} \)
- \( \sigma_{min} = -27 \text{ MPa} \)
Plugging these values into the formula results in:
\[ \sigma_{mean} = \frac{67 \text{ MPa} + (-27 \text{ MPa})}{2} \]
\[ \sigma_{mean} = \frac{67 \text{ MPa} - 27 \text{ MPa}}{2} \]
\[ \sigma_{mean} = \frac{40 \text{ MPa}}{2} \]
\[ \sigma_{mean} = 20 \text{ MPa} \]
Based on this calculation, the mean stress the link is experiencing is 20 MPa.
#### Answer Options
To reinforce understanding, consider the following multiple-choice options provided for determining the mean stress:
- \( \circ \) 47 MPa
- \( \circ \) 44.5 MPa
- \( \circ \) 5375 psi
- \( \circ \) 2313 psi
- \( \circ \) 25.5 MPa
- \( \circ \) 20 MPa **(Correct Answer)**
- \( \circ \) 19.1 MPa
- \( \circ \) -750 psi
Selecting the appropriate answer reinforces the application of stress analysis and understanding in mechanism design under varying conditions.
### Conclusion
Understanding the stress conditions in mechanical components is critical for ensuring their reliability and safety in operation. By calculating the mean stress, engineers can better predict the performance and lifespan of components subjected to fluctuating loads.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a28b893-91ec-4064-8fee-f9f0d1fd8200%2Fe4c04f2b-3a01-43bd-98f3-2a2bb4ca1105%2Frli34s4_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining Mean Stress in a Mechanism Link
In mechanical engineering, it is essential to understand the stress conditions experienced by a component, particularly under varying loading conditions. Here, we examine the stress experienced by a link in a mechanism made from a round bar. This link is subjected to a maximum stress of 67 MPa and a minimum stress of -27 MPa.
The objective is to determine the mean stress that the link is experiencing.
#### Calculation of Mean Stress
The mean stress (\( \sigma_{mean} \)) can be calculated using the following formula:
\[ \sigma_{mean} = \frac{\sigma_{max} + \sigma_{min}}{2} \]
Where:
- \( \sigma_{max} = 67 \text{ MPa} \)
- \( \sigma_{min} = -27 \text{ MPa} \)
Plugging these values into the formula results in:
\[ \sigma_{mean} = \frac{67 \text{ MPa} + (-27 \text{ MPa})}{2} \]
\[ \sigma_{mean} = \frac{67 \text{ MPa} - 27 \text{ MPa}}{2} \]
\[ \sigma_{mean} = \frac{40 \text{ MPa}}{2} \]
\[ \sigma_{mean} = 20 \text{ MPa} \]
Based on this calculation, the mean stress the link is experiencing is 20 MPa.
#### Answer Options
To reinforce understanding, consider the following multiple-choice options provided for determining the mean stress:
- \( \circ \) 47 MPa
- \( \circ \) 44.5 MPa
- \( \circ \) 5375 psi
- \( \circ \) 2313 psi
- \( \circ \) 25.5 MPa
- \( \circ \) 20 MPa **(Correct Answer)**
- \( \circ \) 19.1 MPa
- \( \circ \) -750 psi
Selecting the appropriate answer reinforces the application of stress analysis and understanding in mechanism design under varying conditions.
### Conclusion
Understanding the stress conditions in mechanical components is critical for ensuring their reliability and safety in operation. By calculating the mean stress, engineers can better predict the performance and lifespan of components subjected to fluctuating loads.
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