A vertical load of 100-kN is supported by two rods. The load is static and the allowable stress for the steel rob, AB, is 137.895-MPa. Determine the minimum required diameter of the circular steel rod, AB. 100 KN 2.5 m 4.5 m
A vertical load of 100-kN is supported by two rods. The load is static and the allowable stress for the steel rob, AB, is 137.895-MPa. Determine the minimum required diameter of the circular steel rod, AB. 100 KN 2.5 m 4.5 m
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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![### Determining the Minimum Required Diameter of a Circular Steel Rod
#### Problem Statement:
A vertical load of 100 kN is supported by two rods. The load is static, and the allowable stress for the steel rod, AB, is 137.895 MPa.
Determine the minimum required diameter of the circular steel rod, AB.
#### Diagram Explanation:
The diagram illustrates a setup where a vertical load of 100 kN is applied at point A, suspended by two rods connected to points B and C on a vertical wall. The dimensions provided in the diagram are as follows:
- The horizontal distance from point A to point C is 6 meters.
- The vertical distance between points B and C is 7 meters (2.5 meters from B to the midpoint and 4.5 meters from the midpoint to C).
This setup forms a right triangle with points ABC.
#### Approach:
Given:
- Load (F) = 100 kN
- Allowable stress (\(\sigma_{allow}\)) = 137.895 MPa
1. **Compute the force in rod AB**:
Break the forces into horizontal and vertical components, and use trigonometry to find the forces in the triangle formed.
2. **Calculate the cross-sectional area (A) of rod AB**:
Using the relationship:
\[ \sigma = \frac{F}{A} \]
3. **Determine the diameter (d) from the cross-sectional area**:
Since the rod is circular, use the formula for the area of a circle:
\[ A = \frac{\pi d^2}{4} \]
Rearrange to find \( d \).
#### Calculation Steps:
1. Calculate the angle \(\theta\) from the horizontal for the rod AB using trigonometry.
2. Determine the direct force on AB using vector components.
3. Utilize the allowable stress to calculate the needed cross-sectional area.
4. Derive the diameter from the cross-sectional area for a circular section.
### Conclusion:
By following these steps and considering the given values, you will be able to determine the minimum required diameter of the circular steel rod AB to safely support the given load without exceeding the allowable stress.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a28b893-91ec-4064-8fee-f9f0d1fd8200%2F77a6df2b-5957-4908-9b7f-7d6daa0ce530%2Fzl4cact_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the Minimum Required Diameter of a Circular Steel Rod
#### Problem Statement:
A vertical load of 100 kN is supported by two rods. The load is static, and the allowable stress for the steel rod, AB, is 137.895 MPa.
Determine the minimum required diameter of the circular steel rod, AB.
#### Diagram Explanation:
The diagram illustrates a setup where a vertical load of 100 kN is applied at point A, suspended by two rods connected to points B and C on a vertical wall. The dimensions provided in the diagram are as follows:
- The horizontal distance from point A to point C is 6 meters.
- The vertical distance between points B and C is 7 meters (2.5 meters from B to the midpoint and 4.5 meters from the midpoint to C).
This setup forms a right triangle with points ABC.
#### Approach:
Given:
- Load (F) = 100 kN
- Allowable stress (\(\sigma_{allow}\)) = 137.895 MPa
1. **Compute the force in rod AB**:
Break the forces into horizontal and vertical components, and use trigonometry to find the forces in the triangle formed.
2. **Calculate the cross-sectional area (A) of rod AB**:
Using the relationship:
\[ \sigma = \frac{F}{A} \]
3. **Determine the diameter (d) from the cross-sectional area**:
Since the rod is circular, use the formula for the area of a circle:
\[ A = \frac{\pi d^2}{4} \]
Rearrange to find \( d \).
#### Calculation Steps:
1. Calculate the angle \(\theta\) from the horizontal for the rod AB using trigonometry.
2. Determine the direct force on AB using vector components.
3. Utilize the allowable stress to calculate the needed cross-sectional area.
4. Derive the diameter from the cross-sectional area for a circular section.
### Conclusion:
By following these steps and considering the given values, you will be able to determine the minimum required diameter of the circular steel rod AB to safely support the given load without exceeding the allowable stress.
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