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4-12 Using superposition, find the deflection of the steel shaft at A in the figure. Find the deflection at midspan. By what percentage do these two values differ? Problem 4-12 y -15 in 340 lbf 24 in 150 lbf/ft A 1.5 in-dia. shaft

4-12 Using superposition, find the deflection of the steel shaft at A in the figure. Find the deflection at midspan. By what percentage do these two values differ? Problem 4-12 y -15 in 340 lbf 24 in 150 lbf/ft A 1.5 in-dia. shaft

Elements Of Electromagnetics
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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Solve Problem 4-12 using singularity functions. Use statics to determine the reactions. I have attached a picture of 4-12 below. Thank you in advance!
### Problem 4-12: Deflection of a Steel Shaft Using Superposition #### Problem Statement: Using superposition, find the deflection of the steel shaft at point \( A \) in the figure. Find the deflection at midspan. By what percentage do these two values differ? #### Diagram Description: The diagram displays a simply supported beam subject to two different loads: - The beam extends horizontally from point \( O \) (left support) to point \( B \) (right support). - Point \( A \) is situated between \( O \) and \( B \), specifically 15 inches from support \( O \) and 24 inches from support \( B \). - A vertical load of 340 lbf is applied directly downward on the beam at point \( A \). - A uniformly distributed load of 150 lbf/ft is applied along the entire span of the beam from point \( O \) to point \( B \). - The beam is labeled as a 1.5-inch diameter shaft. #### Steps for Solution: 1. **Static Analysis (Superposition Principle):** - Determine the reactions at the supports \( O \) and \( B \) due to the point load and the distributed load separately. - Compute the deflection caused by the point load at \( A \) and the distributed load separately. - Superimpose the deflection results from the point load and distributed load to obtain the total deflection at point \( A \) and midspan. 2. **Deflection Calculation:** - Use the appropriate beam deflection formulas for point loads and uniformly distributed loads. - Combine the results using the principle of superposition. 3. **Percentage Difference:** - Calculate the percentage difference between the deflection at point \( A \) and the midspan deflection. #### Example Solution: The actual numerical calculations can be done as follows, using engineering mechanics and structural analysis concepts: 1. **Find reactions due to the point load and distributed load**: - For the 340 lbf point load: Use static equilibrium equations to find reactions at \( O \) and \( B \). - For the 150 lbf/ft distributed load: Similarly, find reactions at \( O \) and \( B \). 2. **Calculate deflection due to point load**: - Use the formula for deflection due to a point load at a specific location on a simply
Transcribed Image Text:### Problem 4-12: Deflection of a Steel Shaft Using Superposition #### Problem Statement: Using superposition, find the deflection of the steel shaft at point \( A \) in the figure. Find the deflection at midspan. By what percentage do these two values differ? #### Diagram Description: The diagram displays a simply supported beam subject to two different loads: - The beam extends horizontally from point \( O \) (left support) to point \( B \) (right support). - Point \( A \) is situated between \( O \) and \( B \), specifically 15 inches from support \( O \) and 24 inches from support \( B \). - A vertical load of 340 lbf is applied directly downward on the beam at point \( A \). - A uniformly distributed load of 150 lbf/ft is applied along the entire span of the beam from point \( O \) to point \( B \). - The beam is labeled as a 1.5-inch diameter shaft. #### Steps for Solution: 1. **Static Analysis (Superposition Principle):** - Determine the reactions at the supports \( O \) and \( B \) due to the point load and the distributed load separately. - Compute the deflection caused by the point load at \( A \) and the distributed load separately. - Superimpose the deflection results from the point load and distributed load to obtain the total deflection at point \( A \) and midspan. 2. **Deflection Calculation:** - Use the appropriate beam deflection formulas for point loads and uniformly distributed loads. - Combine the results using the principle of superposition. 3. **Percentage Difference:** - Calculate the percentage difference between the deflection at point \( A \) and the midspan deflection. #### Example Solution: The actual numerical calculations can be done as follows, using engineering mechanics and structural analysis concepts: 1. **Find reactions due to the point load and distributed load**: - For the 340 lbf point load: Use static equilibrium equations to find reactions at \( O \) and \( B \). - For the 150 lbf/ft distributed load: Similarly, find reactions at \( O \) and \( B \). 2. **Calculate deflection due to point load**: - Use the formula for deflection due to a point load at a specific location on a simply
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