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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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![### Structural Analysis Using the Work-Energy Method
#### Problem Statement:
Consider a structure supporting a load \( P = 50 \text{ kN} \). The structure consists of two steel rods with:
- Young's Modulus (\( E \)) = 200 GPa
- Cross-sectional area (\( A \)) = 100 mm².
Rod **AB** has a length \( L_{AB} = 2 \text{ m} \), while rod **BC** has a length \( L_{BC} = 3 \text{ m} \). The angles between the rods and the horizontal are:
- \( \alpha = 30^\circ \)
- \( \beta = 45^\circ \).
Use the **Work-Energy Method** to determine the vertical displacement (\( \Delta B_y \)) at point **B**.
#### Diagram Explanation:
- **Rod AB** is inclined at an angle \( \alpha = 30^\circ \) with respect to the horizontal.
- **Rod BC** is inclined at an angle \( \beta = 45^\circ \) with respect to the horizontal.
- Point **B** is the junction of rods **AB** and **BC**.
- An external load \( P \) is applied vertically downward at point **B**.
#### Recommendations:
- Focus on the method of joints around point **B**.
- There is no need to find the reactionary loads at points **A** and **B**; this approach simplifies and saves time.
#### Calculation of Vertical Displacement \( (\Delta B_y) \):
\[ \Delta B_y = \underline{\hspace{10cm}} \text{ mm} \]
Please continue to solve using the Work-Energy Method as per your coursework guidelines and empirical formulas related to structural mechanics and material properties.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a6f1e3b-9c39-4224-9682-34613cae85d1%2Ffaa84fe9-7ca5-4e85-957a-f95c31d5e533%2Fmrjpmb4.jpeg&w=3840&q=75)
Transcribed Image Text:### Structural Analysis Using the Work-Energy Method
#### Problem Statement:
Consider a structure supporting a load \( P = 50 \text{ kN} \). The structure consists of two steel rods with:
- Young's Modulus (\( E \)) = 200 GPa
- Cross-sectional area (\( A \)) = 100 mm².
Rod **AB** has a length \( L_{AB} = 2 \text{ m} \), while rod **BC** has a length \( L_{BC} = 3 \text{ m} \). The angles between the rods and the horizontal are:
- \( \alpha = 30^\circ \)
- \( \beta = 45^\circ \).
Use the **Work-Energy Method** to determine the vertical displacement (\( \Delta B_y \)) at point **B**.
#### Diagram Explanation:
- **Rod AB** is inclined at an angle \( \alpha = 30^\circ \) with respect to the horizontal.
- **Rod BC** is inclined at an angle \( \beta = 45^\circ \) with respect to the horizontal.
- Point **B** is the junction of rods **AB** and **BC**.
- An external load \( P \) is applied vertically downward at point **B**.
#### Recommendations:
- Focus on the method of joints around point **B**.
- There is no need to find the reactionary loads at points **A** and **B**; this approach simplifies and saves time.
#### Calculation of Vertical Displacement \( (\Delta B_y) \):
\[ \Delta B_y = \underline{\hspace{10cm}} \text{ mm} \]
Please continue to solve using the Work-Energy Method as per your coursework guidelines and empirical formulas related to structural mechanics and material properties.
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