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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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**Problem Description:**

The rigid, T-shaped bar shown below is supported by a pin at \( A \) and a smooth surface at \( B \). A linear elastic spring connects at \( C \); its stretch and spring constant (\( k \)) are provided on the figure. The spring is elongated (stretched out), and the system is at equilibrium. Figure is not drawn to scale.

**Tasks:**

a) Sketch a complete Free Body Diagram (FBD) of the T-shaped bar appropriate for determining the support reactions.

b) Use your FBD to determine the support reaction(s) at points \( A \) and \( B \). Show all work.

**Figure Explanation:**

- **Diagram Elements:**
  - The T-shaped bar is shown with a vertical and horizontal part.
  - Point \( A \) is a pin support located at the top-left.
  - Point \( B \) is a smooth surface contact on the far right.
  - Point \( C \) is where the spring is connected to the horizontal part, located 10 inches down from the horizontal top.
  - The spring is shown attached vertically below \( C \) with a spring constant \( k = 50 \, \text{lb/in} \) and a stretch of \( 0.25 \, \text{in} \).

- **Distances:**
  - The horizontal distances \( A \) to \( C \) and \( C \) to \( B \) are both 6 inches.
  - The vertical distance from the horizontal beam to point \( C \) is 10 inches.

- **Angles:**
  - The horizontal angle from \( C \) to \( B \) is labeled with a right triangle, showing opposite as 3 and adjacent as 4, implying a trigonometrical relationship.

This setup is used for analyzing mechanical equilibrium in a structure supported with a spring and determining the reactions at the supports.
Transcribed Image Text:**Problem Description:** The rigid, T-shaped bar shown below is supported by a pin at \( A \) and a smooth surface at \( B \). A linear elastic spring connects at \( C \); its stretch and spring constant (\( k \)) are provided on the figure. The spring is elongated (stretched out), and the system is at equilibrium. Figure is not drawn to scale. **Tasks:** a) Sketch a complete Free Body Diagram (FBD) of the T-shaped bar appropriate for determining the support reactions. b) Use your FBD to determine the support reaction(s) at points \( A \) and \( B \). Show all work. **Figure Explanation:** - **Diagram Elements:** - The T-shaped bar is shown with a vertical and horizontal part. - Point \( A \) is a pin support located at the top-left. - Point \( B \) is a smooth surface contact on the far right. - Point \( C \) is where the spring is connected to the horizontal part, located 10 inches down from the horizontal top. - The spring is shown attached vertically below \( C \) with a spring constant \( k = 50 \, \text{lb/in} \) and a stretch of \( 0.25 \, \text{in} \). - **Distances:** - The horizontal distances \( A \) to \( C \) and \( C \) to \( B \) are both 6 inches. - The vertical distance from the horizontal beam to point \( C \) is 10 inches. - **Angles:** - The horizontal angle from \( C \) to \( B \) is labeled with a right triangle, showing opposite as 3 and adjacent as 4, implying a trigonometrical relationship. This setup is used for analyzing mechanical equilibrium in a structure supported with a spring and determining the reactions at the supports.
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