3- For the loaded beam shown below, calculate the magnitude of force F such that the resultant couple moment is 15 kN*m CCW. Describe the location on the beam where this resultant couple moment acts. -F F \30 30° 8 kN - 0.3 m 1.2 m 0.4 m- 8 kN

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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ChapterMA: Math Assessment
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**Problem Statement:**

3 – For the loaded beam shown below, calculate the magnitude of force \( F \) such that the resultant couple moment is \( 15 \, \text{kN} \cdot \text{m} \) counterclockwise (CCW). Describe the location on the beam where this resultant couple moment acts.

**Diagram Explanation:**

The diagram features a vertical beam subjected to several forces:

- At the top of the beam, there are two forces \( F \) angled at \( 30^\circ \) with respect to the horizontal. One force acts to the right and upwards, while the negative of the force \( -F \) acts to the left and downwards, forming a couple.
  
- Two horizontal forces, both \( 8 \, \text{kN} \), are applied at different points. One force is applied to the left at a point 0.3 meters from the top, and the other force is applied to the right at a point 1.2 meters from the top.
  
- The vertical distances are marked from the top as 0.3 meters and 1.2 meters, with an additional 0.4-meter segment from 1.2 meters to the bottom of the beam.

**Objective:**

Find the magnitude of force \( F \) that results in a net couple moment of \( 15 \, \text{kN} \cdot \text{m} \) counterclockwise, and determine the specific location along the beam where this couple moment acts.
Transcribed Image Text:**Problem Statement:** 3 – For the loaded beam shown below, calculate the magnitude of force \( F \) such that the resultant couple moment is \( 15 \, \text{kN} \cdot \text{m} \) counterclockwise (CCW). Describe the location on the beam where this resultant couple moment acts. **Diagram Explanation:** The diagram features a vertical beam subjected to several forces: - At the top of the beam, there are two forces \( F \) angled at \( 30^\circ \) with respect to the horizontal. One force acts to the right and upwards, while the negative of the force \( -F \) acts to the left and downwards, forming a couple. - Two horizontal forces, both \( 8 \, \text{kN} \), are applied at different points. One force is applied to the left at a point 0.3 meters from the top, and the other force is applied to the right at a point 1.2 meters from the top. - The vertical distances are marked from the top as 0.3 meters and 1.2 meters, with an additional 0.4-meter segment from 1.2 meters to the bottom of the beam. **Objective:** Find the magnitude of force \( F \) that results in a net couple moment of \( 15 \, \text{kN} \cdot \text{m} \) counterclockwise, and determine the specific location along the beam where this couple moment acts.
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