Given the beam problem shown in Fig 1.1

Elements Of Electromagnetics
7th Edition
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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### Beam Problem Analysis

**Problem Statement (4-1):**  
Given the beam problem shown in Figure 1.1.

- A beam is fixed on one end with a support that resists 1000 lb vertically. 
- The beam extends horizontally and experiences additional uniform loading.
- A distributed load of 200 lb/ft acts over a 4-foot span.
- The beam has two points marked as A and B.

### Diagram Details

#### Figure 4.1:

- **Left End:** Fixed support resisting 1000 lb.
- **Span:** Total length of the beam with labeled sections: 2 feet before point A, 2 feet between points A and B, and a 4-foot section after point B bearing the distributed load.

### Tasks

#### a) Free Body Diagram

**Objective:**  
Apply all known and unknown forces to create a free body diagram.

**Diagram Components:**  
- Mark points A and B on the beam.
- Indicate the direction of forces acting on the beam.

#### b) Hand Calculations

**Objective:**  
Determine the true magnitude and direction of the reactions at points A and B.

**Calculation Requirements:**  
- Utilize equilibrium equations for force and moment balance to compute unknown reactions.
- Document calculations and assumptions clearly.

#### c) Balanced Free Body Diagram

**Objective:**  
Revise the free body diagram to reflect the true magnitude and direction of all forces.

**Diagram Components:**  
- Update the representation at points A and B based on calculated forces.
- Ensure the diagram accurately shows equilibrium state.

By completing these tasks, students can better understand beam loading effects and the principles of static equilibrium in structural analysis.
Transcribed Image Text:### Beam Problem Analysis **Problem Statement (4-1):** Given the beam problem shown in Figure 1.1. - A beam is fixed on one end with a support that resists 1000 lb vertically. - The beam extends horizontally and experiences additional uniform loading. - A distributed load of 200 lb/ft acts over a 4-foot span. - The beam has two points marked as A and B. ### Diagram Details #### Figure 4.1: - **Left End:** Fixed support resisting 1000 lb. - **Span:** Total length of the beam with labeled sections: 2 feet before point A, 2 feet between points A and B, and a 4-foot section after point B bearing the distributed load. ### Tasks #### a) Free Body Diagram **Objective:** Apply all known and unknown forces to create a free body diagram. **Diagram Components:** - Mark points A and B on the beam. - Indicate the direction of forces acting on the beam. #### b) Hand Calculations **Objective:** Determine the true magnitude and direction of the reactions at points A and B. **Calculation Requirements:** - Utilize equilibrium equations for force and moment balance to compute unknown reactions. - Document calculations and assumptions clearly. #### c) Balanced Free Body Diagram **Objective:** Revise the free body diagram to reflect the true magnitude and direction of all forces. **Diagram Components:** - Update the representation at points A and B based on calculated forces. - Ensure the diagram accurately shows equilibrium state. By completing these tasks, students can better understand beam loading effects and the principles of static equilibrium in structural analysis.
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a) Free body diagram of known and unknown forces:

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