a) Solve for the reactions. Draw the shear and moment diagram. Be sure to provide equations at each cut. 400 N/m 200 N/m В A 3 m -3 m

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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**Problem 2**

a) Solve for the reactions.

b) Draw the shear and moment diagram. Be sure to provide equations at each cut.

**Description of the Diagram:**

The provided diagram illustrates a simply supported beam with the following characteristics:

- The beam is supported at two points, labeled as A and B. 
- The distance between the supports is 6 meters, divided into two segments of 3 meters each.
- There is a triangular distributed load acting on the beam between A and B. This load varies linearly from 200 N/m at support A to 400 N/m at support B.
- The positions of the supports, A and B, are depicted with standard symbols for a pinned support at A and a roller support at B. 

To solve for reactions and draw the shear and moment diagrams, follow these steps:

1. **Calculate the Reactions:**
   - Use equilibrium equations (sum of vertical forces and moments) to find the reactions at supports A and B.

2. **Shear Force Diagram:**
   - Determine the shear force at various sections along the beam using the distributed load function.
   - Plot the shear force values to create the shear diagram.

3. **Moment Diagram:**
   - Use the shear diagram to find the bending moment at various points.
   - Integrate the shear force diagram if necessary to obtain the moment values.

4. **Equations:**
   - Provide detailed equations for both shear force and bending moment at each segment of the beam, especially where the load varies.

This analysis will help in understanding how the beam behaves under the given loading conditions.
Transcribed Image Text:**Problem 2** a) Solve for the reactions. b) Draw the shear and moment diagram. Be sure to provide equations at each cut. **Description of the Diagram:** The provided diagram illustrates a simply supported beam with the following characteristics: - The beam is supported at two points, labeled as A and B. - The distance between the supports is 6 meters, divided into two segments of 3 meters each. - There is a triangular distributed load acting on the beam between A and B. This load varies linearly from 200 N/m at support A to 400 N/m at support B. - The positions of the supports, A and B, are depicted with standard symbols for a pinned support at A and a roller support at B. To solve for reactions and draw the shear and moment diagrams, follow these steps: 1. **Calculate the Reactions:** - Use equilibrium equations (sum of vertical forces and moments) to find the reactions at supports A and B. 2. **Shear Force Diagram:** - Determine the shear force at various sections along the beam using the distributed load function. - Plot the shear force values to create the shear diagram. 3. **Moment Diagram:** - Use the shear diagram to find the bending moment at various points. - Integrate the shear force diagram if necessary to obtain the moment values. 4. **Equations:** - Provide detailed equations for both shear force and bending moment at each segment of the beam, especially where the load varies. This analysis will help in understanding how the beam behaves under the given loading conditions.
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