Determine the location of the resultant force acting on the beam from point A. Draw a free body diagram of the beam with the resultant force and it's location clearly labeled. Make sure you include the reactions at the supports in your free body diagram. 800 N/m A 3 m 500 N/m 3 m B

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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### Problem Description

**Objective:**  
Determine the location of the resultant force acting on the beam from point A. Draw a free body diagram of the beam with the resultant force and its location clearly labeled. Make sure you include the reactions at the supports in your free body diagram.

### Diagram Explanation

The diagram depicts a beam AB, which is subject to a linearly varying distributed load. The load intensity decreases from 800 N/m at point A to 500 N/m at point B. The beam is supported at point A by a pin support and at point B by a roller support, indicating that the beam is statically determinate.

**Details:**

- **Distributed Load:**
  - Load starts at 800 N/m at point A.
  - Load decreases linearly to 500 N/m at point B.

- **Beam:**
  - Length: 6 meters, divided into two segments of 3 meters each.

- **Supports:**
  - **Point A:** Pin support allowing rotation but no translation.
  - **Point B:** Roller support allowing horizontal translation but no vertical translation.

### Instructions

1. **Calculate the Resultant Force:**
   - Integrate the load distribution function over the length of the beam to find the resultant force.
   
2. **Determine the Location of the Resultant Force:**
   - Use the principle of moments or centroid of the loading distribution to find the location of the resultant force.

3. **Draw the Free Body Diagram:**
   - Show the resultant force at its calculated location.
   - Include reactions at A and B, indicating direction and magnitude.

### Solution Steps

The resultant force and its location can be found using principles of static equilibrium and geometry.
Transcribed Image Text:### Problem Description **Objective:** Determine the location of the resultant force acting on the beam from point A. Draw a free body diagram of the beam with the resultant force and its location clearly labeled. Make sure you include the reactions at the supports in your free body diagram. ### Diagram Explanation The diagram depicts a beam AB, which is subject to a linearly varying distributed load. The load intensity decreases from 800 N/m at point A to 500 N/m at point B. The beam is supported at point A by a pin support and at point B by a roller support, indicating that the beam is statically determinate. **Details:** - **Distributed Load:** - Load starts at 800 N/m at point A. - Load decreases linearly to 500 N/m at point B. - **Beam:** - Length: 6 meters, divided into two segments of 3 meters each. - **Supports:** - **Point A:** Pin support allowing rotation but no translation. - **Point B:** Roller support allowing horizontal translation but no vertical translation. ### Instructions 1. **Calculate the Resultant Force:** - Integrate the load distribution function over the length of the beam to find the resultant force. 2. **Determine the Location of the Resultant Force:** - Use the principle of moments or centroid of the loading distribution to find the location of the resultant force. 3. **Draw the Free Body Diagram:** - Show the resultant force at its calculated location. - Include reactions at A and B, indicating direction and magnitude. ### Solution Steps The resultant force and its location can be found using principles of static equilibrium and geometry.
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