400 N/m 200 N/m A B 4 m 3 m
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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Determine the horizontal and vertical components of the reaction at the support A for equilibrium of the beam. Determine the normal reaction at the support B for equilibrium of the beam.

Transcribed Image Text:### Structural Analysis of a Beam with Varying Load
#### Diagram Description:
The diagram illustrates a beam subjected to varying loads between two supports.
- **Supports:**
- Support A is represented as a fixed support (left side of the beam).
- Support B is shown as a roller support (right side of the beam).
- **Beam:**
- The beam extends horizontally and rests on the supports A and B.
- The total length of the beam is 7 meters.
- **Load Distribution:**
- The load on the beam varies linearly between the supports A and B.
- At point A, a uniformly distributed load (UDL) of 200 N/m is applied.
- The load increases linearly to 400 N/m at point B.
- **Dimensions:**
- The distance between supports A and B is divided into two segments:
- The segment from A to the midpoint of the load is 4 meters.
- The segment from the midpoint to B is 3 meters.
#### Analysis Explanation:
The given diagram shows a common structural engineering problem designed to determine the reactions at the supports and the effects of the varying distributed load on the beam.
- **Fixed Support (A):**
- This type of support can resist vertical and horizontal forces as well as a moment.
- The reaction forces at A will include vertical and horizontal components, as well as a moment due to the fixed nature of the support.
- **Roller Support (B):**
- This type of support allows for horizontal movement but restricts vertical movement.
- The reaction force at B will be purely vertical as the roller permits horizontal displacement.
- **Load Distribution:**
- The varying distributed load means that the beam experiences different intensities of force along its length.
- The total load acting on the beam can be found by integrating the load distribution function from A to B.
The next steps in this analysis typically involve:
1. **Calculating Shear Force and Bending Moment:**
- Shear force and bending moment diagrams are plotted to understand the internal forces in the beam.
- This involves integrating the load distribution function to find expressions for shear force and bending moment at any given point on the beam.
2. **Determining Reactions at Supports:**
- The reactions at A and B are determined using the equilibrium conditions for the beam.
- Sum of all vertical forces must be
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