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400 N/m 200 N/m A B 4 m 3 m

400 N/m 200 N/m A B 4 m 3 m

Elements Of Electromagnetics
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.

### 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
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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