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shear and bending moment diagram for the beam to the right. Make sure your graph is neat and drawn on graph pa

shear and bending moment diagram for the beam to the right. Make sure your graph is neat and drawn on graph pa

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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a.) Derive the shear and bending moment
equations for the entire beam.
b.) Draw the complete shear and bending
moment diagram for the beam to the right. Make
sure your graph is neat and drawn on graph paper
or with a computer aided graphing program.

 

 

### Analysis of a Beam under Various Loads #### Diagram Description: The provided diagram illustrates a beam with several types of loads and supports. The beam is labeled with two reference points, A and B, and is subjected to the following loads: 1. A concentrated vertical load of 4 kN acting downward at a distance of 2 meters from the left end (point A). 2. A uniformly distributed load (UDL) of 1 kN/m applied between points A and B. 3. A triangular load varying from 1 kN/m to 3 kN/m over a span of 2 meters, starting from point B towards the right end of the beam. #### Support Conditions: - The beam is supported by a fixed support at point A, which prevents any translational and rotational movement. - The beam is supported by a roller support at point B, which allows horizontal translation but restricts vertical movement and rotation. #### Dimensional Details: - The total length of the beam is 6 meters. - The distance between point A and the position of the 4 kN load is 2 meters. - The distance between point A and B is 4 meters. - The distance between point B and the right end of the beam is 2 meters. #### Load Distribution: - **Concentrated Load:** A vertical force of 4 kN is positioned 2 meters from point A. - **Uniformly Distributed Load (UDL):** The UDL of 1 kN/m extends from point A to point B (4 meters in length). - **Triangular Load:** The triangular load varies linearly from 1 kN/m at point B to 3 kN/m at the right end of the beam over a 2-meter distance. #### Steps to Analyze the Beam: 1. **Support Reactions:** - Calculate the reactions at supports A (fixed) and B (roller). - Summing moments about point A to find the reaction at B. - Summing vertical forces to find the vertical reaction at A. 2. **Shear Force and Bending Moment:** - Create shear force and bending moment diagrams by integrating the effects of the loads from left to right. - Account for the distributed loads by converting them into equivalent point loads at their centroids. - Apply the boundary conditions at supports to find constants of integration. 3. **Deflection:** - Use calculus to determine the def
Transcribed Image Text:### Analysis of a Beam under Various Loads #### Diagram Description: The provided diagram illustrates a beam with several types of loads and supports. The beam is labeled with two reference points, A and B, and is subjected to the following loads: 1. A concentrated vertical load of 4 kN acting downward at a distance of 2 meters from the left end (point A). 2. A uniformly distributed load (UDL) of 1 kN/m applied between points A and B. 3. A triangular load varying from 1 kN/m to 3 kN/m over a span of 2 meters, starting from point B towards the right end of the beam. #### Support Conditions: - The beam is supported by a fixed support at point A, which prevents any translational and rotational movement. - The beam is supported by a roller support at point B, which allows horizontal translation but restricts vertical movement and rotation. #### Dimensional Details: - The total length of the beam is 6 meters. - The distance between point A and the position of the 4 kN load is 2 meters. - The distance between point A and B is 4 meters. - The distance between point B and the right end of the beam is 2 meters. #### Load Distribution: - **Concentrated Load:** A vertical force of 4 kN is positioned 2 meters from point A. - **Uniformly Distributed Load (UDL):** The UDL of 1 kN/m extends from point A to point B (4 meters in length). - **Triangular Load:** The triangular load varies linearly from 1 kN/m at point B to 3 kN/m at the right end of the beam over a 2-meter distance. #### Steps to Analyze the Beam: 1. **Support Reactions:** - Calculate the reactions at supports A (fixed) and B (roller). - Summing moments about point A to find the reaction at B. - Summing vertical forces to find the vertical reaction at A. 2. **Shear Force and Bending Moment:** - Create shear force and bending moment diagrams by integrating the effects of the loads from left to right. - Account for the distributed loads by converting them into equivalent point loads at their centroids. - Apply the boundary conditions at supports to find constants of integration. 3. **Deflection:** - Use calculus to determine the def
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