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P12.2. For the beam shown in Figure P12.2, draw the influence lines for the reactions M and RA and the shear and moment at point B. A 3 m P12.2 B 2 m

P12.2. For the beam shown in Figure P12.2, draw the influence lines for the reactions M and RA and the shear and moment at point B. A 3 m P12.2 B 2 m

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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### Problem P12.2 - Influence Lines for Beam Reactions and Internal Forces **Problem Statement:** For the beam shown in Figure P12.2, draw the influence lines for the reactions \( M_A \) and \( R_A \) and the shear and moment at point \( B \). #### Figure P12.2 Description: - A beam \( ABC \) is illustrated. - Point \( A \) is supported. - The beam spans a total length of 5 meters. - The segment \( AB \) is 3 meters. - The segment \( BC \) is 2 meters. **Explanation:** - **Reactions \( M_A \) and \( R_A \):** - **\( M_A \)** represents the moment reaction at point \( A \). - **\( R_A \)** represents the vertical reaction at point \( A \). - **Internal Forces at Point \( B \):** - **Shear at point \( B \)** is the internal shear force present at point \( B \) of the beam. - **Moment at point \( B \)** is the internal bending moment present at point \( B \). To solve this, follow these steps: 1. **Determine the Reaction Influence Lines at \( A \):** - Influence lines graphically represent the variation of reaction forces at point \( A \) as a unit load moves across the beam. 2. **Draw the Influence Line for Shear at \( B \):** - This line shows how the internal shear force at point \( B \) changes as a unit load moves along the length of the beam. 3. **Draw the Influence Line for Moment at \( B \):** - This line represents the variation of the bending moment at point \( B \) for different positions of a unit load along the beam. By plotting these influence lines, you can determine how different loads affect the internal forces and reactions at specified points on the beam. This is essential for understanding load distribution and for the design and analysis of structural components. #### Diagram Details The provided beam diagram has: - A left vertical support at point \( A \). - A beam extending horizontally from \( A \) to \( C \). - A vertical section label at point \( B \) dividing the beam into segments \( AB \) and \( BC \) with lengths of 3 meters and 2 meters, respectively.
Transcribed Image Text:### Problem P12.2 - Influence Lines for Beam Reactions and Internal Forces **Problem Statement:** For the beam shown in Figure P12.2, draw the influence lines for the reactions \( M_A \) and \( R_A \) and the shear and moment at point \( B \). #### Figure P12.2 Description: - A beam \( ABC \) is illustrated. - Point \( A \) is supported. - The beam spans a total length of 5 meters. - The segment \( AB \) is 3 meters. - The segment \( BC \) is 2 meters. **Explanation:** - **Reactions \( M_A \) and \( R_A \):** - **\( M_A \)** represents the moment reaction at point \( A \). - **\( R_A \)** represents the vertical reaction at point \( A \). - **Internal Forces at Point \( B \):** - **Shear at point \( B \)** is the internal shear force present at point \( B \) of the beam. - **Moment at point \( B \)** is the internal bending moment present at point \( B \). To solve this, follow these steps: 1. **Determine the Reaction Influence Lines at \( A \):** - Influence lines graphically represent the variation of reaction forces at point \( A \) as a unit load moves across the beam. 2. **Draw the Influence Line for Shear at \( B \):** - This line shows how the internal shear force at point \( B \) changes as a unit load moves along the length of the beam. 3. **Draw the Influence Line for Moment at \( B \):** - This line represents the variation of the bending moment at point \( B \) for different positions of a unit load along the beam. By plotting these influence lines, you can determine how different loads affect the internal forces and reactions at specified points on the beam. This is essential for understanding load distribution and for the design and analysis of structural components. #### Diagram Details The provided beam diagram has: - A left vertical support at point \( A \). - A beam extending horizontally from \( A \) to \( C \). - A vertical section label at point \( B \) dividing the beam into segments \( AB \) and \( BC \) with lengths of 3 meters and 2 meters, respectively.
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