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6–27. Draw the shear and moment diagrams for the beam. Wo В A L 3 2L 3

6–27. Draw the shear and moment diagrams for the beam. Wo В A L 3 2L 3

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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Please!! Use only graphical method.

### Problem 6-27 **Objective:** Draw the shear and moment diagrams for the beam. **Description:** A beam is subjected to a varying load that increases linearly from zero at the left end to \( w_0 \) at the right end. The beam is simply supported, with a roller support at point A and a pin support at point B. **Specifications:** - Distance between the supports A and B is divided in the following way: - Length from the left edge to the support at A is \( \frac{L}{3} \). - Length from the support at A to the support at B is \( \frac{2L}{3} \). **Diagram Explanation:** - The beam is represented horizontally. - A triangle representing the increasing load is placed on top of the beam, with arrows pointing downwards to symbolize the direction of the load. - The load intensity starts at zero at the left end of the beam and linearly increases to \( w_0 \) at the right end of the beam. #### Supports: - **A (Roller Support)** - allows for horizontal displacement but not vertical. - **B (Pin Support)** - restricts both vertical and horizontal displacements. The objective of this problem is to analyze the given beam under the specified loading conditions and determine the shear force and bending moment diagrams. **Next Steps:** 1. **Calculate Reaction Forces:** Determine the reactions at supports A and B using equilibrium equations. 2. **Shear Force Diagram:** Use the calculated reactions to sketch the shear force distribution along the length of the beam. 3. **Bending Moment Diagram:** Integrate the shear force distribution to obtain the bending moment distribution along the length of the beam. **Problem Reference:** Prob. 6-27 --- **Note:** Understanding how to draw shear and moment diagrams is crucial for analyzing the structural integrity of beams under various loading conditions. The varying load in this problem introduces complexities that strengthen conceptual understanding of how distributed loads affect shear forces and bending moments.
Transcribed Image Text:### Problem 6-27 **Objective:** Draw the shear and moment diagrams for the beam. **Description:** A beam is subjected to a varying load that increases linearly from zero at the left end to \( w_0 \) at the right end. The beam is simply supported, with a roller support at point A and a pin support at point B. **Specifications:** - Distance between the supports A and B is divided in the following way: - Length from the left edge to the support at A is \( \frac{L}{3} \). - Length from the support at A to the support at B is \( \frac{2L}{3} \). **Diagram Explanation:** - The beam is represented horizontally. - A triangle representing the increasing load is placed on top of the beam, with arrows pointing downwards to symbolize the direction of the load. - The load intensity starts at zero at the left end of the beam and linearly increases to \( w_0 \) at the right end of the beam. #### Supports: - **A (Roller Support)** - allows for horizontal displacement but not vertical. - **B (Pin Support)** - restricts both vertical and horizontal displacements. The objective of this problem is to analyze the given beam under the specified loading conditions and determine the shear force and bending moment diagrams. **Next Steps:** 1. **Calculate Reaction Forces:** Determine the reactions at supports A and B using equilibrium equations. 2. **Shear Force Diagram:** Use the calculated reactions to sketch the shear force distribution along the length of the beam. 3. **Bending Moment Diagram:** Integrate the shear force distribution to obtain the bending moment distribution along the length of the beam. **Problem Reference:** Prob. 6-27 --- **Note:** Understanding how to draw shear and moment diagrams is crucial for analyzing the structural integrity of beams under various loading conditions. The varying load in this problem introduces complexities that strengthen conceptual understanding of how distributed loads affect shear forces and bending moments.
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