### Shear and Moment Diagram of a BeamThis example demonstrates how to find the shear and moment diagram of a beam using the graphical method. The beam is subjected to uniformly distributed load \( w \) and point loads \( F1 \) and \( F2 \), with supports at points \( R1 \) and \( R2 \).#### Diagram Breakdown:1. **Beam Configuration:** - **Loads:** - A uniformly distributed load \( w \) spans across the length of the beam. - Point loads \( F1 \) and \( F2 \) act downward on the beam. 2. **Dimensions:** - The total length of the beam is \( L \). - \( F1 \) is located \( \frac{L}{3} \) from the left support \( R1 \). - \( F2 \) is located \( \frac{2L}{3} \) from the left support \( R1 \).3. **Reactions at Supports:** - Support reaction at \( R1 \): \( R1 = \frac{4}{3} wL \) - Support reaction at \( R2 \): \( R2 = \frac{7}{6} wL \)4. **Point Loads:** - \( F1 = wL \) - \( F2 = \frac{wL}{2} \)#### Steps to Create Shear and Moment Diagrams:1. **Shear Diagram:** - Start from the left end of the beam. - The initial value at \( R1 \) is \( \frac{4}{3} wL \). - Subtract the shear effect of the distributed load \( w \) and the point loads \( F1 \) and \( F2 \) as you move from left to right along the beam.2. **Moment Diagram:** - Calculate the areas under the shear diagram to find the moment at various points along the beam. - Integrate the shear diagram: The area of each segment of the shear diagram translates to the value of the moment diagram at that point.Use the values derived above to plot the shear and moment at several key points along the beam length. Ensure to label critical points where loads act and reactions occur for clarity in analysis.

Solution:-1. Shear force at various sections:

Answered: F2 RI Find the shear and moment diagram…

F2 RI Find the shear and moment diagram of this beam. Use graphical method and show how each area is calculated to get the moment diagram.R1=4/3 wL and R2= 7/6 wL. F1=wL and F2=wL/2

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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### Shear and Moment Diagram of a Beam

This example demonstrates how to find the shear and moment diagram of a beam using the graphical method. The beam is subjected to uniformly distributed load \( w \) and point loads \( F1 \) and \( F2 \), with supports at points \( R1 \) and \( R2 \).

#### Diagram Breakdown:

1. **Beam Configuration:**
- **Loads:**
- A uniformly distributed load \( w \) spans across the length of the beam.
- Point loads \( F1 \) and \( F2 \) act downward on the beam.

2. **Dimensions:**
- The total length of the beam is \( L \).
- \( F1 \) is located \( \frac{L}{3} \) from the left support \( R1 \).
- \( F2 \) is located \( \frac{2L}{3} \) from the left support \( R1 \).

3. **Reactions at Supports:**
- Support reaction at \( R1 \): \( R1 = \frac{4}{3} wL \)
- Support reaction at \( R2 \): \( R2 = \frac{7}{6} wL \)

4. **Point Loads:**
- \( F1 = wL \)
- \( F2 = \frac{wL}{2} \)

#### Steps to Create Shear and Moment Diagrams:

1. **Shear Diagram:**
- Start from the left end of the beam.
- The initial value at \( R1 \) is \( \frac{4}{3} wL \).
- Subtract the shear effect of the distributed load \( w \) and the point loads \( F1 \) and \( F2 \) as you move from left to right along the beam.

2. **Moment Diagram:**
- Calculate the areas under the shear diagram to find the moment at various points along the beam.
- Integrate the shear diagram: The area of each segment of the shear diagram translates to the value of the moment diagram at that point.

Use the values derived above to plot the shear and moment at several key points along the beam length. Ensure to label critical points where loads act and reactions occur for clarity in analysis.

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