Draw the shear force and the bending moment diagrams of the beam

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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3. Draw the shear force and the bending moment diagrams of the beam

### Beam Loading Diagram

The image depicts a simply supported beam subjected to a combination of distributed and point loads. Below is a detailed description suitable for an educational context.

#### Beam Description

- **Support Points:**
  - Point **A** (on the left) is a hinged support.
  - Point **B** (on the right) is a roller support.

#### Loads Acting on the Beam

1. **Uniformly Distributed Load (UDL)**:
   - Magnitude: **2 kN/m**
   - Length: **5 meters**
   - Distributed from point **A** to a point 5 meters to the right of **A**.

2. **Point Load**:
   - Magnitude: **10 kN**
   - Applied at a point 8 meters from the left end of the beam (3 meters from the end of the UDL).

#### Beam Dimensions

- Total length of the beam: **10 meters**
  - Distance between **A** and B**: **10 meters**
  - Position of UDL: Starting at **A** and extending 5 meters to the right.
  - Position of Point Load: Placed 8 meters from **A** (3 meters from the end of the UDL).

This configuration is typically analyzed to determine the reactions at the supports and to draw shear force and bending moment diagrams.

#### Explanation of Diagram Components

1. **Supports**:
   - **A**: Hinged support, allowing rotation but preventing translation in any direction.
   - **B**: Roller support, allowing horizontal movement but preventing vertical translation.

2. **Load Distribution**:
   - The UDL creates a uniformly spread load over the specified 5 meters, resulting in a distributed force that will vary linearly.
   - The point load imposes a concentrated force, sharply affecting the shear force and bending moment diagrams.

### Educational Importance

Understanding this configuration helps in analyzing real-world structures like bridges, where beams are subjected to various load types. Calculating reactions, shear forces, and bending moments are fundamental skills in structural engineering and mechanics of materials.

Diagrams of such configurations are routinely used in studying the behavior of structural elements under load and are critical in the design and safety assessment of engineering structures.
Transcribed Image Text:### Beam Loading Diagram The image depicts a simply supported beam subjected to a combination of distributed and point loads. Below is a detailed description suitable for an educational context. #### Beam Description - **Support Points:** - Point **A** (on the left) is a hinged support. - Point **B** (on the right) is a roller support. #### Loads Acting on the Beam 1. **Uniformly Distributed Load (UDL)**: - Magnitude: **2 kN/m** - Length: **5 meters** - Distributed from point **A** to a point 5 meters to the right of **A**. 2. **Point Load**: - Magnitude: **10 kN** - Applied at a point 8 meters from the left end of the beam (3 meters from the end of the UDL). #### Beam Dimensions - Total length of the beam: **10 meters** - Distance between **A** and B**: **10 meters** - Position of UDL: Starting at **A** and extending 5 meters to the right. - Position of Point Load: Placed 8 meters from **A** (3 meters from the end of the UDL). This configuration is typically analyzed to determine the reactions at the supports and to draw shear force and bending moment diagrams. #### Explanation of Diagram Components 1. **Supports**: - **A**: Hinged support, allowing rotation but preventing translation in any direction. - **B**: Roller support, allowing horizontal movement but preventing vertical translation. 2. **Load Distribution**: - The UDL creates a uniformly spread load over the specified 5 meters, resulting in a distributed force that will vary linearly. - The point load imposes a concentrated force, sharply affecting the shear force and bending moment diagrams. ### Educational Importance Understanding this configuration helps in analyzing real-world structures like bridges, where beams are subjected to various load types. Calculating reactions, shear forces, and bending moments are fundamental skills in structural engineering and mechanics of materials. Diagrams of such configurations are routinely used in studying the behavior of structural elements under load and are critical in the design and safety assessment of engineering structures.
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