20 kN 40 kN/m Al C 150 KN•M 8 m- - 3 m

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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### Problem Statement for Structural Analysis

5) Draw the Shear and Moment diagram for the beam to the right. Be sure to indicate the maximum bending moment and its location in the beam.

#### Description of Beam Loading and Supports

- The beam is supported at point A by a pin connection and at point B by a roller support.
- The length of the beam from A to B is 8 meters, and from B to C is 3 meters.
- A uniformly distributed load (UDL) of 40 kN/m is applied across the span from point A to point B.
- An additional point load of 20 kN is applied at the end of the beam at point C.
- There is also a clockwise moment of 150 kN·m applied at the end of the beam at point C.

The task is to generate the Shear Force Diagram (SFD) and the Bending Moment Diagram (BMD) for the given loading conditions and to locate the point of maximum bending moment on the beam.

#### Parts to Transcribe:

1. **Uniformly Distributed Load (UDL)**: 40 kN/m over a distance of 8 meters from point A to point B.
2. **Point Load**: 20 kN at point C.
3. **Applied Moment**: 150 kN·m at point C.
4. **Span Lengths**: 8 meters between A and B, 3 meters between B and C.
5. **Support Reactions**: 
   - Pin support at A.
   - Roller support at B.

### Steps:

1. **Calculate Support Reactions**:
    - Calculate using equilibrium equations (sum of vertical forces and moments).

2. **Shear Force Diagram (SFD) Construction**:
    - Break down the beam into segments.
    - Determine shear forces at significant points (immediately before and after load application points).

3. **Bending Moment Diagram (BMD) Construction**:
    - Use the SFD to determine moments at significant points.
    - Plot the BMD using relationships between loads, shear forces, and bending moments.

4. **Locate Maximum Bending Moment**:
    - Inspect BMD to find the maximum value and its location along the beam.

In an educational setting, this analysis helps students understand the step-by-step process for structural analysis of different types of loads on beams, enhancing their comprehension of concepts and their real-world applications in
Transcribed Image Text:### Problem Statement for Structural Analysis 5) Draw the Shear and Moment diagram for the beam to the right. Be sure to indicate the maximum bending moment and its location in the beam. #### Description of Beam Loading and Supports - The beam is supported at point A by a pin connection and at point B by a roller support. - The length of the beam from A to B is 8 meters, and from B to C is 3 meters. - A uniformly distributed load (UDL) of 40 kN/m is applied across the span from point A to point B. - An additional point load of 20 kN is applied at the end of the beam at point C. - There is also a clockwise moment of 150 kN·m applied at the end of the beam at point C. The task is to generate the Shear Force Diagram (SFD) and the Bending Moment Diagram (BMD) for the given loading conditions and to locate the point of maximum bending moment on the beam. #### Parts to Transcribe: 1. **Uniformly Distributed Load (UDL)**: 40 kN/m over a distance of 8 meters from point A to point B. 2. **Point Load**: 20 kN at point C. 3. **Applied Moment**: 150 kN·m at point C. 4. **Span Lengths**: 8 meters between A and B, 3 meters between B and C. 5. **Support Reactions**: - Pin support at A. - Roller support at B. ### Steps: 1. **Calculate Support Reactions**: - Calculate using equilibrium equations (sum of vertical forces and moments). 2. **Shear Force Diagram (SFD) Construction**: - Break down the beam into segments. - Determine shear forces at significant points (immediately before and after load application points). 3. **Bending Moment Diagram (BMD) Construction**: - Use the SFD to determine moments at significant points. - Plot the BMD using relationships between loads, shear forces, and bending moments. 4. **Locate Maximum Bending Moment**: - Inspect BMD to find the maximum value and its location along the beam. In an educational setting, this analysis helps students understand the step-by-step process for structural analysis of different types of loads on beams, enhancing their comprehension of concepts and their real-world applications in
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