**Beam Analysis with Pin and Roller Supports**This instructional figure illustrates the analysis of internal shear force and bending moment for a simply supported beam. The beam is uniformly loaded with a force intensity "w" and has two supports: - A pin support at point A (indicated by a triangle), which allows rotation but no translation.- A roller support at point B (indicated by a circle), which allows horizontal translation. The beam length is divided into two equal segments:- Segment "a" from the pin support, where \( a = \frac{L}{2} \).- Segment "b" from the roller support, where \( b = \frac{L}{2} \).**Load Distribution:**- The load is uniformly distributed across the entire span of the beam.- The reaction forces at the supports (denoted by upward arrows) are crucial for equilibrium.To sketch the internal shear force and moment as a function of the beam length, consider:1. **Shear Force Diagram (SFD):** - Begins with the reaction force at A. - Decreases linearly with the distribution of load \( w \) across the beam.2. **Bending Moment Diagram (BMD):** - Starts at zero at both the pin and roller supports. - Reaches a maximum at the center of the beam.**Boundary Conditions:**- At the pin support (point A), the beam cannot translate vertically or horizontally.- At the roller support (point B), the beam can translate horizontally.This configuration is fundamental in structural engineering, providing insight into how loads are resisted by supports and how internal forces develop over the beam's length.

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Answered: Sketch the internal shear and moment as…

Sketch the internal shear and moment as a function of the beam length (triangle denotes a pin boundary condition): a = b = L/2 W M A a b B

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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Question

**Beam Analysis with Pin and Roller Supports**

This instructional figure illustrates the analysis of internal shear force and bending moment for a simply supported beam. The beam is uniformly loaded with a force intensity "w" and has two supports:

- A pin support at point A (indicated by a triangle), which allows rotation but no translation.
- A roller support at point B (indicated by a circle), which allows horizontal translation.

The beam length is divided into two equal segments:

- Segment "a" from the pin support, where \( a = \frac{L}{2} \).
- Segment "b" from the roller support, where \( b = \frac{L}{2} \).

**Load Distribution:**

- The load is uniformly distributed across the entire span of the beam.
- The reaction forces at the supports (denoted by upward arrows) are crucial for equilibrium.

To sketch the internal shear force and moment as a function of the beam length, consider:

1. **Shear Force Diagram (SFD):**
- Begins with the reaction force at A.
- Decreases linearly with the distribution of load \( w \) across the beam.

2. **Bending Moment Diagram (BMD):**
- Starts at zero at both the pin and roller supports.
- Reaches a maximum at the center of the beam.

**Boundary Conditions:**

- At the pin support (point A), the beam cannot translate vertically or horizontally.
- At the roller support (point B), the beam can translate horizontally.

This configuration is fundamental in structural engineering, providing insight into how loads are resisted by supports and how internal forces develop over the beam's length.

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