M=Pa а С а C M=2Pa a 2P B

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Use singularity functions to obtain shear force, bending moment, and deflections of the beams for the following 2 cases
The image shows two structural diagrams, both illustrating beams under loading conditions.

### Diagram 1 (Left Side)

- **Beam AB**: This is a horizontal beam with fixed support at point A and free end at point B.
- **Loading**:
  - At point B, there is a vertical downward force labeled as **P**.
  - At point C, which is midpoint between A and B (distance **a** from both), a counterclockwise moment **M = Pa** is applied.
- **Dimensions**: The beam is divided into two equal segments of length **a**.

### Diagram 2 (Right Side)

- **Beam AB**: This is a simply supported beam with a support at point A and a roller support at point B.
- **Loading**:
  - At point C (distance **a** from A), a vertical downward force labeled as **P** is applied.
  - At point D (distance **a** from C), there is a vertical downward force labeled as **2P**.
  - A counterclockwise moment **M = 2Pa** is applied at point C.
- **Dimensions**: The beam is divided into three equal segments of length **a** each.

### Explanation

Both diagrams represent typical problems studied in structural analysis courses to examine the effects of different loading conditions on beams. These analyses often involve determining reactions at the supports, internal shear forces, and bending moments along the beam.
Transcribed Image Text:The image shows two structural diagrams, both illustrating beams under loading conditions. ### Diagram 1 (Left Side) - **Beam AB**: This is a horizontal beam with fixed support at point A and free end at point B. - **Loading**: - At point B, there is a vertical downward force labeled as **P**. - At point C, which is midpoint between A and B (distance **a** from both), a counterclockwise moment **M = Pa** is applied. - **Dimensions**: The beam is divided into two equal segments of length **a**. ### Diagram 2 (Right Side) - **Beam AB**: This is a simply supported beam with a support at point A and a roller support at point B. - **Loading**: - At point C (distance **a** from A), a vertical downward force labeled as **P** is applied. - At point D (distance **a** from C), there is a vertical downward force labeled as **2P**. - A counterclockwise moment **M = 2Pa** is applied at point C. - **Dimensions**: The beam is divided into three equal segments of length **a** each. ### Explanation Both diagrams represent typical problems studied in structural analysis courses to examine the effects of different loading conditions on beams. These analyses often involve determining reactions at the supports, internal shear forces, and bending moments along the beam.
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