**Problem 3: Analysis of a Compound Beam**The compound beam illustrated in the figure consists of two beams, AB and BC, which are connected at point B with a pin. This system is subjected to a variety of loads, including a distributed force, a point load, and a couple moment.1. **Support Reactions:** - Calculate the reaction forces at supports A (left end) and C (right end), as well as the force exerted at pin B.2. **Shear-Force and Bending-Moment Diagrams:** - Use the shortcut method to construct the shear-force and bending-moment diagrams for the entire beam assembly.3. **Maximum Values:** - Identify the maximum shear force and bending moment values along with their precise locations on the beam.**Figure Explanation:**- **Beam AB:** - The left portion (AB) begins at support A. - It is subjected to a linearly distributed load increasing from 0 to 12 lb/in over a span of 6 inches (5 in to 11 in).- **Beam BC:** - Middle beam BC starts at B and ends at C. - Immediately after A, a point load of 60 lb is applied 8 inches to the right of pin B. - A couple moment of 120 lb·in acts 5 inches before support C.- **Supports:** - A is a fixed support. - C is a roller support. The entire beam spans 31 inches: 5 inches to the first section, plus 6 inches to the peak of the triangular distributed load, 7 inches to pin B, another 5 inches past B, and a final 7 inches to support C.

3. The compound beam given in the figure is composed of a pair of beams, AB and BC, connected by a pin at B. The compound beam is subjected to a distributed force, a point force, and a couple moment. a. Compute the reactions at the supports A and C, and the force on pin B. b. Use the shortcut method to draw the shear-force and bending-moment diagrams for the entire compound beam. c. Determine the maximum values of shear force and bending moment for the compound beam along with their locations. A 5 in 6 in 12 lb/in 7 in Pin 8 in 60 lb I B 5 in 120 lb.in 7 in C

3. The compound beam given in the figure is composed of a pair of beams, AB and BC, connected by a pin at B. The compound beam is subjected to a distributed force, a point force, and a couple moment. a. Compute the reactions at the supports A and C, and the force on pin B. b. Use the shortcut method to draw the shear-force and bending-moment diagrams for the entire compound beam. c. Determine the maximum values of shear force and bending moment for the compound beam along with their locations. A 5 in 6 in 12 lb/in 7 in Pin 8 in 60 lb I B 5 in 120 lb.in 7 in C

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

**Problem 3: Analysis of a Compound Beam**

The compound beam illustrated in the figure consists of two beams, AB and BC, which are connected at point B with a pin. This system is subjected to a variety of loads, including a distributed force, a point load, and a couple moment.

1. **Support Reactions:**
- Calculate the reaction forces at supports A (left end) and C (right end), as well as the force exerted at pin B.

2. **Shear-Force and Bending-Moment Diagrams:**
- Use the shortcut method to construct the shear-force and bending-moment diagrams for the entire beam assembly.

3. **Maximum Values:**
- Identify the maximum shear force and bending moment values along with their precise locations on the beam.

**Figure Explanation:**

- **Beam AB:**
- The left portion (AB) begins at support A.
- It is subjected to a linearly distributed load increasing from 0 to 12 lb/in over a span of 6 inches (5 in to 11 in).
- **Beam BC:**
- Middle beam BC starts at B and ends at C.
- Immediately after A, a point load of 60 lb is applied 8 inches to the right of pin B.
- A couple moment of 120 lb·in acts 5 inches before support C.
- **Supports:**
- A is a fixed support.
- C is a roller support.

The entire beam spans 31 inches: 5 inches to the first section, plus 6 inches to the peak of the triangular distributed load, 7 inches to pin B, another 5 inches past B, and a final 7 inches to support C.

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Step 2: Convert uniformly distributed and varying load into point loads

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Step 3: Calculation of support reactions

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Step 4: Calculation of shear force diagram

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Step 5: Calculation of bending moment diagram

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Step 6: Calculation of bending moment diagram

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Step 7: Calculation of maximum bending moment and its location

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Step 8: Draw shear force and bending moment diagram

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