### Problem 5#### Using the **conjugate-beam method**, determine the displacement at D and the slope at D. Assume A is fixed support, B is a pin, and C is a roller. Take \( E = 29 \times 10^3 \) ksi, \( I = 650 \text{ in}^4 \).#### Diagram Description:- The diagram presents a beam that is 36 feet in length, divided into three segments of 12 feet each.- The leftmost support (A) is fixed.- The second support (B) is a pin located 12 feet from point A.- The third support (C) is a roller located another 12 feet from point B.- At point D, which is 12 feet beyond support C (at the far right end of the beam), there is a downward vertical force of 24 kips (24 k).#### Important Variables and Parameters:- **E (Modulus of Elasticity):** \( 29 \times 10^3 \) ksi- **I (Moment of Inertia):** \( 650 \text{ in}^4 \)### Analysis:To solve this problem using the conjugate-beam method, follow these steps:1. **Beam Identification:** - Identify the type of beam, its supports, and its loading conditions.2. **Create Shear and Moment Diagrams of the Original Beam:** - Compute the reactions at supports. - Establish the shear force diagram and moment diagram.3. **Convert the Original Beam to a Conjugate Beam:** - Change the boundary conditions: Fixed support becomes free end, pin becomes a hinge, and roller becomes a free end. - The lengths of spans remain the same, and the distributed load will be based on the moment diagram of the original beam divided by EI.4. **Analyze the Conjugate Beam:** - Calculate the reactions for the conjugate beam. - Draw the shear and moment diagrams for the conjugate beam.5. **Determine Slope and Deflection:** - The slope at a point in the original beam is equal to the vertical deflection at that point in the conjugate beam. - The deflection at a point in the original beam is equal to the slope at that point in the conjugate beam.Following through these calculations will allow determination of the displacement and slope at point

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Using the conjugate-beam method, determine the displacement at D and the slope at D. Assume A is fixed support, B is a pin, and C is a roller. Take E = 29×10³ ksi, I = 650 in¹. A -12 ft- B 12 ft- Ic 12 ft- 24 k

Using the conjugate-beam method, determine the displacement at D and the slope at D. Assume A is fixed support, B is a pin, and C is a roller. Take E = 29×10³ ksi, I = 650 in¹. A -12 ft- B 12 ft- Ic 12 ft- 24 k

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

### Problem 5

#### Using the **conjugate-beam method**, determine the displacement at D and the slope at D. Assume A is fixed support, B is a pin, and C is a roller. Take \( E = 29 \times 10^3 \) ksi, \( I = 650 \text{ in}^4 \).

#### Diagram Description:

- The diagram presents a beam that is 36 feet in length, divided into three segments of 12 feet each.
- The leftmost support (A) is fixed.
- The second support (B) is a pin located 12 feet from point A.
- The third support (C) is a roller located another 12 feet from point B.
- At point D, which is 12 feet beyond support C (at the far right end of the beam), there is a downward vertical force of 24 kips (24 k).

#### Important Variables and Parameters:

- **E (Modulus of Elasticity):** \( 29 \times 10^3 \) ksi
- **I (Moment of Inertia):** \( 650 \text{ in}^4 \)

### Analysis:

To solve this problem using the conjugate-beam method, follow these steps:

1. **Beam Identification:**
- Identify the type of beam, its supports, and its loading conditions.

2. **Create Shear and Moment Diagrams of the Original Beam:**
- Compute the reactions at supports.
- Establish the shear force diagram and moment diagram.

3. **Convert the Original Beam to a Conjugate Beam:**
- Change the boundary conditions: Fixed support becomes free end, pin becomes a hinge, and roller becomes a free end.
- The lengths of spans remain the same, and the distributed load will be based on the moment diagram of the original beam divided by EI.

4. **Analyze the Conjugate Beam:**
- Calculate the reactions for the conjugate beam.
- Draw the shear and moment diagrams for the conjugate beam.

5. **Determine Slope and Deflection:**
- The slope at a point in the original beam is equal to the vertical deflection at that point in the conjugate beam.
- The deflection at a point in the original beam is equal to the slope at that point in the conjugate beam.

Following through these calculations will allow determination of the displacement and slope at point

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Step 3: Apply conjugate beam method to find unknowns

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Step 4: conjugate beam method continued

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