### 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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