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4- For the beam shown in Figure, determine the displacements and the slopes at the nodes, the forces in each element, and the reactions. E = 30 x 10 psi, and I = 200 in¹.

4- For the beam shown in Figure, determine the displacements and the slopes at the nodes, the forces in each element, and the reactions. E = 30 x 10 psi, and I = 200 in¹.

Elements Of Electromagnetics
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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This is Mechanical Engineering. Please answer with clear work and answers. Thank you

**Problem Statement:** 4 - For the beam shown in the figure, determine the displacements and the slopes at the nodes, the forces in each element, and the reactions. \( E = 30 \times 10^6 \, \text{psi} \), and \( I = 200 \, \text{in}^4 \). **Diagram Explanation:** The diagram shows a horizontal beam with three nodes labeled 1, 2, and 3. The beam is fixed at the left end (node 1) and is supported by a roller at node 2, with a 0.5-inch gap between the roller and the beam. At node 3, a vertical force of 500 lb is applied downward. - **Span Details:** - The beam is 40 feet long in total, divided into two spans of 20 feet each between nodes 1, 2, and 3. - **Support Conditions:** - Node 1 is fixed. - Node 2 is supported by a roller located directly under it, with a 0.5-inch gap. - Node 3 has an applied downward force of 500 lb. **Material Properties:** - Modulus of Elasticity, \( E = 30 \times 10^6 \) psi. - Moment of Inertia, \( I = 200 \, \text{in}^4 \). The task is to calculate the displacements and slopes at each node, forces in the beam segments, and the reactions at the supports based on the given conditions.
Transcribed Image Text:**Problem Statement:** 4 - For the beam shown in the figure, determine the displacements and the slopes at the nodes, the forces in each element, and the reactions. \( E = 30 \times 10^6 \, \text{psi} \), and \( I = 200 \, \text{in}^4 \). **Diagram Explanation:** The diagram shows a horizontal beam with three nodes labeled 1, 2, and 3. The beam is fixed at the left end (node 1) and is supported by a roller at node 2, with a 0.5-inch gap between the roller and the beam. At node 3, a vertical force of 500 lb is applied downward. - **Span Details:** - The beam is 40 feet long in total, divided into two spans of 20 feet each between nodes 1, 2, and 3. - **Support Conditions:** - Node 1 is fixed. - Node 2 is supported by a roller located directly under it, with a 0.5-inch gap. - Node 3 has an applied downward force of 500 lb. **Material Properties:** - Modulus of Elasticity, \( E = 30 \times 10^6 \) psi. - Moment of Inertia, \( I = 200 \, \text{in}^4 \). The task is to calculate the displacements and slopes at each node, forces in the beam segments, and the reactions at the supports based on the given conditions.
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