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25 KN Using the method that has been covered, find the displacement of the node 2 if E1 = 100 GPa and A1=10-6 m² and E2= 200 GPa and A2=2x10-6 m². N2 5 cm 2 30° |N3 N1 Note: The stiffness matrix of individual elements should be first written, then the equilibrium equations at each node should be written, expanded in terms of nodal displacement, and used to perform the assembly of the global stiffness matrix of the problem. Then, the appropriate boundary conditions should be applied and the nodal displacement vector should be found. Every step should be shown; missing any step would result in point deduction even if the final answer is correct

25 KN Using the method that has been covered, find the displacement of the node 2 if E1 = 100 GPa and A1=10-6 m² and E2= 200 GPa and A2=2x10-6 m². N2 5 cm 2 30° |N3 N1 Note: The stiffness matrix of individual elements should be first written, then the equilibrium equations at each node should be written, expanded in terms of nodal displacement, and used to perform the assembly of the global stiffness matrix of the problem. Then, the appropriate boundary conditions should be applied and the nodal displacement vector should be found. Every step should be shown; missing any step would result in point deduction even if the final answer is correct

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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**Problem:** Using the method that has been covered, find the displacement of node 2 if \( E_1 = 100 \, \text{GPa} \) and \( A_1 = 10^{-6} \, \text{m}^2 \) and \( E_2 = 200 \, \text{GPa} \) and \( A_2 = 2 \times 10^{-6} \, \text{m}^2 \). *Diagram:* The diagram shows a truss with three nodes: \( N_1, N_2, \) and \( N_3 \). - Member 1 connects \( N_1 \) and \( N_2 \) at a 30° angle with respect to the horizontal. - Member 2 is vertical, connecting \( N_2 \) and \( N_3 \). - A load of 25 kN is applied vertically at \( N_2 \). - There is a vertical distance of 5 cm between \( N_2 \) and \( N_3 \). - \( N_1 \) and \( N_3 \) are fixed supports. **Note:** The stiffness matrix of individual elements should be first written, then the equilibrium equations at each node should be written, expanded in terms of nodal displacement, and used to perform the assembly of the global stiffness matrix of the problem. Then, the appropriate boundary conditions should be applied and the nodal displacement vector should be found. Every step should be shown; missing any step would result in point deduction even if the final answer is correct.
Transcribed Image Text:**Problem:** Using the method that has been covered, find the displacement of node 2 if \( E_1 = 100 \, \text{GPa} \) and \( A_1 = 10^{-6} \, \text{m}^2 \) and \( E_2 = 200 \, \text{GPa} \) and \( A_2 = 2 \times 10^{-6} \, \text{m}^2 \). *Diagram:* The diagram shows a truss with three nodes: \( N_1, N_2, \) and \( N_3 \). - Member 1 connects \( N_1 \) and \( N_2 \) at a 30° angle with respect to the horizontal. - Member 2 is vertical, connecting \( N_2 \) and \( N_3 \). - A load of 25 kN is applied vertically at \( N_2 \). - There is a vertical distance of 5 cm between \( N_2 \) and \( N_3 \). - \( N_1 \) and \( N_3 \) are fixed supports. **Note:** The stiffness matrix of individual elements should be first written, then the equilibrium equations at each node should be written, expanded in terms of nodal displacement, and used to perform the assembly of the global stiffness matrix of the problem. Then, the appropriate boundary conditions should be applied and the nodal displacement vector should be found. Every step should be shown; missing any step would result in point deduction even if the final answer is correct.
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