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Determine the rertical diplacement of point A. Assume members arc Pin connected at their ende. Take A-100 mm? and E-200 GPa for each member. use the method ot virtual work. 3 m A 4m 4 m 20 kN 20 kN 20 kN

Determine the rertical diplacement of point A. Assume members arc Pin connected at their ende. Take A-100 mm? and E-200 GPa for each member. use the method ot virtual work. 3 m A 4m 4 m 20 kN 20 kN 20 kN

Structural Analysis
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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### Problem Statement **Topic:** Structural Analysis - Use of Virtual Work Method **Objective:** Determine the vertical displacement of point A. **Given:** - Members of the structure are pin-connected at their ends. - Cross-sectional area (A) of each member: 100 mm² - Young's Modulus (E) of each member: 200 GPa **Instructions:** Use the method of virtual work for the calculation. ### Diagram Description A truss structure is illustrated, consisting of multiple members connected in a specific arrangement. Key points and dimensions within the structure are as follows: - **Point A**: The point of interest for vertical displacement determination. - **Loads**: - There are three vertical loads, each measuring 20 kN, applied downward on the structure. - The loads are positioned at points A, B, and C. - **Members**: Connecting various points (A, B, C, D, E). - Member AE spans horizontally from point A to point E (4 m). - Member EB spans horizontally from point E to point B (4 m). - Vertical member EC is 3 m. - Diagonal members include one connecting points E and B and another connecting points E and C. ### Explanation of Virtual Work Method The method of virtual work involves applying a hypothetical (virtual) unit load at the point and in the direction of the desired displacement. The calculation proceeds by determining the internal forces from this unit load and then integrating these forces along with the real load-induced internal stresses over the structure to compute the displacement. ### Solution Steps 1. **Assign a unit load at point A in the vertical direction**: - Calculate the internal forces generated by this unit load. 2. **Determine the real internal forces**: - Analyze the truss under the given 20 kN loads at points A, B, and C. 3. **Calculate the internal strain energy**: - Use the given cross-sectional area (A) and Young’s Modulus (E) with the computed forces. 4. **Integrate to find vertical displacement**: - Apply the Virtual Work principle to sum contributions from each member. **Note to Students:** Detailed calculation steps using equilibrium equations, compatibility conditions, and the principle of virtual work should be meticulously followed to ensure the accuracy of the result.
Transcribed Image Text:### Problem Statement **Topic:** Structural Analysis - Use of Virtual Work Method **Objective:** Determine the vertical displacement of point A. **Given:** - Members of the structure are pin-connected at their ends. - Cross-sectional area (A) of each member: 100 mm² - Young's Modulus (E) of each member: 200 GPa **Instructions:** Use the method of virtual work for the calculation. ### Diagram Description A truss structure is illustrated, consisting of multiple members connected in a specific arrangement. Key points and dimensions within the structure are as follows: - **Point A**: The point of interest for vertical displacement determination. - **Loads**: - There are three vertical loads, each measuring 20 kN, applied downward on the structure. - The loads are positioned at points A, B, and C. - **Members**: Connecting various points (A, B, C, D, E). - Member AE spans horizontally from point A to point E (4 m). - Member EB spans horizontally from point E to point B (4 m). - Vertical member EC is 3 m. - Diagonal members include one connecting points E and B and another connecting points E and C. ### Explanation of Virtual Work Method The method of virtual work involves applying a hypothetical (virtual) unit load at the point and in the direction of the desired displacement. The calculation proceeds by determining the internal forces from this unit load and then integrating these forces along with the real load-induced internal stresses over the structure to compute the displacement. ### Solution Steps 1. **Assign a unit load at point A in the vertical direction**: - Calculate the internal forces generated by this unit load. 2. **Determine the real internal forces**: - Analyze the truss under the given 20 kN loads at points A, B, and C. 3. **Calculate the internal strain energy**: - Use the given cross-sectional area (A) and Young’s Modulus (E) with the computed forces. 4. **Integrate to find vertical displacement**: - Apply the Virtual Work principle to sum contributions from each member. **Note to Students:** Detailed calculation steps using equilibrium equations, compatibility conditions, and the principle of virtual work should be meticulously followed to ensure the accuracy of the result.
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