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1. Find the support reactions at A and C. Using method of joints, determine the force in each member of the three-bar truss shown to the right. Specify tension or compression for each member force. (Note: joint A is a pin and joint C is a roller.)

1. Find the support reactions at A and C. Using method of joints, determine the force in each member of the three-bar truss shown to the right. Specify tension or compression for each member force. (Note: joint A is a pin and joint C is a roller.)

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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### Example Truss Problem **Problem Statement:** 1. Find the support reactions at points A and C. Using the method of joints, determine the force in each member of the three-bar truss shown to the right. Specify tension or compression for each member force. - (Note: Joint A is a pin and joint C is a roller.) **Solution:** - Reactions at supports: - \( A_x = 48 \, \text{kN} \rightarrow \) - \( A_y = 84 \, \text{kN} \uparrow \) - \( C_x = 48 \, \text{kN} \leftarrow \) - Forces in truss members: - \( F_{AB} = 52 \, \text{kN} \) (Tension) - \( F_{AC} = 64 \, \text{kN} \) (Tension) - \( F_{BC} = 80 \, \text{kN} \) (Compression) **Diagram Explanation:** - The truss is a triangular structure with joints at points A, B, and C. - The truss is supported at A (a pin joint that can support both horizontal and vertical forces) and at C (a roller joint which can only support vertical forces plus horizontal force at C in this problem). - The load applied is 84 kN downwards at point B. - The dimensions of the truss are given, with the horizontal distance from A to B as 3 meters, the vertical distance from B to C as 4 meters, and a vertical offset of 1.25 meters from A to B along the vertical line through A.
Transcribed Image Text:### Example Truss Problem **Problem Statement:** 1. Find the support reactions at points A and C. Using the method of joints, determine the force in each member of the three-bar truss shown to the right. Specify tension or compression for each member force. - (Note: Joint A is a pin and joint C is a roller.) **Solution:** - Reactions at supports: - \( A_x = 48 \, \text{kN} \rightarrow \) - \( A_y = 84 \, \text{kN} \uparrow \) - \( C_x = 48 \, \text{kN} \leftarrow \) - Forces in truss members: - \( F_{AB} = 52 \, \text{kN} \) (Tension) - \( F_{AC} = 64 \, \text{kN} \) (Tension) - \( F_{BC} = 80 \, \text{kN} \) (Compression) **Diagram Explanation:** - The truss is a triangular structure with joints at points A, B, and C. - The truss is supported at A (a pin joint that can support both horizontal and vertical forces) and at C (a roller joint which can only support vertical forces plus horizontal force at C in this problem). - The load applied is 84 kN downwards at point B. - The dimensions of the truss are given, with the horizontal distance from A to B as 3 meters, the vertical distance from B to C as 4 meters, and a vertical offset of 1.25 meters from A to B along the vertical line through A.
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