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Show all Free Body Diagrams   A) Use the Method of Joints to find the forces in AB and BC. Indicate whether its tension or compression.

Show all Free Body Diagrams   A) Use the Method of Joints to find the forces in AB and BC. Indicate whether its tension or compression.

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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Show all Free Body Diagrams

 

A) Use the Method of Joints to find the forces in AB and BC. Indicate whether its tension or compression.

**Instruction:** Use the method of joints to find the forces in AB & BC. Indicate T (tension) or C (compression). **Diagram Explanation:** The diagram is a truss structure with labeled joints and known forces. 1. **Structure Geometry:** - Right triangle with vertices labeled A, B, C, and D. - Vertical height at point B is 12 feet from the base (6' + 6'). - Horizontal base stretches 16 feet total (8' from A to C and 8' from C to D). 2. **Truss Members:** - Members AB, BC, CD, and AD are the truss elements. - Joint A is connected to B and D. - Joint B is connected to A and C. - Joint C is connected to B and D. 3. **Load and Supports:** - A force of 1000 lb is applied horizontally to the right at joint C. - A force of 5000 lb is applied vertically downward at joint D. - Supports at joints A and B (as indicated by typical roller and pin support symbols). 4. **Task:** - Determine the forces in members AB and BC. - Indicate whether the forces in these members are in tension (T) or compression (C) using the method of joints. The task involves analyzing the static equilibrium of the truss to solve for unknown forces in specific members.
Transcribed Image Text:**Instruction:** Use the method of joints to find the forces in AB & BC. Indicate T (tension) or C (compression). **Diagram Explanation:** The diagram is a truss structure with labeled joints and known forces. 1. **Structure Geometry:** - Right triangle with vertices labeled A, B, C, and D. - Vertical height at point B is 12 feet from the base (6' + 6'). - Horizontal base stretches 16 feet total (8' from A to C and 8' from C to D). 2. **Truss Members:** - Members AB, BC, CD, and AD are the truss elements. - Joint A is connected to B and D. - Joint B is connected to A and C. - Joint C is connected to B and D. 3. **Load and Supports:** - A force of 1000 lb is applied horizontally to the right at joint C. - A force of 5000 lb is applied vertically downward at joint D. - Supports at joints A and B (as indicated by typical roller and pin support symbols). 4. **Task:** - Determine the forces in members AB and BC. - Indicate whether the forces in these members are in tension (T) or compression (C) using the method of joints. The task involves analyzing the static equilibrium of the truss to solve for unknown forces in specific members.
Expert Solution
Step 1

Given:

Mechanical Engineering homework question answer, step 1, image 1

Step 2

Take moment about point B

∑MB=0-RAX12+5000×16-1000×6=0RAX=6166.67 lb

Ballance the force in x and y directions

∑Fx=0RAX+RBX+1000=0RBX=-7166.67 lb

∑Fy=0RBY+5000=0RBY=-5000 lb

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