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Using the method of joints, determine the force in each member of the truss shown below. Summarize the results on a force summation diagram, and indicate whether each member is in tension or compression. 30° 1000 lb 10' F 10' 1000 Ib 10' 10'

Using the method of joints, determine the force in each member of the truss shown below. Summarize the results on a force summation diagram, and indicate whether each member is in tension or compression. 30° 1000 lb 10' F 10' 1000 Ib 10' 10'

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 3. Using the method of joints, determine the force in each member of the truss shown below. Summarize the results on a force summation diagram and indicate whether each member is in tension or compression. ### Diagram Description The diagram depicts a truss structure with the following specifications: - **Members**: The truss consists of several triangular units formed by members AC, AB, BC, BD, DE, EC, EF, and CF. - **Connected Joints**: - Joint A is connected to joints B and C. - Joint B is connected to joints A, C, and D. - Joint C is connected to joints A, B, E, and F. - Joint D is connected to joints B and E. - Joint E is connected to joints C, D, and F. - Joint F is connected to joints C and E. - **Support Reactions**: - Joint A is pinned to a wall, providing horizontal and vertical support. - Joint D is similarly pinned to a wall. - **Dimensions**: The truss has specified horizontal distances: - The horizontal distance between AB, BC, CD, and DE is 10 feet each. - **Loads**: - There is a 1000 lb downward force acting on joint F. - There is an inclined 1000 lb force acting at joint E at a 30-degree angle to the horizontal axis. ### Solution Approach To solve this problem, apply the method of joints by analyzing each joint under equilibrium conditions. Each joint satisfies the conditions of equilibrium: - Sum of forces in the horizontal direction (ΣF_x) = 0 - Sum of forces in the vertical direction (ΣF_y) = 0 Determine the force in each member and label it as either: - **Tension (T)**: If the member is being stretched or pulled. - **Compression (C)**: If the member is being squashed or compressed. By systematically analyzing each joint, calculate the forces and deduce the nature (tension or compression) of each member.
Transcribed Image Text:### Problem Statement 3. Using the method of joints, determine the force in each member of the truss shown below. Summarize the results on a force summation diagram and indicate whether each member is in tension or compression. ### Diagram Description The diagram depicts a truss structure with the following specifications: - **Members**: The truss consists of several triangular units formed by members AC, AB, BC, BD, DE, EC, EF, and CF. - **Connected Joints**: - Joint A is connected to joints B and C. - Joint B is connected to joints A, C, and D. - Joint C is connected to joints A, B, E, and F. - Joint D is connected to joints B and E. - Joint E is connected to joints C, D, and F. - Joint F is connected to joints C and E. - **Support Reactions**: - Joint A is pinned to a wall, providing horizontal and vertical support. - Joint D is similarly pinned to a wall. - **Dimensions**: The truss has specified horizontal distances: - The horizontal distance between AB, BC, CD, and DE is 10 feet each. - **Loads**: - There is a 1000 lb downward force acting on joint F. - There is an inclined 1000 lb force acting at joint E at a 30-degree angle to the horizontal axis. ### Solution Approach To solve this problem, apply the method of joints by analyzing each joint under equilibrium conditions. Each joint satisfies the conditions of equilibrium: - Sum of forces in the horizontal direction (ΣF_x) = 0 - Sum of forces in the vertical direction (ΣF_y) = 0 Determine the force in each member and label it as either: - **Tension (T)**: If the member is being stretched or pulled. - **Compression (C)**: If the member is being squashed or compressed. By systematically analyzing each joint, calculate the forces and deduce the nature (tension or compression) of each member.
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