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4-63. Determine the magnitude of the moment of the force F= {50i – 20j – 80k} N about the base line CA of the tripod. D 4 m 2 m 1.5 m 2.5 m 2 m 0.5 m B Probs. 4–61/62/63

4-63. Determine the magnitude of the moment of the force F= {50i – 20j – 80k} N about the base line CA of the tripod. D 4 m 2 m 1.5 m 2.5 m 2 m 0.5 m B Probs. 4–61/62/63

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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Question
The problem, labeled as 4–63, requires you to calculate the magnitude of the moment of the force \( \mathbf{F} = \{50\mathbf{i} - 20\mathbf{j} - 80\mathbf{k}\} \, \text{N} \) around the base line \( CA \) of the tripod structure. ### Diagram Explanation The diagram depicts a 3D structure, resembling a tripod, with three main points—A, B, and C—forming the base on the xy-plane and a point D elevated along the z-axis. - **Points and Distances:** - **Point A:** Positioned 2.5 m along the y-axis. - **Point B:** Positioned 0.5 m along the x-axis and 1 m along the y-axis. - **Point C:** Positioned 1.5 m along the x-axis. - **Point D:** Elevated 4 m above the xy-plane (z-axis). - **Force \( \mathbf{F} \):** This force is applied at point D, directed downward. ### Structural Elements - The tripod has triangular elements formed by lines connecting the base corners (A, B, C) and the top point D. These lines represent the tripod legs. ### Contextual Framework The task involves determining the rotational effect of the force \( \mathbf{F} \) about a line segment (CA) on the structure, using principles of vector mechanics, specifically involving the calculation of moments. ### Problem References - The problem is part of a sequence: Probs. 4–61/62/63, suggesting it is related to similar problems involving vector dynamics and force analysis. For a thorough understanding and solution, one would typically apply concepts of cross-product to compute the moment and follow the specific geometry of the tripod structure and the force's line of action.
Transcribed Image Text:The problem, labeled as 4–63, requires you to calculate the magnitude of the moment of the force \( \mathbf{F} = \{50\mathbf{i} - 20\mathbf{j} - 80\mathbf{k}\} \, \text{N} \) around the base line \( CA \) of the tripod structure. ### Diagram Explanation The diagram depicts a 3D structure, resembling a tripod, with three main points—A, B, and C—forming the base on the xy-plane and a point D elevated along the z-axis. - **Points and Distances:** - **Point A:** Positioned 2.5 m along the y-axis. - **Point B:** Positioned 0.5 m along the x-axis and 1 m along the y-axis. - **Point C:** Positioned 1.5 m along the x-axis. - **Point D:** Elevated 4 m above the xy-plane (z-axis). - **Force \( \mathbf{F} \):** This force is applied at point D, directed downward. ### Structural Elements - The tripod has triangular elements formed by lines connecting the base corners (A, B, C) and the top point D. These lines represent the tripod legs. ### Contextual Framework The task involves determining the rotational effect of the force \( \mathbf{F} \) about a line segment (CA) on the structure, using principles of vector mechanics, specifically involving the calculation of moments. ### Problem References - The problem is part of a sequence: Probs. 4–61/62/63, suggesting it is related to similar problems involving vector dynamics and force analysis. For a thorough understanding and solution, one would typically apply concepts of cross-product to compute the moment and follow the specific geometry of the tripod structure and the force's line of action.
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