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Q.3) Determine the tensions in the three cables supporting a weight of 100 N as shown in figure below. Draw the necessary free-body diagram. B 1 4 m 5 m 6 m 8 m 8 m i 5m

Q.3) Determine the tensions in the three cables supporting a weight of 100 N as shown in figure below. Draw the necessary free-body diagram. B 1 4 m 5 m 6 m 8 m 8 m i 5m

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 3:** Determine the tensions in the three cables supporting a weight of 100 N as shown in the figure below. Draw the necessary free-body diagram. **Explanation:** The diagram provided shows a three-dimensional view of a traffic signal supported by three cables attached to points A, B, and C. The traffic signal is subjected to a gravitational force of 100 N acting downward. ### Diagram Analysis: - **Points of Attachment:** - **Point A:** Located 4 meters along the x-axis, no displacement along the y-axis, and 5 meters above the origin along the z-axis. - **Point B:** Located 6 meters along the y-axis, 4 meters above the origin along the z-axis. - **Point C:** Located 8 meters along the y-axis and 5 meters above the origin along the z-axis. - **Cables:** - **Cable AB:** Runs from point A to point B. - **Cable AC:** Runs from point A to point C. - **Cable BC:** Runs from point B to point C. - **Distances:** - **AB:** Vertical and horizontal split defined by a 4-meter distance on the X-axis and a 6-meter distance on the Y-axis. - **CA:** Vertical split of 4 meters on the Y-axis - **BC:** Horizontal split of 8 meters on the X-axis and 5 meters on the Y-axis ### Free-Body Diagram: To determine the tensions in the cables, we need to draw the free-body diagram for the point where the cables are connected. This point will be the origin as it is the point where all the forces are acting on the traffic signal. 1. **Weight (W):** - Acts downward with a force of 100 N. 2. **Tensions (T):** - **Tension in Cable AB (Tab):** Acts along the line connecting points A and B. - **Tension in Cable AC (Tac):** Acts along the line connecting points A and C. - **Tension in Cable BC (Tbc):** Acts along the line connecting points B and C. ### Steps to Determine Tensions: 1. **Equilibrium Conditions:** - The sum of forces in the x, y, and z directions must each equate to zero because the system is in equilibrium. 2. **Components
Transcribed Image Text:**Question 3:** Determine the tensions in the three cables supporting a weight of 100 N as shown in the figure below. Draw the necessary free-body diagram. **Explanation:** The diagram provided shows a three-dimensional view of a traffic signal supported by three cables attached to points A, B, and C. The traffic signal is subjected to a gravitational force of 100 N acting downward. ### Diagram Analysis: - **Points of Attachment:** - **Point A:** Located 4 meters along the x-axis, no displacement along the y-axis, and 5 meters above the origin along the z-axis. - **Point B:** Located 6 meters along the y-axis, 4 meters above the origin along the z-axis. - **Point C:** Located 8 meters along the y-axis and 5 meters above the origin along the z-axis. - **Cables:** - **Cable AB:** Runs from point A to point B. - **Cable AC:** Runs from point A to point C. - **Cable BC:** Runs from point B to point C. - **Distances:** - **AB:** Vertical and horizontal split defined by a 4-meter distance on the X-axis and a 6-meter distance on the Y-axis. - **CA:** Vertical split of 4 meters on the Y-axis - **BC:** Horizontal split of 8 meters on the X-axis and 5 meters on the Y-axis ### Free-Body Diagram: To determine the tensions in the cables, we need to draw the free-body diagram for the point where the cables are connected. This point will be the origin as it is the point where all the forces are acting on the traffic signal. 1. **Weight (W):** - Acts downward with a force of 100 N. 2. **Tensions (T):** - **Tension in Cable AB (Tab):** Acts along the line connecting points A and B. - **Tension in Cable AC (Tac):** Acts along the line connecting points A and C. - **Tension in Cable BC (Tbc):** Acts along the line connecting points B and C. ### Steps to Determine Tensions: 1. **Equilibrium Conditions:** - The sum of forces in the x, y, and z directions must each equate to zero because the system is in equilibrium. 2. **Components
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