3) The cable shown below is supported by two pins at A and B. The maximum cable tension due to the applied forces is 1200 lb. Determine the tensions in all four segments of the cable and the sags of the load points P1, P2, and P3. B A 1.5 ft P₁ 200 lb 3 ft P₂ 300 lb 5 ft P3 400 lb 3.5 ft- 2.5 ft X
3) The cable shown below is supported by two pins at A and B. The maximum cable tension due to the applied forces is 1200 lb. Determine the tensions in all four segments of the cable and the sags of the load points P1, P2, and P3. B A 1.5 ft P₁ 200 lb 3 ft P₂ 300 lb 5 ft P3 400 lb 3.5 ft- 2.5 ft X
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:### Cable Tension and Sag Analysis
**Problem Statement:**
The cable shown in the diagram is supported by two pins at points A and B. The maximum allowable cable tension due to the applied forces is 1200 lb. Determine the tensions in all four segments of the cable and the sags at the load points P1, P2, and P3.
**Diagram Explanation:**
The diagram illustrates a cable suspended between two pin supports at points A and B. Four segments of the cable are under different loading conditions with the following details:
1. **Points and Loads:**
- Point P1 is located 1.5 feet horizontally from point A and bears a load of 200 lb.
- Point P2 is located 3 feet horizontally from point P1 and bears a load of 300 lb.
- Point P3 is located 5 feet horizontally from point P2 and bears a load of 400 lb.
- The horizontal distance from P3 to point B is 3.5 feet.
2. **Distances and Layout:**
- The horizontal distance from A to B is indicated.
- The vertical height difference between B and the horizontal line passing through A is 2.5 feet.
**Coordinate System:**
- The vertical direction is denoted as the y-axis.
- The horizontal direction is denoted as the x-axis.
**Objective:**
Using the given dimensions and loads, calculate:
- The tension in each of the four cable segments.
- The sag at points P1, P2, and P3.
This problem encompasses principles from static equilibrium, trigonometry, and cable mechanics, making it an insightful example for students studying structural engineering and mechanics.
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