Find the tension in leg AC of the cable if the sag, h = 4¹. с 400#
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![### Cable Tension Calculation
Find the tension in leg AC of the cable if the sag, \( h = 4' \).
#### Diagram Description:
The diagram presents a system where a cable is suspended between two points, \( A \) and \( B \), with a vertical sag. There's a load of \( 400\# \) suspended at point \( C \), the lowest point of the cable.
- Point \( A \) is 3 feet horizontally away from the vertical axis through point \( C \).
- Point \( B \) is 7 feet horizontally away from the vertical axis through point \( C \).
- The vertical distance from points \( A \) and \( B \) to point \( C \) (sag) is \( h = 4' \).
#### Detailed Diagram Explanation:
- The horizontal dashed line from \( A \) to \( B \) indicates the horizontal distance between the anchor points of the cable.
- Points \( A \) and \( B \) are at the same horizontal level.
- A vertical dashed line from the midpoint between \( A \) and \( B \) extends downwards to point \( C \), showing the vertical sag \( h = 4' \).
- The cable segments \( AC \) and \( BC \) form two triangles with the horizontal line and the vertical line down to point \( C \).
- The load at point \( C \) is denoted as "400\#".
To find the tension in leg \( AC \) of the cable, geometric and static equilibrium analysis techniques will be utilized. The total horizontal distance between \( A \) and \( B \) is \( 3' + 7' = 10' \).
By considering the balance of forces and the geometry of the system, the tension in each leg of the cable can be determined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6abdb772-2674-4ccf-b97c-7a87bba16f16%2F52bf280f-290d-4c4d-823f-4a9785b737e8%2Fwmvey6o_processed.png&w=3840&q=75)
Transcribed Image Text:### Cable Tension Calculation
Find the tension in leg AC of the cable if the sag, \( h = 4' \).
#### Diagram Description:
The diagram presents a system where a cable is suspended between two points, \( A \) and \( B \), with a vertical sag. There's a load of \( 400\# \) suspended at point \( C \), the lowest point of the cable.
- Point \( A \) is 3 feet horizontally away from the vertical axis through point \( C \).
- Point \( B \) is 7 feet horizontally away from the vertical axis through point \( C \).
- The vertical distance from points \( A \) and \( B \) to point \( C \) (sag) is \( h = 4' \).
#### Detailed Diagram Explanation:
- The horizontal dashed line from \( A \) to \( B \) indicates the horizontal distance between the anchor points of the cable.
- Points \( A \) and \( B \) are at the same horizontal level.
- A vertical dashed line from the midpoint between \( A \) and \( B \) extends downwards to point \( C \), showing the vertical sag \( h = 4' \).
- The cable segments \( AC \) and \( BC \) form two triangles with the horizontal line and the vertical line down to point \( C \).
- The load at point \( C \) is denoted as "400\#".
To find the tension in leg \( AC \) of the cable, geometric and static equilibrium analysis techniques will be utilized. The total horizontal distance between \( A \) and \( B \) is \( 3' + 7' = 10' \).
By considering the balance of forces and the geometry of the system, the tension in each leg of the cable can be determined.
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