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Find the tension in leg AC of the cable if the sag, h = 4¹. с 400#

Find the tension in leg AC of the cable if the sag, h = 4¹. с 400#

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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### 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.
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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