5.58 The homogeneous 860-kg bar AB is supported by a ball-and-socket joint at A and two cables attached to B. Find the tension in cable CB. 4 m 3 m 4.5 m 2.6 m 3 m 2.2 m D Figure P5.58

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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**Problem 5.58**

The homogeneous 860-kg bar \( AB \) is supported by a ball-and-socket joint at \( A \) and two cables attached to \( B \). Find the tension in cable \( CB \).

**Diagram Description (Figure P5.58):**

The diagram illustrates a three-dimensional setup where a bar \( AB \) is supported by a joint at point \( A \) and two cables extending from point \( B \).

- The bar \( AB \) is leaning upwards and away from the coordinate plane, attached at the bottom by a ball-and-socket joint located at point \( A \).
- Point \( B \) is situated above and slightly forward of the joint, at a height of 4 meters along the \( z \)-axis.
- The base coordinates measure distances from \( A \) as follows:
  - \( B \) is located 4.5 meters along the \( y \)-axis.
- Two additional points, \( C \) and \( D \), serve as anchoring positions for the cables:
  - Point \( C \) is 3 meters along the \( x \)-axis and 2.6 meters along the \( y \)-axis.
  - Point \( D \) is 3 meters along the \( x \)-axis and 2.2 meters along the \( y \)-axis.
  
This configuration shows the spatial relationship and measurement points necessary to calculate the tension in cable \( CB \).
Transcribed Image Text:**Problem 5.58** The homogeneous 860-kg bar \( AB \) is supported by a ball-and-socket joint at \( A \) and two cables attached to \( B \). Find the tension in cable \( CB \). **Diagram Description (Figure P5.58):** The diagram illustrates a three-dimensional setup where a bar \( AB \) is supported by a joint at point \( A \) and two cables extending from point \( B \). - The bar \( AB \) is leaning upwards and away from the coordinate plane, attached at the bottom by a ball-and-socket joint located at point \( A \). - Point \( B \) is situated above and slightly forward of the joint, at a height of 4 meters along the \( z \)-axis. - The base coordinates measure distances from \( A \) as follows: - \( B \) is located 4.5 meters along the \( y \)-axis. - Two additional points, \( C \) and \( D \), serve as anchoring positions for the cables: - Point \( C \) is 3 meters along the \( x \)-axis and 2.6 meters along the \( y \)-axis. - Point \( D \) is 3 meters along the \( x \)-axis and 2.2 meters along the \( y \)-axis. This configuration shows the spatial relationship and measurement points necessary to calculate the tension in cable \( CB \).
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