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A 48-in. boom is held by a ball-and-socket joint at Cand by two cables BF and DAE, cable DAE passes around a frictionless pulley at A. 48 in. B W D 20 in. E lb) i + 16 in F 30 in. For W 490 lb, determine the tension in each cable and the reaction at C. The tension in cable DAE is The tension in cable BF is The reaction at Cis- lb. lb. 20 in. lb)j + lb) k.

A 48-in. boom is held by a ball-and-socket joint at Cand by two cables BF and DAE, cable DAE passes around a frictionless pulley at A. 48 in. B W D 20 in. E lb) i + 16 in F 30 in. For W 490 lb, determine the tension in each cable and the reaction at C. The tension in cable DAE is The tension in cable BF is The reaction at Cis- lb. lb. 20 in. lb)j + lb) k.

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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**Required Information** **NOTE:** This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A 48-inch boom is held by a ball-and-socket joint at \( C \) and by two cables \( BF \) and \( DAE \); cable \( DAE \) passes around a frictionless pulley at \( A \). **Diagram Explanation:** The diagram shows a boom structure with various components: - **Boom \( AC \):** A 48-inch boom extending from point \( A \) to point \( C \). - **Cables \( DAE \) and \( BF \):** Support cables attached to the boom. - **Frictionless Pulley at \( A \):** The cable \( DAE \) loops around this pulley. - **Coordinates:** - \( x \)-axis along the horizontal direction from \( A \). - \( y \)-axis vertically upward. - \( z \)-axis extends along the boom from \( A \) to \( C \). - **Geometric Details:** - Points \( D \), \( E \), and \( F \) are positioned along the structure. - \( D \) is positioned 20 inches above and along the vertical direction of \( A \). - \( E \) is 16 inches from the \( y \)-axis vertical. - \( F \) is 20 inches above point \( C \) horizontally along the \( x \)-axis at 30 inches from \( A \). **Problem Statement:** For \( W = 490 \, \text{lb} \), determine the tension in each cable and the reaction at \( C \). - The tension in cable \( DAE \) is ______ lb. - The tension in cable \( BF \) is ______ lb. - The reaction at \( C \) is \( -(\, \_\_ \, \text{lb}) \, i \ + \ (\_\_ \, \text{lb}) \, j \ + \ (\_\_ \, \text{lb}) \, k \).
Transcribed Image Text:**Required Information** **NOTE:** This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A 48-inch boom is held by a ball-and-socket joint at \( C \) and by two cables \( BF \) and \( DAE \); cable \( DAE \) passes around a frictionless pulley at \( A \). **Diagram Explanation:** The diagram shows a boom structure with various components: - **Boom \( AC \):** A 48-inch boom extending from point \( A \) to point \( C \). - **Cables \( DAE \) and \( BF \):** Support cables attached to the boom. - **Frictionless Pulley at \( A \):** The cable \( DAE \) loops around this pulley. - **Coordinates:** - \( x \)-axis along the horizontal direction from \( A \). - \( y \)-axis vertically upward. - \( z \)-axis extends along the boom from \( A \) to \( C \). - **Geometric Details:** - Points \( D \), \( E \), and \( F \) are positioned along the structure. - \( D \) is positioned 20 inches above and along the vertical direction of \( A \). - \( E \) is 16 inches from the \( y \)-axis vertical. - \( F \) is 20 inches above point \( C \) horizontally along the \( x \)-axis at 30 inches from \( A \). **Problem Statement:** For \( W = 490 \, \text{lb} \), determine the tension in each cable and the reaction at \( C \). - The tension in cable \( DAE \) is ______ lb. - The tension in cable \( BF \) is ______ lb. - The reaction at \( C \) is \( -(\, \_\_ \, \text{lb}) \, i \ + \ (\_\_ \, \text{lb}) \, j \ + \ (\_\_ \, \text{lb}) \, k \).
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