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2/93 SS If the tension in the gantry-crane hoisting cable is T = 14 kN, determine the unit vector n in the direction of T and use n to determine the scalar components of T. Point B is located at the center of the container top. 201 3 m 12 m m B 16 m ·x 3 m

2/93 SS If the tension in the gantry-crane hoisting cable is T = 14 kN, determine the unit vector n in the direction of T and use n to determine the scalar components of T. Point B is located at the center of the container top. 201 3 m 12 m m B 16 m ·x 3 m

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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**Problem 2/93: Vector Analysis in Gantry Crane Hoisting System** **Objective:** To determine the unit vector \(\mathbf{n}\) in the direction of the tension \(\mathbf{T}\) in the gantry-crane hoisting cable and to use \(\mathbf{n}\) to find the scalar components of \(\mathbf{T}\). The given tension \(T = 14 \, \text{kN}\). Point \(B\) is located at the center of the container top. **Diagram Description:** The diagram features a gantry-crane setup with a hoisting cable lifting a container. The crane is positioned above the ground on two vertical supports, forming a gantry (a beam or bridge-like structure). 1. **Coordinates:** - Point \(O\): Origin, at the base of one of the crane supports (left side support). - Point \(A\): Position of the pulley or attachment, at the top end of the left support. - Point \(B\): Center of the container top position, on the ground. 2. **Dimensions:** - Height of Point \(A\) from Point \(O\): 20 meters (along the z-axis). - Distance along the x-axis from O to B: 12 meters. - Distance along the x-axis from B to the edge of container: 16 meters. - Distance along the y-axis from O to the container: 5 meters. - Distance along the y-axis from the near container edge to the center of the container (Point B) is an additional 3 meters, making the total distance from O to B along the y-axis: 5 + 3 = 8 meters. - The container is 8 meters along its longest side and 3 meters along its shortest side. **Problem Analysis:** To solve the problem, we need to: 1. **Find the position vector \(\mathbf{r}_{AB}\):** - From \(A\) to \(B\), using the coordinates of \(A\) and \(B\). 2. **Determine the unit vector \(\mathbf{n}\) in the direction of \(\mathbf{T}\):** - A unit vector has a magnitude of 1 and points in the direction of \(\mathbf{T}\). 3. **Calculate the scalar components of \(\mathbf{T
Transcribed Image Text:**Problem 2/93: Vector Analysis in Gantry Crane Hoisting System** **Objective:** To determine the unit vector \(\mathbf{n}\) in the direction of the tension \(\mathbf{T}\) in the gantry-crane hoisting cable and to use \(\mathbf{n}\) to find the scalar components of \(\mathbf{T}\). The given tension \(T = 14 \, \text{kN}\). Point \(B\) is located at the center of the container top. **Diagram Description:** The diagram features a gantry-crane setup with a hoisting cable lifting a container. The crane is positioned above the ground on two vertical supports, forming a gantry (a beam or bridge-like structure). 1. **Coordinates:** - Point \(O\): Origin, at the base of one of the crane supports (left side support). - Point \(A\): Position of the pulley or attachment, at the top end of the left support. - Point \(B\): Center of the container top position, on the ground. 2. **Dimensions:** - Height of Point \(A\) from Point \(O\): 20 meters (along the z-axis). - Distance along the x-axis from O to B: 12 meters. - Distance along the x-axis from B to the edge of container: 16 meters. - Distance along the y-axis from O to the container: 5 meters. - Distance along the y-axis from the near container edge to the center of the container (Point B) is an additional 3 meters, making the total distance from O to B along the y-axis: 5 + 3 = 8 meters. - The container is 8 meters along its longest side and 3 meters along its shortest side. **Problem Analysis:** To solve the problem, we need to: 1. **Find the position vector \(\mathbf{r}_{AB}\):** - From \(A\) to \(B\), using the coordinates of \(A\) and \(B\). 2. **Determine the unit vector \(\mathbf{n}\) in the direction of \(\mathbf{T}\):** - A unit vector has a magnitude of 1 and points in the direction of \(\mathbf{T}\). 3. **Calculate the scalar components of \(\mathbf{T
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