Determine the tension in each cable and the components of reaction at D
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Determine the tension in each cable and the components of reaction at D

Transcribed Image Text:### Problem Statement
**Objective:**
Determine the tension in each cable and the components of the reaction at point D needed to support the load.
### Diagram Explanation
The diagram presents a three-dimensional structure with a rigid beam pinned at point A and supported by cables running to points B, C, and D.
**Details:**
- **Coordinates and Measurements:**
- Point B is located 4 meters along the z-axis from point D.
- Point C is 3 meters along the y-axis and 6 meters along the z-axis from point D.
- There is a beam connecting point A to point D, inclined at a 30° angle with respect to the x-axis.
- **Force and Load:**
- A force of 460 N is applied downwards at a 30° angle to the vertical at point A.
**Axes Reference:**
- The x-axis appears to run horizontally from left to right.
- The y-axis runs vertically upwards.
- The z-axis is perpendicular to both x and y axes, coming forward from the plane.
### Task
Calculate:
1. The tension in each of the cables connected through the points B and C.
2. The reaction components at point D, considering the given force and beam orientation.
This setup is an application of static equilibrium analysis in three-dimensional space, requiring balance of forces and moments around key points in the structure.

Transcribed Image Text:This diagram illustrates a structural analysis problem involving a 3D coordinate system with points A, B, C, and D.
- **Point A** is the starting point of the structure, located at the origin of the x, y, and z axes.
- A force of 460 N is applied at point A, directed at an angle of 30° from the negative x-axis.
- **Point B** is 4 meters above point C along the z-axis.
- The distance between points A and B is 6 meters along the x-z plane.
- **Point C** is inline with point D, 3 meters apart along the x-axis.
- **Point D** is connected by a rod extending from point A.
- The structure is set up within a 3D coordinate system, represented by x, y, and z axes to assess the different vector components and resulting forces.
The diagram serves as a reference for analyzing spatial forces and torques in engineering contexts.
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