### Problem StatementThe force \( F \) has a magnitude of 2 kN and is directed from A to B.1. **Calculate the projection \( F_{CD} \) of \( F \) onto line CD.**2. **Determine the angle \( \theta \) between \( F \) and the line CD.**3. **Determine the magnitude of the moment of this force about the point D.**### Diagram ExplanationThe diagram shows a three-dimensional representation of a parallelepiped with vertices labeled A, B, C, and D. A force vector \( F \) is shown, originating from point A and directed towards point B, with a magnitude of 2 kN. The lengths between the points are given as follows:- The distance from A to C is 0.2 m.- The distance from C to D is 0.4 m.- Vertical distance (height) from the base plane at A to point B is 0.2 m.The goal is to solve three problems involving the force vector \( F \), its projection onto line CD, the angle between the force and the line, and the moment about point D.

Coordinates of point A, B, C, and D: A 0.2,0,0 mB 0.4,0.4,-0.2 mC 0,0,-0.2 mD 0,0,-0.2 m Calculating…

. The force F has a magnitude of 2 kN and is directed from A to B. Calculate the projection Fcp of F onto line CD. b. Deteremine the angle 0 between F and the line CD. c. Determine the magnitude of the moment of this force about the point D. + Narrative B F 0.2 m 0.2 m A 0.2 m 0.4 m

. The force F has a magnitude of 2 kN and is directed from A to B. Calculate the projection Fcp of F onto line CD. b. Deteremine the angle 0 between F and the line CD. c. Determine the magnitude of the moment of this force about the point D. + Narrative B F 0.2 m 0.2 m A 0.2 m 0.4 m

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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Concept explainers

Graphical Methods

The graphical method is a method of solving equations involving more than one variable using the Cartesian coordinate system. In civil engineering, the use of the graphical method is limited to the problems involving two variables. The graphical method has a great impact in solving the questions regarding engineering mechanics.

Question

### Problem Statement

The force \( F \) has a magnitude of 2 kN and is directed from A to B.

1. **Calculate the projection \( F_{CD} \) of \( F \) onto line CD.**
2. **Determine the angle \( \theta \) between \( F \) and the line CD.**
3. **Determine the magnitude of the moment of this force about the point D.**

### Diagram Explanation

The diagram shows a three-dimensional representation of a parallelepiped with vertices labeled A, B, C, and D. A force vector \( F \) is shown, originating from point A and directed towards point B, with a magnitude of 2 kN. The lengths between the points are given as follows:

- The distance from A to C is 0.2 m.
- The distance from C to D is 0.4 m.
- Vertical distance (height) from the base plane at A to point B is 0.2 m.

The goal is to solve three problems involving the force vector \( F \), its projection onto line CD, the angle between the force and the line, and the moment about point D.

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