### Pulley Assembly Reaction Components**Diagram Explanation:**The diagram depicts an assembly with two pulleys. A load \( P \) is applied vertically downward at point \( A \). The system includes three rigid links: \( AB \), \( BD \), and \( CE \); each link is connected at points \( B \), \( D \), and \( E \) through pivots. The distance between \( A \) to \( B \), and \( B \) to \( D \), is 2 meters each. The vertical distance from \( D \) to \( E \) is 1.5 meters.**Task:**Given that each pulley has a radius of 250 mm and the load \( P \) is 6.8 kN, calculate the components of the reactions at points \( D \) and \( E \).**Components of the Reactions:**- **At \( D \):** - \( D_x = \) [Blank] kN → - \( D_y = \) [Blank] kN ↑- **At \( E \):** - \( E_x = \) [Blank] kN ← - \( E_y = \) [Blank] kN ↓### Calculation ApproachTo determine the reaction components, consider the static equilibrium of the system, and apply the relevant equations:1. Sum of forces in the horizontal direction (\(\Sigma F_x = 0\))2. Sum of forces in the vertical direction (\(\Sigma F_y = 0\))3. Sum of moments about any point (\(\Sigma M = 0\))These principles will help determine the unknown reactions at \( D \) and \( E \). Use the given dimensions and force to set up the equations, and solve them systematically.

Given ,Radius of pully = 250 mmload P = 6.8 kN

Two pulleys are used in an assembly as shown. - 2 m - -2 m- B D 1.5 m E Knowing that each pulley has a radius of 250 mm and the load Pis 6.8 kN, determine the components of the reactions at D and E. The components of the reactions at Dare: Dx= Dy= The components of the reactions at Eare: Ex = |kN → |KN ↑ kN - Ey= kN I

Two pulleys are used in an assembly as shown. - 2 m - -2 m- B D 1.5 m E Knowing that each pulley has a radius of 250 mm and the load Pis 6.8 kN, determine the components of the reactions at D and E. The components of the reactions at Dare: Dx= Dy= The components of the reactions at Eare: Ex = |kN → |KN ↑ kN - Ey= kN I

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

Equilibrium and Support Reactions

Civil engineers deal with structures that are composed of several members connected or with individual members such as beams and columns. To analyze such structures, the condition of statics must be applied. Under the static condition, the members are considered to be in equilibrium under the action of forces, that is, the members are assumed to be having negligible velocity.

Question

### Pulley Assembly Reaction Components

**Diagram Explanation:**
The diagram depicts an assembly with two pulleys. A load \( P \) is applied vertically downward at point \( A \). The system includes three rigid links: \( AB \), \( BD \), and \( CE \); each link is connected at points \( B \), \( D \), and \( E \) through pivots. The distance between \( A \) to \( B \), and \( B \) to \( D \), is 2 meters each. The vertical distance from \( D \) to \( E \) is 1.5 meters.

**Task:**
Given that each pulley has a radius of 250 mm and the load \( P \) is 6.8 kN, calculate the components of the reactions at points \( D \) and \( E \).

**Components of the Reactions:**

- **At \( D \):**
- \( D_x = \) [Blank] kN →
- \( D_y = \) [Blank] kN ↑

- **At \( E \):**
- \( E_x = \) [Blank] kN ←
- \( E_y = \) [Blank] kN ↓

### Calculation Approach

To determine the reaction components, consider the static equilibrium of the system, and apply the relevant equations:

1. Sum of forces in the horizontal direction (\(\Sigma F_x = 0\))
2. Sum of forces in the vertical direction (\(\Sigma F_y = 0\))
3. Sum of moments about any point (\(\Sigma M = 0\))

These principles will help determine the unknown reactions at \( D \) and \( E \). Use the given dimensions and force to set up the equations, and solve them systematically.

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