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Q.3) The rod is supported by a roller at A and a smooth collar at B. The collar is fixed to the rod AB but is allowed to slip along rod CD. Determine the support reactions at A and at B, the moment reaction in the collar at B. A 900 N -1.5 m -1.5 m

Q.3) The rod is supported by a roller at A and a smooth collar at B. The collar is fixed to the rod AB but is allowed to slip along rod CD. Determine the support reactions at A and at B, the moment reaction in the collar at B. A 900 N -1.5 m -1.5 m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Example Problem: Support Reactions and Moment Reaction Analysis in a Rod System #### Question 3: Support Reactions and Moment Calculation **Problem Statement:** The rod is supported by a roller at point A and a smooth collar at point B. The collar is fixed to the rod AB but is allowed to slip along rod CD. Determine the support reactions at points A and B, as well as the moment reaction in the collar at B. **Diagram Explanation:** The diagram provided illustrates the rod system described in the problem: 1. **Support Setup:** - Roller support at A: This indicates that there can be a vertical reaction force at A but no horizontal force. - Smooth collar at B: The collar is fixed on rod AB but can slide along rod CD. This produces reactions but prevents moments at point B. 2. **Dimensions and Forces:** - The distance between points A and B is \(3 \, \text{meters}\). - There is a vertical force of \(900 \, \text{N}\) acting downwards, located \(1.5 \, \text{meters}\) from point B. - At point D, which is on rod CD, there is an \(800 \, \text{N-m}\) moment acting in a clockwise direction. - The other distances include \(1.5 \, \text{meters}\) horizontally from point B to the point where the 900 N force acts. - The angle between the rods AB and CD is \(45^\circ\). **Analysis:** To solve for the reactions at supports A and B, as well as the moment reaction at B, the following steps are generally involved: - **Step 1: Resolve all forces into horizontal and vertical components.** - **Step 2: Apply equilibrium equations:** - Sum of horizontal forces (\( \sum F_X = 0 \)) - Sum of vertical forces (\( \sum F_Y = 0 \)) - Sum of moments about a point (often taken around one of the supports to simplify the calculation) (\( \sum M = 0 \)) By applying these principles and analyzing the system, you can solve for the unknown support reactions and the resultant moments. **Example Calculation:** Let's assume \( A_y \) is the vertical reaction at the roller A, \( B_y \) is the vertical reaction at B, \(
Transcribed Image Text:### Example Problem: Support Reactions and Moment Reaction Analysis in a Rod System #### Question 3: Support Reactions and Moment Calculation **Problem Statement:** The rod is supported by a roller at point A and a smooth collar at point B. The collar is fixed to the rod AB but is allowed to slip along rod CD. Determine the support reactions at points A and B, as well as the moment reaction in the collar at B. **Diagram Explanation:** The diagram provided illustrates the rod system described in the problem: 1. **Support Setup:** - Roller support at A: This indicates that there can be a vertical reaction force at A but no horizontal force. - Smooth collar at B: The collar is fixed on rod AB but can slide along rod CD. This produces reactions but prevents moments at point B. 2. **Dimensions and Forces:** - The distance between points A and B is \(3 \, \text{meters}\). - There is a vertical force of \(900 \, \text{N}\) acting downwards, located \(1.5 \, \text{meters}\) from point B. - At point D, which is on rod CD, there is an \(800 \, \text{N-m}\) moment acting in a clockwise direction. - The other distances include \(1.5 \, \text{meters}\) horizontally from point B to the point where the 900 N force acts. - The angle between the rods AB and CD is \(45^\circ\). **Analysis:** To solve for the reactions at supports A and B, as well as the moment reaction at B, the following steps are generally involved: - **Step 1: Resolve all forces into horizontal and vertical components.** - **Step 2: Apply equilibrium equations:** - Sum of horizontal forces (\( \sum F_X = 0 \)) - Sum of vertical forces (\( \sum F_Y = 0 \)) - Sum of moments about a point (often taken around one of the supports to simplify the calculation) (\( \sum M = 0 \)) By applying these principles and analyzing the system, you can solve for the unknown support reactions and the resultant moments. **Example Calculation:** Let's assume \( A_y \) is the vertical reaction at the roller A, \( B_y \) is the vertical reaction at B, \(
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