**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, and the moment reaction in the collar at point B.**Diagram Description:**- The rod forms an angled structure with a roller support at point A and a smooth collar at point B.- The collar at point B allows rod AB to slide along rod CD.- There are two 45-degree angles in the rod – one between points A and B, and another between points B and C.- The rod CD extends 3 meters horizontally to the right from point A, where the rod forms a 45-degree angle.- There is a segment of the structure between points B and C that measures 1.5 meters, with an additional 1.5-meter segment between the applied load and point B.- A vertical downward force of 900 N acts at the midpoint between B and the load.- An external moment of 800 N·m acts clockwise around the collar at point B.- The structure includes detailed length measurements and 45-degree angle indications.**Support Reactions to Determine:**1. **Reaction at Support A (Roller)**2. **Reaction at Collar B (Smooth collar allowing slip along CD)**3. **Moment Reaction at Collar B**This setup often appears in mechanical and structural engineering contexts, where analyzing support reactions is crucial to ensuring structural stability and integrity. The combination of different supports (roller and collar) adds complexity to the problem and requires the application of static equilibrium equations to solve for the unknown reactions. ---**Equilibrium Equations:**To solve this problem, we can use the static equilibrium equations:1. Sum of Forces in the x-direction: \(\Sigma F_x = 0\)2. Sum of Forces in the y-direction: \(\Sigma F_y = 0\)3. Sum of Moments about a point: \(\Sigma M = 0\)By applying these equations, we can find the reactions at points A and B, as well as the moment reaction in the collar at point B.

Answered: Image /qna-images/answer/e4576c23-009b-44a1-9de6-b99d53eda187.jpg

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. 900 N -1.5 m + -1.5 m B 45% 800 N-m 3 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. 900 N -1.5 m + -1.5 m B 45% 800 N-m 3 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

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

**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, and the moment reaction in the collar at point B.

**Diagram Description:**

- The rod forms an angled structure with a roller support at point A and a smooth collar at point B.
- The collar at point B allows rod AB to slide along rod CD.
- There are two 45-degree angles in the rod – one between points A and B, and another between points B and C.
- The rod CD extends 3 meters horizontally to the right from point A, where the rod forms a 45-degree angle.
- There is a segment of the structure between points B and C that measures 1.5 meters, with an additional 1.5-meter segment between the applied load and point B.
- A vertical downward force of 900 N acts at the midpoint between B and the load.
- An external moment of 800 N·m acts clockwise around the collar at point B.
- The structure includes detailed length measurements and 45-degree angle indications.

**Support Reactions to Determine:**

1. **Reaction at Support A (Roller)**
2. **Reaction at Collar B (Smooth collar allowing slip along CD)**
3. **Moment Reaction at Collar B**

This setup often appears in mechanical and structural engineering contexts, where analyzing support reactions is crucial to ensuring structural stability and integrity. The combination of different supports (roller and collar) adds complexity to the problem and requires the application of static equilibrium equations to solve for the unknown reactions.

---

**Equilibrium Equations:**

To solve this problem, we can use the static equilibrium equations:

1. Sum of Forces in the x-direction: \(\Sigma F_x = 0\)
2. Sum of Forces in the y-direction: \(\Sigma F_y = 0\)
3. Sum of Moments about a point: \(\Sigma M = 0\)

By applying these equations, we can find the reactions at points A and B, as well as the moment reaction in the collar at point B.

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