A bent bar ABC are supported and subjected to forces as shown below. Find the reactions on the bar at A, B and C. Neglect friction and the weight of the bars. 200 N 30° B. A 5 ft 5 ft Smooth slot 45° 3 ft 3 ft 300 N
A bent bar ABC are supported and subjected to forces as shown below. Find the reactions on the bar at A, B and C. Neglect friction and the weight of the bars. 200 N 30° B. A 5 ft 5 ft Smooth slot 45° 3 ft 3 ft 300 N
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter5: Three-dimensional Equilibrium
Section: Chapter Questions
Problem 5.39P: The bent rod of negligible weight is supported by the ball-and-socket joint at B and the cables...
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**Problem 2: Force Analysis on a Bent Bar ABC**
**Problem Statement:**
A bent bar ABC is supported and subjected to forces as depicted in the diagram. Determine the reactions at points A, B, and C, assuming negligible friction and bar weight.
**Diagram Description:**
The provided diagram illustrates the bent bar ABC, consisting of two segments joined at point B:
- The horizontal segment AB, which is 10 feet long (5 feet from A to B).
- The inclined segment BC, which forms an angle of 45° with a horizontal smooth slot and is 6 feet long (3 feet from B to C).
The bar is supported by:
- A horizontal smooth slot at point A.
- A pinned connection at point B.
- A vertical smooth slot at point C, inclined at an angle of 45° to the horizontal.
The forces acting on the bar are:
- A vertical downward force of 200 N at point A.
- A 300 N force acting vertically downward on point C.
**Diagram Explanation:**
1. **Point A:**
- A smooth horizontal slot supports this point, allowing only vertical movement. Therefore, the reaction at A (R_A) is a vertical force.
2. **Point B:**
- This point features a pinned connection, which can support forces in both the horizontal and vertical directions, denoted as \( B_x \) for the horizontal component and \( B_y \) for the vertical component.
3. **Point C:**
- The smooth slot here is inclined at 45°, indicating that it can exert an equal reaction force component in both the horizontal and vertical directions. This reaction force can be decomposed into \( C_x \) and \( C_y \).
---
**Analysis Approach:**
1. **Static Equilibrium Equations:**
- Sum of forces in the horizontal direction (ΣF_x = 0)
- Sum of forces in the vertical direction (ΣF_y = 0)
- Sum of moments about point B (ΣM_B = 0)
2. **Force Components:**
- The inclined reaction at C results in components:
- \( C_x = C \cos(45°) \)
- \( C_y = C \sin(45°) \)
- Given \( \cos(45°) = \sin(45°) = \frac{1}{\sqrt{2}}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57103f69-f6d8-477a-b236-0336011ee35d%2Fc35220cc-8b9c-4b77-84b7-e00945178bb5%2Fpzuy71e_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Problem 2: Force Analysis on a Bent Bar ABC**
**Problem Statement:**
A bent bar ABC is supported and subjected to forces as depicted in the diagram. Determine the reactions at points A, B, and C, assuming negligible friction and bar weight.
**Diagram Description:**
The provided diagram illustrates the bent bar ABC, consisting of two segments joined at point B:
- The horizontal segment AB, which is 10 feet long (5 feet from A to B).
- The inclined segment BC, which forms an angle of 45° with a horizontal smooth slot and is 6 feet long (3 feet from B to C).
The bar is supported by:
- A horizontal smooth slot at point A.
- A pinned connection at point B.
- A vertical smooth slot at point C, inclined at an angle of 45° to the horizontal.
The forces acting on the bar are:
- A vertical downward force of 200 N at point A.
- A 300 N force acting vertically downward on point C.
**Diagram Explanation:**
1. **Point A:**
- A smooth horizontal slot supports this point, allowing only vertical movement. Therefore, the reaction at A (R_A) is a vertical force.
2. **Point B:**
- This point features a pinned connection, which can support forces in both the horizontal and vertical directions, denoted as \( B_x \) for the horizontal component and \( B_y \) for the vertical component.
3. **Point C:**
- The smooth slot here is inclined at 45°, indicating that it can exert an equal reaction force component in both the horizontal and vertical directions. This reaction force can be decomposed into \( C_x \) and \( C_y \).
---
**Analysis Approach:**
1. **Static Equilibrium Equations:**
- Sum of forces in the horizontal direction (ΣF_x = 0)
- Sum of forces in the vertical direction (ΣF_y = 0)
- Sum of moments about point B (ΣM_B = 0)
2. **Force Components:**
- The inclined reaction at C results in components:
- \( C_x = C \cos(45°) \)
- \( C_y = C \sin(45°) \)
- Given \( \cos(45°) = \sin(45°) = \frac{1}{\sqrt{2}}
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