Find the reactions and force in Pin C. A 10' क 5k 5' C 5' 8k 10' 6' B
Find the reactions and force in Pin C. A 10' क 5k 5' C 5' 8k 10' 6' B
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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Question
Find the reactions and force in Pin C.
![### Structural Analysis: Finding Reactions and Forces in a Pin
In this example, we examine a symmetrical arch ABC, supported by two pins at points A and B and featuring a pin at the apex, point C. The task is to determine the reactions at supports A and B and the force exerted at pin C.
#### Diagram Interpretation:
The diagram provided features an arch structure with the following specifications:
- The span of the arch between supports A and B is 20 feet.
- The pin at point C is located at the apex and midway along the span, at a height of 6 feet from the base.
- There are two vertical loads applied on the arch:
- A 5 kips (5k) load positioned 5 feet to the left of the pin C.
- An 8 kips (8k) load positioned 5 feet to the right of the pin C.
#### Aim:
To determine the reactions at supports A and B, and the force at the pin C.
#### Key Points for Calculation:
1. **Support Reactions:**
- The supports at A and B are pinned, allowing them to provide vertical reactions.
- Both reactions are necessary to balance the vertical loads applied on the arch.
Here is a stepwise approach:
1. **Calculate Vertical Reactions at Supports:**
- Sum of vertical forces acting on the arch must equal zero (ΣFy = 0).
- Moment balance around one of the supports, commonly used to simplify the calculation.
2. **Determine the Force at Pin C:**
- Since pin C is a hinged connection, there are typically no moments resisted at C, but it can transmit horizontal and vertical forces.
### Example Calculation (Indicative, not computed):
1. **Summing Moments about point A:**
\[
(5 kips \times 5 feet) + (8 kips \times 15 feet) = R_B \times 20 feet
\]
- Solve for \( R_B \).
2. **Using the sum of forces in vertical direction (ΣFy = 0):**
\[
R_A + R_B = 5 kips + 8 kips
\]
- Solve for \( R_A \) once \( R_B \) is known.
3. **Force at Pin C:**
- Calculate horizontal and vertical components, considering equilibrium of forces between segments AC and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe6008fe-2b46-432b-a1f5-59ac85f5ef57%2Fa852c2fd-f7ee-4ee9-8444-2fa109ccc5ee%2Fa6upgpe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Structural Analysis: Finding Reactions and Forces in a Pin
In this example, we examine a symmetrical arch ABC, supported by two pins at points A and B and featuring a pin at the apex, point C. The task is to determine the reactions at supports A and B and the force exerted at pin C.
#### Diagram Interpretation:
The diagram provided features an arch structure with the following specifications:
- The span of the arch between supports A and B is 20 feet.
- The pin at point C is located at the apex and midway along the span, at a height of 6 feet from the base.
- There are two vertical loads applied on the arch:
- A 5 kips (5k) load positioned 5 feet to the left of the pin C.
- An 8 kips (8k) load positioned 5 feet to the right of the pin C.
#### Aim:
To determine the reactions at supports A and B, and the force at the pin C.
#### Key Points for Calculation:
1. **Support Reactions:**
- The supports at A and B are pinned, allowing them to provide vertical reactions.
- Both reactions are necessary to balance the vertical loads applied on the arch.
Here is a stepwise approach:
1. **Calculate Vertical Reactions at Supports:**
- Sum of vertical forces acting on the arch must equal zero (ΣFy = 0).
- Moment balance around one of the supports, commonly used to simplify the calculation.
2. **Determine the Force at Pin C:**
- Since pin C is a hinged connection, there are typically no moments resisted at C, but it can transmit horizontal and vertical forces.
### Example Calculation (Indicative, not computed):
1. **Summing Moments about point A:**
\[
(5 kips \times 5 feet) + (8 kips \times 15 feet) = R_B \times 20 feet
\]
- Solve for \( R_B \).
2. **Using the sum of forces in vertical direction (ΣFy = 0):**
\[
R_A + R_B = 5 kips + 8 kips
\]
- Solve for \( R_A \) once \( R_B \) is known.
3. **Force at Pin C:**
- Calculate horizontal and vertical components, considering equilibrium of forces between segments AC and
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