30° A F B 45° Search The diagram shows the free body diagram of a joint in a truss which is supporting a load, F. In the FBD the direction (sense) of forces A and B are assumed, so may not be correct. Given: F = 425 kN and C = 100 KN 1. Draw draw a neat, labeled free body diagram representing the situation 2. Write two equilibrium equations, symbolically, based on your free body diagram. 3. Solve your equations to determine the magnitudes of forces A and B necessary for equilibrium. 4. Indicate whether forces A and B are in tension or compression.
30° A F B 45° Search The diagram shows the free body diagram of a joint in a truss which is supporting a load, F. In the FBD the direction (sense) of forces A and B are assumed, so may not be correct. Given: F = 425 kN and C = 100 KN 1. Draw draw a neat, labeled free body diagram representing the situation 2. Write two equilibrium equations, symbolically, based on your free body diagram. 3. Solve your equations to determine the magnitudes of forces A and B necessary for equilibrium. 4. Indicate whether forces A and B are in tension or compression.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Expected answers-
A=887.9kN Compression
B=1229kN Compression
![### Free Body Diagram Analysis for a Truss Joint
**Objective:**
To analyze a truss joint subjected to different forces and determine the magnitudes of the forces \( A \) and \( B \), and their nature (tension or compression).
**Diagram Explanation:**
The given diagram is a free body diagram of a joint in a truss. The joint is under a vertical load \( F \). The forces acting on the joint include \( F \), \( A \), \( B \), and \( C \). The directions of the forces \( A \) and \( B \) are assumed and indicated by arrows.
1. **Force \( F \)** is acting vertically downward.
2. **Force \( A \)** is inclined at 30° to the horizontal and directed to the left.
3. **Force \( B \)** is inclined at 45° to the horizontal and directed upwards to the right.
4. **Force \( C \)** is acting horizontally to the right.
**Given Data:**
- \( F = 425 \, \text{kN} \)
- \( C = 100 \, \text{kN} \)
### Steps to Solve
1. **Draw a Neat, Labeled Free Body Diagram:**
- Clearly indicate all forces with their respective angles and directions.
- Label the angles between the forces and the horizontal axis.
2. **Write Two Equilibrium Equations:**
Formulate the equilibrium equations based on the sum of forces in the horizontal and vertical directions:
- **Sum of horizontal forces (\( \Sigma F_x = 0 \)):**
\[
-A \cos(30^\circ) + B \cos(45^\circ) + C = 0
\]
- **Sum of vertical forces (\( \Sigma F_y = 0 \)):**
\[
-F + A \sin(30^\circ) + B \sin(45^\circ) = 0
\]
3. **Solve the Equations:**
Use the given values of \( F \) and \( C \) to solve the system of equations for \( A \) and \( B \).
4. **Determine the Nature of Forces \( A \) and \( B \):**
- If the values calculated for \( A \) and \( B \) are positive, the forces are in tension.
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F848bc833-9fb3-4eda-a7de-b585ddd0b1dc%2F950e6d6c-6140-4baa-9762-44a1d42656b1%2F47vc0q_processed.png&w=3840&q=75)
Transcribed Image Text:### Free Body Diagram Analysis for a Truss Joint
**Objective:**
To analyze a truss joint subjected to different forces and determine the magnitudes of the forces \( A \) and \( B \), and their nature (tension or compression).
**Diagram Explanation:**
The given diagram is a free body diagram of a joint in a truss. The joint is under a vertical load \( F \). The forces acting on the joint include \( F \), \( A \), \( B \), and \( C \). The directions of the forces \( A \) and \( B \) are assumed and indicated by arrows.
1. **Force \( F \)** is acting vertically downward.
2. **Force \( A \)** is inclined at 30° to the horizontal and directed to the left.
3. **Force \( B \)** is inclined at 45° to the horizontal and directed upwards to the right.
4. **Force \( C \)** is acting horizontally to the right.
**Given Data:**
- \( F = 425 \, \text{kN} \)
- \( C = 100 \, \text{kN} \)
### Steps to Solve
1. **Draw a Neat, Labeled Free Body Diagram:**
- Clearly indicate all forces with their respective angles and directions.
- Label the angles between the forces and the horizontal axis.
2. **Write Two Equilibrium Equations:**
Formulate the equilibrium equations based on the sum of forces in the horizontal and vertical directions:
- **Sum of horizontal forces (\( \Sigma F_x = 0 \)):**
\[
-A \cos(30^\circ) + B \cos(45^\circ) + C = 0
\]
- **Sum of vertical forces (\( \Sigma F_y = 0 \)):**
\[
-F + A \sin(30^\circ) + B \sin(45^\circ) = 0
\]
3. **Solve the Equations:**
Use the given values of \( F \) and \( C \) to solve the system of equations for \( A \) and \( B \).
4. **Determine the Nature of Forces \( A \) and \( B \):**
- If the values calculated for \( A \) and \( B \) are positive, the forces are in tension.
-
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