Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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![### Equilibrium of a Truss System
**Problem Statement:**
The members of a truss are pin connected at joint O. Determine the magnitude of \( F_1 \) and its angle for equilibrium.
#### Diagram Description:
The diagram shows a truss system with forces acting at specific angles from the pin joint O:
- A force of 5 kN is acting in the negative y-direction.
- A force of 6 kN is acting in the positive x-direction.
- A force of 7 kN is acting at an angle of 30° below the negative x-axis.
- An unknown force \( F_1 \) is acting at an angle θ below the positive x-axis.
The diagram also depicts an xy-coordinate system with the origin at the pin joint O.
#### Steps to Solve:
1. **Resolve All Forces into Components:**
- For the 5 kN force: only the y-component.
- For the 6 kN force: only the x-component.
- For the 7 kN force: both x and y-components.
- For the unknown force \( F_1 \): dependent on the angle θ.
2. **Apply Equilibrium Conditions:**
- Sum of all horizontal forces must be zero.
- Sum of all vertical forces must be zero.
3. **Equations Derived:**
- ΣF_x = 0 (Total horizontal forces must balance)
- ΣF_y = 0 (Total vertical forces must balance)
#### Inputs for Solution:
- **Angle and Forces:**
- \( F_x = F_1 \cos(θ) - 6 kN + 7\cos(30°) kN = 0 \)
- \( F_y = F_1 \sin(θ) - 5 kN - 7\sin(30°) kN = 0 \)
**After solving these equations, the magnitude of \( F_1 \) and its angle θ can be determined.**
#### Answer Submission
Your answer: [text box for student's answer]
---
**Notes:**
1. Never submit passwords through Google Forms.
2. This form was created inside the University of Mosul. Report Abuse.
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By understanding and solving such equilibrium problems, it helps in designing stable and efficient truss structures for various engineering applications.](https://content.bartleby.com/qna-images/question/c0b11d39-f5e1-41ce-ac57-6a97833c6023/bd40ca69-54ac-4836-9b89-87ecbd5f0d89/wa78mbl_processed.jpeg)
Transcribed Image Text:### Equilibrium of a Truss System
**Problem Statement:**
The members of a truss are pin connected at joint O. Determine the magnitude of \( F_1 \) and its angle for equilibrium.
#### Diagram Description:
The diagram shows a truss system with forces acting at specific angles from the pin joint O:
- A force of 5 kN is acting in the negative y-direction.
- A force of 6 kN is acting in the positive x-direction.
- A force of 7 kN is acting at an angle of 30° below the negative x-axis.
- An unknown force \( F_1 \) is acting at an angle θ below the positive x-axis.
The diagram also depicts an xy-coordinate system with the origin at the pin joint O.
#### Steps to Solve:
1. **Resolve All Forces into Components:**
- For the 5 kN force: only the y-component.
- For the 6 kN force: only the x-component.
- For the 7 kN force: both x and y-components.
- For the unknown force \( F_1 \): dependent on the angle θ.
2. **Apply Equilibrium Conditions:**
- Sum of all horizontal forces must be zero.
- Sum of all vertical forces must be zero.
3. **Equations Derived:**
- ΣF_x = 0 (Total horizontal forces must balance)
- ΣF_y = 0 (Total vertical forces must balance)
#### Inputs for Solution:
- **Angle and Forces:**
- \( F_x = F_1 \cos(θ) - 6 kN + 7\cos(30°) kN = 0 \)
- \( F_y = F_1 \sin(θ) - 5 kN - 7\sin(30°) kN = 0 \)
**After solving these equations, the magnitude of \( F_1 \) and its angle θ can be determined.**
#### Answer Submission
Your answer: [text box for student's answer]
---
**Notes:**
1. Never submit passwords through Google Forms.
2. This form was created inside the University of Mosul. Report Abuse.
---
By understanding and solving such equilibrium problems, it helps in designing stable and efficient truss structures for various engineering applications.
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