ALT 4/8 Determine the force in each member of the loaded truss. 2m D 4m] 5 kN. B 3 m C 15°

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4/8 Determine the force in each member of the loaded truss.

2m

D

4 m

5 kN.

B

3 m

15°

 

### Statics: Truss Analysis

**Problem 4/7:**

Determine the force in each member of the loaded truss.

---

#### Diagram Description

The diagram presented is a truss structure labeled with points A, B, C, and D. Each point is connected by members with specific lengths:

- Member AD is 2 meters long.
- Member AB is 4 meters long.
- Member BC is 3 meters long.

Additionally, point C has an external downward force of 5 kN acting at an angle of 15 degrees from vertical.

Points A and D form a vertical line, indicating a member of the truss with point A at the top and point D at the bottom connected by a vertical member. 

Point B is horizontally aligned with point A and C but at a higher elevation relative to point C, forming a triangle.

### Detailed Steps to Solve:

1. **Identify the structure and the equilibrium conditions:**
   - All nodes are in static equilibrium.
   - Sum of forces in horizontal and vertical directions at each joint should be zero.
   - Sum of moments about any point should be zero.

2. **Break the external force at point C into horizontal and vertical components:**
   - \( F_C = 5 \text{ kN} \)
   - Horizontal component, \( F_{C_x} = 5 \times \cos(15^\circ) \)
   - Vertical component, \( F_{C_y} = 5 \times \sin(15^\circ) \)

3. **Apply the method of joints or sections:**
   - Use either the method of joints to solve for unknown forces by isolating each joint.
   - Alternatively, use the method of sections to cut through the members and solve directly for the forces in the members of interest.

### Conclusion

By following the above steps, applying equilibrium equations at each joint or section, you can solve for the forces in each member of the truss structure. Be mindful of the direction of forces (tension or compression) while solving for each member’s internal force.
Transcribed Image Text:### Statics: Truss Analysis **Problem 4/7:** Determine the force in each member of the loaded truss. --- #### Diagram Description The diagram presented is a truss structure labeled with points A, B, C, and D. Each point is connected by members with specific lengths: - Member AD is 2 meters long. - Member AB is 4 meters long. - Member BC is 3 meters long. Additionally, point C has an external downward force of 5 kN acting at an angle of 15 degrees from vertical. Points A and D form a vertical line, indicating a member of the truss with point A at the top and point D at the bottom connected by a vertical member. Point B is horizontally aligned with point A and C but at a higher elevation relative to point C, forming a triangle. ### Detailed Steps to Solve: 1. **Identify the structure and the equilibrium conditions:** - All nodes are in static equilibrium. - Sum of forces in horizontal and vertical directions at each joint should be zero. - Sum of moments about any point should be zero. 2. **Break the external force at point C into horizontal and vertical components:** - \( F_C = 5 \text{ kN} \) - Horizontal component, \( F_{C_x} = 5 \times \cos(15^\circ) \) - Vertical component, \( F_{C_y} = 5 \times \sin(15^\circ) \) 3. **Apply the method of joints or sections:** - Use either the method of joints to solve for unknown forces by isolating each joint. - Alternatively, use the method of sections to cut through the members and solve directly for the forces in the members of interest. ### Conclusion By following the above steps, applying equilibrium equations at each joint or section, you can solve for the forces in each member of the truss structure. Be mindful of the direction of forces (tension or compression) while solving for each member’s internal force.
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