Problems Using the method of joints, determine the force in each member of the truss shown. Summarize the results on a force summation diagram, and indicate whether each mem- ber is in tension or compression. You may want to try the "quick" method for Problems 3.14 through 3.17. Fal 3.12 300 31 1000# E 10¹ F 1 10² 10¹ A s 1000# 1000

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### Problem 3.12: Force Analysis on Truss

**Objective:**
Using the method of joints, determine the force in each member of the truss shown. Summarize the results on a force summation diagram, and indicate whether each member is in tension or compression. 

**Instructions:**
You may want to try the "quick" method for Problems 3.14 through 3.17.

#### Truss Specifications:
- The truss has joints labeled as A, B, C, D, and E.
- The horizontal distance between joints is 10 feet.
- The vertical height between joints A and B, and between joints B and C is 10 feet each.
- A force of 1000 pounds is applied vertically downward at joint C.
- Another force of 1000 pounds is applied at an angle of 30 degrees to the horizontal at joint E.

#### Diagram:
The provided diagram illustrates a truss with members connected at different joints. Two external loads are acting on the truss:
- A downward load of 1000 pounds at joint C.
- An angled (30 degrees) load of 1000 pounds at joint E.

#### Steps to Solve:
1. **Isolate each joint**: Start with the joints having known forces (usually where external loads are applied) and proceed to adjacent joints.
2. **Apply equilibrium equations**: For each joint, use the conditions of equilibrium (sum of horizontal forces = 0 and sum of vertical forces = 0) to solve for the unknown forces.
3. **Determine force types**: Assess if each member force is in tension (pulling apart) or compression (pushing together).

This problem requires a systematic approach to solve for the internal forces in the truss members, ensuring that all equilibrium conditions are satisfied.

#### Annotations:
- A solid analysis diagram is crucial. Draw and label each force, including dimensions and angles.
- Use trigonometric relationships to resolve angled forces into horizontal and vertical components.
- Summarize findings indicating whether each member is in tension or compression to provide a clear understanding of the structural behavior under given loads.
Transcribed Image Text:### Problem 3.12: Force Analysis on Truss **Objective:** Using the method of joints, determine the force in each member of the truss shown. Summarize the results on a force summation diagram, and indicate whether each member is in tension or compression. **Instructions:** You may want to try the "quick" method for Problems 3.14 through 3.17. #### Truss Specifications: - The truss has joints labeled as A, B, C, D, and E. - The horizontal distance between joints is 10 feet. - The vertical height between joints A and B, and between joints B and C is 10 feet each. - A force of 1000 pounds is applied vertically downward at joint C. - Another force of 1000 pounds is applied at an angle of 30 degrees to the horizontal at joint E. #### Diagram: The provided diagram illustrates a truss with members connected at different joints. Two external loads are acting on the truss: - A downward load of 1000 pounds at joint C. - An angled (30 degrees) load of 1000 pounds at joint E. #### Steps to Solve: 1. **Isolate each joint**: Start with the joints having known forces (usually where external loads are applied) and proceed to adjacent joints. 2. **Apply equilibrium equations**: For each joint, use the conditions of equilibrium (sum of horizontal forces = 0 and sum of vertical forces = 0) to solve for the unknown forces. 3. **Determine force types**: Assess if each member force is in tension (pulling apart) or compression (pushing together). This problem requires a systematic approach to solve for the internal forces in the truss members, ensuring that all equilibrium conditions are satisfied. #### Annotations: - A solid analysis diagram is crucial. Draw and label each force, including dimensions and angles. - Use trigonometric relationships to resolve angled forces into horizontal and vertical components. - Summarize findings indicating whether each member is in tension or compression to provide a clear understanding of the structural behavior under given loads.
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