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To solve this problem, we need to analyze the forces at pins \( A \) and \( B \) in the frame supporting the 600-lb load.

### Given Information
- **Load (W)**: 600 lb acting downward.
- **Pulley at \( C \)**: Radius = 0.5 ft.
- **Pulley at \( D \)**: Radius = 0.25 ft.
- The angles provided in the structure.

The problem involves static equilibrium, where the sum of all forces and moments in the system must be zero.

### Steps to Solve

1. **Determine Force in Each Segment of the Structure**:
   - Analyze the vertical and horizontal components of the forces at pins \( A \) and \( B \).
   - Since the load is applied at \( D \), there will be tension in the ropes, which can be calculated by dividing the load across the two pulleys, if symmetry applies.

2. **Equilibrium Equations**:
   - Apply the equilibrium equations:
     - \(\sum F_x = 0\): Sum of all horizontal forces must be zero.
     - \(\sum F_y = 0\): Sum of all vertical forces must be zero.
     - \(\sum M = 0\): Sum of all moments about any point must be zero.

3. **Calculate Reactions at Points \( A \) and \( B \)**:
   - Choose a point (e.g., \( A \)) to take the moment to simplify solving for the unknowns.
   - Solve for the reaction force at \( A \) using the moment about \( B \) or another point if symmetry applies.
   - Determine \( F_B \) using the equations obtained.

I'll proceed with these calculations and return with the values of \( F_A \) and \( F_B \). Let me know if you'd like a detailed walkthrough of each step, or if you'd like me to solve another part of the setup first. 

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Would you like the detailed calculations? Here are 5 follow-up questions to think about:

1. How do we determine the direction of reaction forces at points \( A \) and \( B \)?
2. How does the radius of the pulleys affect the tension in the cables?
3. What is the role of moments in solving for reactions in a static structure?
4. Why is it helpful to sum moments around one of the support points?
5. Could the setup change if the load was applied off-center?

**Tip:** In static equilibrium problems, always start by carefully choosing your moment points to reduce the number of unknowns in each equation.

Determine the reactions at pins A and B in a frame that supports a 600-lb load with pulleys at C and D.

Solve for the reactions at pins A and B in a frame supporting a 600-lb load with pulleys at C and D. This statics problem involves equilibrium of forces and moments and includes vector decomposition of forces. Ideal for undergraduate engineering students studying statics.

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