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Yes, I can help you resolve this problem.

### Given:
- \( T_A = 8 \, \text{kips} \)
- \( T_B = 15 \, \text{kips} \)
- The structure is in equilibrium.

The goal is to draw a free-body diagram (FBD) and determine the magnitudes of forces \( T_C \) and \( T_D \).

### Solution Steps:

#### Step 1: Free-Body Diagram
The free-body diagram will display all the forces acting on the welded connection. Since the system is in equilibrium, the sum of forces in both the horizontal and vertical directions must equal zero.

- **Force \( T_A \):** Horizontal force (8 kips) acting to the right.
- **Force \( T_B \):** Horizontal force (15 kips) acting to the right.
- **Force \( T_C \):** Vertical force acting downward. We need to find its magnitude.
- **Force \( T_D \):** Force at an angle of 45° to the horizontal. We need to find its magnitude.

#### Step 2: Set Up Equilibrium Equations
Because the system is in equilibrium, we apply the following conditions:
1. **Sum of forces in the horizontal direction (x-axis) = 0:**

   \[
   T_A + T_B = T_D \cdot \cos(45^\circ)
   \]
   Simplifying this equation:

   \[
   8 + 15 = T_D \cdot \frac{1}{\sqrt{2}}
   \]
   \[
   23 = T_D \cdot 0.707
   \]
   \[
   T_D = \frac{23}{0.707} \approx 32.53 \, \text{kips}
   \]

2. **Sum of forces in the vertical direction (y-axis) = 0:**

   \[
   T_C = T_D \cdot \sin(45^\circ)
   \]
   \[
   T_C = T_D \cdot \frac{1}{\sqrt{2}} = 32.53 \cdot 0.707 \approx 23 \, \text{kips}
   \]

#### Step 3: Conclusion
- \( T_C = 23 \, \text{kips} \)
- \( T_D = 32.53 \, \text{kips} \)

Would you like more details on any specific part of the solution?

### Related Questions:
1. How do we resolve forces into components?
2. What are the conditions for static equilibrium?
3. How is the direction of a force determined in a free-body diagram?
4. Can this method be used for forces at different angles?
5. Why is the angle important in resolving forces?

**Tip:** Always resolve forces into their components along the x-axis and y-axis for easier calculations when analyzing equilibrium.

Learn how to solve an equilibrium problem involving a welded connection with forces acting at an angle. This statics problem includes solving for unknown forces using trigonometric functions and the principles of static equilibrium. Suitable for high school and undergraduate students.

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