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To solve for the force in member CD, we need to analyze the truss structure shown in the image. Here's a step-by-step breakdown of the process:

### Step-by-Step Solution

1. **Identify the Geometry and Forces**:
   - We have a truss structure with a roller support at point B and a pin support at point A.
   - There is a load of 10,000 lbs applied vertically downward at point F.
   - Points E and D form a diagonal member CD, which we need to solve for.

2. **Determine Support Reactions**:
   - Since point A is a pin support, it can have both horizontal (Ax) and vertical (Ay) reactions.
   - Point B, being a roller support, only has a vertical reaction (By).

3. **Apply Equilibrium Equations**:
   - For the system to be in equilibrium, the sum of forces and moments must be zero.

4. **Sum of Moments About Point A**:
   To eliminate the unknown reactions at point A, we sum moments about point A:

   \[
   \sum M_A = 0
   \]

   Taking counterclockwise moments as positive:

   \[
   -10,000 \times 40 + By \times 20 = 0
   \]

   Solving for \(By\):

   \[
   By = \frac{10,000 \times 40}{20} = 20,000 \text{ lbs}
   \]

5. **Sum of Vertical Forces**:
   Using the equilibrium of vertical forces:

   \[
   \sum F_y = 0 \implies Ay + By - 10,000 = 0
   \]

   Substitute \(By = 20,000\):

   \[
   Ay + 20,000 - 10,000 = 0 \implies Ay = -10,000 \text{ lbs}
   \]

   (Ay is acting downward since it's negative.)

6. **Sum of Horizontal Forces**:
   For the horizontal forces:

   \[
   \sum F_x = 0 \implies Ax = 0
   \]

7. **Analyze Joint D**:
   Now we analyze joint D to solve for member CD. At joint D, we have:

   - Force in member CD (\(F_{CD}\))
   - Force in member DE (\(F_{DE}\)), but its value is not necessary for CD.

   Since it's a truss, and using trigonometry from the provided dimensions:
   
   Let's consider the angles, using triangle trigonometry for the slope (40 degrees):

   - The horizontal component of \(F_{CD}\): \(F_{CD} \cos(40^\circ)\)
   - The vertical component of \(F_{CD}\): \(F_{CD} \sin(40^\circ)\)

   At joint D:
   
   \[
   \sum F_y = 0 \implies F_{CD} \sin(40^\circ) = 0 \implies F_{CD} = 0
   \]

   This implies there is no vertical force, hence, \(F_{CD} = 0\).

### Conclusion

The force in member CD is **0 lbs**.

Would you like to see more details, or do you have any questions? Here are some related questions you might consider:

1. What are the reactions at points A and B for different load scenarios?
2. How do we calculate the force in other members of this truss?
3. What changes if the load is applied at a different point?
4. How does the angle of member CD affect the forces in the truss?
5. What if member CD was under a different loading condition?

**Tip:** When solving truss problems, always start by finding the support reactions first and then use joint equilibrium equations to find the forces in each member.

Learn how to solve for the force in member CD in a truss structure with a detailed step-by-step analysis. This problem involves statics and truss analysis, including the application of equilibrium equations such as sum of forces and sum of moments. Suitable for undergraduate students studying civil or mechanical engineering.

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