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The problem presented involves a truss structure subjected to a force of 10 kN. The goal is to determine the normal and shear stresses on plane P, given that the members are cylindrical solid bars with a radius of 40 mm. Here's a breakdown of the steps needed to solve this problem:

### 1. **Truss Analysis:**
   We need to analyze the forces in each member of the truss to find the internal forces at the plane P. This can be done using **static equilibrium equations**:
   \[
   \sum F_x = 0, \quad \sum F_y = 0, \quad \sum M = 0
   \]
   From the diagram:
   - The angles provided for the members (60° and 30°) help break down the force components in horizontal and vertical directions.
   - You can assume point **D** to be a pin joint with reactions in both x and y directions.

### 2. **Cross-sectional Area Calculation:**
   Given that the members are cylindrical with a radius of 40 mm, the cross-sectional area \( A \) of each member is:
   \[
   A = \pi r^2 = \pi (0.04)^2 \, \text{m}^2
   \]

### 3. **Normal Stress Calculation:**
   Once the internal force in each member is determined, the normal stress \( \sigma \) on the plane P is given by:
   \[
   \sigma = \frac{F_{\text{normal}}}{A}
   \]
   where \( F_{\text{normal}} \) is the axial force in the member, and \( A \) is the cross-sectional area calculated above.

### 4. **Shear Stress Calculation:**
   The shear stress \( \tau \) on the plane P can be calculated using the shear force component:
   \[
   \tau = \frac{F_{\text{shear}}}{A}
   \]
   where \( F_{\text{shear}} \) is the force acting perpendicular to the plane P.

### 5. **Solve Using Trigonometry:**
   The truss geometry provides angles which will help in resolving the force components acting on plane P. You’ll need to use trigonometry to separate the forces into components along and perpendicular to the plane.

Do you want me to proceed with the detailed solution and calculations for each step, or would you like to ask specific questions about the problem? 

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Here are 5 related questions to expand on this:
1. How are normal and shear stresses different in terms of their effects on materials?
2. What role do the angles of 30° and 60° play in resolving forces in a truss structure?
3. Why is it important to calculate the cross-sectional area of the members?
4. How would the analysis change if the truss members were hollow cylinders instead of solid bars?
5. How can you determine whether the truss members are in tension or compression?

### Tip:
In truss problems, always start by identifying support reactions and break forces into components using the given angles to simplify your calculations.

La armadura que se muestra en la figura soporta una fuerza de 10 kN. Sus miembros son barras cilíndricas sólidas con un radio de 40 mm. Determine los esfuerzos normales y cortantes sobre el plano P.

Determine the normal and shear stresses on plane P of a truss structure subjected to a 10 kN force. The members are cylindrical with a radius of 40 mm. This problem involves trigonometry, statics, and stress analysis, suitable for undergraduate engineering students.

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