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To solve this problem, let's analyze the data and the given requirements:

### Problem Analysis
1. **System**: A rigid bar is suspended by three wires, labeled A, B, and A.
2. **Wire Specifications**:
   - Material: Same for all three wires.
   - Diameter (\(d\)) = 12 mm, so the cross-sectional area \(A\) can be calculated.
   - Modulus of Elasticity (\(E\)) = 200,000 N/mm².
3. **Wire Lengths**:
   - Length of wire A = 2 m (2,000 mm).
   - Length of wire B = 3 m (3,000 mm).
4. **Strain Limit**: Maximum allowable strain is 0.001.

### Solution Steps
1. **Calculate Cross-Sectional Area of Each Wire**:
   \[
   A = \frac{\pi d^2}{4} = \frac{\pi (12 \, \text{mm})^2}{4} = 113.1 \, \text{mm}^2
   \]

2. **Calculate Allowable Stress**:
   Since the strain (\( \epsilon \)) is defined by:
   \[
   \epsilon = \frac{\sigma}{E}
   \]
   Rearranging, the allowable stress (\( \sigma \)) is:
   \[
   \sigma = \epsilon \cdot E = 0.001 \times 200,000 = 200 \, \text{N/mm}^2
   \]

3. **Determine the Force in Each Wire**:
   Using \( \sigma = \frac{F}{A} \), where \( F \) is the force each wire can hold:
   \[
   F = \sigma \cdot A = 200 \, \text{N/mm}^2 \times 113.1 \, \text{mm}^2 = 22,620 \, \text{N}
   \]

4. **Calculate the Total Load \( P \)**:
   Since there are three wires, and each can support 22,620 N:
   \[
   P = 2 \cdot 22,620 + 22,620 = 67,860 \, \text{N}
   \]

### Answer
The maximum load \( P \) that can be supported by the wires is **67,860 N**.

Would you like a detailed breakdown of any specific steps, or do you have additional questions?

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#### Related Questions:
1. What is the impact of changing the wire diameter on the maximum load \( P \)?
2. How would a different modulus of elasticity affect the result?
3. What if the lengths of wires A and B were equal?
4. How would you calculate \( P \) if the wires had different diameters?
5. What happens if the allowable strain changes?

#### Tip
In structural problems involving elastic deformation, knowing the relationship between stress, strain, and modulus of elasticity is essential for calculating load limits.

Find the maximum load P that a rigid bar can support, suspended by three wires of the same material with a diameter of 12 mm and elasticity modulus of 200,000 N/mm². This problem involves calculating cross-sectional area, allowable stress, and total load capacity based on given wire lengths and strain limits.

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