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?

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.