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The question you have provided is focused on the mechanical properties of a brass alloy. Let me break it down and solve it step by step.

### Problem:
Given:
- The stress at which plastic deformation begins (yield stress) = 345 MPa
- Modulus of Elasticity = 103 GPa
- Cross-sectional area = \( 130 \, \text{mm}^2 \)

The task is to calculate the maximum load that can be applied without causing plastic deformation.

#### Part (a):
We know that:
\[
\text{Stress} = \frac{\text{Force}}{\text{Area}}
\]
Rearranging for Force (or Load):
\[
\text{Force} = \text{Stress} \times \text{Area}
\]

### Step-by-step Calculation:
1. Convert the area to meters squared (\( \text{m}^2 \)) because stress is in MPa (which is equivalent to \( \text{N/mm}^2 \)).
   \[
   130 \, \text{mm}^2 = 130 \times 10^{-6} \, \text{m}^2 = 1.3 \times 10^{-4} \, \text{m}^2
   \]

2. Multiply the stress by the area to find the maximum load:
   \[
   \text{Force} = 345 \, \text{MPa} \times 130 \times 10^{-6} \, \text{m}^2
   \]
   \[
   \text{Force} = 345 \times 10^6 \, \text{N/m}^2 \times 1.3 \times 10^{-4} \, \text{m}^2
   \]

Let me calculate that for you.The maximum load that can be applied to the specimen without causing plastic deformation is approximately **44,850 N** (or **44.85 kN**).

Would you like further details on any of the steps? Here are a few related questions that might expand your understanding:

1. How is the modulus of elasticity related to stress and strain?
2. What happens to the material when the stress exceeds the yield stress?
3. How can the cross-sectional area affect the force that a material can withstand?
4. How does plastic deformation differ from elastic deformation?
5. What is the significance of using MPa for stress measurements?

**Tip:** Always convert all units to a consistent system (SI units, for example) before performing calculations to avoid errors.

For brass alloy, the stress at which plastic deformation begins is 345 MPa and the modulus of elasticity is 103 GPa. Calculate the maximum load that can be applied to a specimen with a cross-sectional area of 130 mm^2 without plastic deformation.

This example shows how to calculate the maximum load that can be applied to a brass alloy specimen with a cross-sectional area of 130 mm². The material's yield stress is 345 MPa, and the modulus of elasticity is 103 GPa. The calculation uses the stress-force relationship and is ideal for students studying mechanics and materials science at the senior high school or university level.

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