Calculating Working Stress for Mild Steel

The question asks us to find the working stress for a mild steel specimen given its yield strength and a factor of safety.

We are provided with the following information:

• Yield strength of the mild steel specimen = 250 N/mm²
• Factor of safety = 2

The working stress is also known as the allowable stress or design stress. It is the maximum stress that a material is allowed to withstand in service, ensuring that it remains within the elastic limit and provides a margin of safety.

The relationship between yield strength, factor of safety, and working stress is given by the formula:

\( \text{Working Stress} = \frac{\text{Yield Strength}}{\text{Factor of Safety}} \)

Using the given values, we can calculate the working stress:

\( \text{Working Stress} = \frac{250 \text{ N/mm}^2}{2} \)

\( \text{Working Stress} = 125 \text{ N/mm}^2 \)

Thus, the working stress for the mild steel specimen, considering a factor of safety of 2, is 125 N/mm². This means that for safe operation, the stress in the material should not exceed 125 N/mm².

Let's look at the options provided:

1. 250 N/mm²
2. 125 N/mm²
3. 500 N/mm²
4. 150 N/mm²

Our calculated working stress is 125 N/mm², which matches Option 2.

The working stress is always less than the yield strength when the factor of safety is greater than 1. The factor of safety is used to account for uncertainties in material properties, loads, and manufacturing processes.

Therefore, the working stress is 125 N/mm².