Understanding the Problem: Steel Bar Under Axial Pull

The question asks us to find the longitudinal strain produced in a steel bar when it is subjected to an axial pull. We are given the stress induced in the bar and its Young's modulus.

Given Parameters

• Axial Pull (Force, P) = 84 kN (This information is provided but not directly needed for calculating strain from stress and Young's modulus)
• Stress induced in the bar, σ = 140 N/mm²
• Young's modulus of the steel, E = 2 x 10⁵ N/mm²

Relevant Formula: Hooke's Law

Hooke's Law states that within the elastic limit, the stress induced in a material is directly proportional to the strain produced. The constant of proportionality is known as Young's modulus (E).

The relationship is given by the formula:

$$ \sigma = E \times \epsilon_L $$

Where:

• σ is the stress
• E is the Young's modulus
• ε_L is the longitudinal strain

Calculating Longitudinal Strain

To find the longitudinal strain (ε_L), we can rearrange the formula:

$$ \epsilon_L = \frac{\sigma}{E} $$

Step-by-Step Calculation

Now, we substitute the given values into the rearranged formula:

• Stress, σ = 140 N/mm²
• Young's modulus, E = 2 x 10⁵ N/mm²

$$ \epsilon_L = \frac{140 \text{ N/mm}^2}{2 \times 10^5 \text{ N/mm}^2} $$

$$ \epsilon_L = \frac{140}{200000} $$

$$ \epsilon_L = \frac{14}{20000} $$

$$ \epsilon_L = \frac{7}{10000} $$

$$ \epsilon_L = 0.0007 $$

Conclusion

The calculated longitudinal strain produced in the steel bar is 0.0007. This matches one of the provided options.