Two elastic bars of equal length and same material, one is of circular cross-section of 80 mm diameter and the other of square cross-section of 80 mm side. Both absorb the same amount of strain energy under axial force. What will be the ratio of stress in the circular cross-section to that of the square cross-section?

Question

Question

This question was previously asked in

SJVN ET Mechanical 2019 Official Paper

Attempt Online

Answer 1

Concept:

Strain energy under axial load is given by:

\( U = \frac{\sigma^2}{2E} \times A \times L \)

Since both bars have same material and length and absorb the same strain energy:

\( \frac{\sigma_1^2}{\sigma_2^2} = \frac{A_2}{A_1} \Rightarrow \frac{\sigma_1}{\sigma_2} = \sqrt{ \frac{A_2}{A_1} } \)

Given:

\( A_1 = \frac{\pi}{4} d^2 = 5026.55~\text{mm}^2 \)

\( A_2 = a^2 = 6400~\text{mm}^2 \)

\( \frac{\sigma_{\text{circular}}}{\sigma_{\text{square}}} = \sqrt{ \frac{6400}{5026.55} } = \sqrt{1.273} \approx \boxed{1.128} \)