Question

A solid circular shaft of diameter $20mm$ is subjected to tensile loads over a gauge length of $100mm$. If the observed elongation of the bar is $1.3cm$, the true strain in the shaft is:

• A. $0.1302$
• B. $0.1136$
• C. $0.1222$
• D. $0.2221$

Answer 1

The correct option is C $0.1222$



True strain, ${\epsilon }_t=ln\left(\frac{L}{L_0}\right)$
Where, $L=$ final length
$L_0=$ Initial length
$L_0=100mm$
$L=L_0+\Delta$
$L=100+13=113mm$
$\Rightarrow {\epsilon }_t=ln\left(\frac{113}{100}\right)=0.1222$