A bar is compressed to half of its original length. The magnitude of true strain produced in the deformed bar is _________________ (correct to two decimal places).

To find the magnitude of the true strain produced in the deformed bar, let us understand the concepts step-by-step:

1. Define Initial and Final Lengths:
Let the initial length of the bar be denoted by ₀.
According to the problem description, the bar is compressed to half of its original length. Therefore, the final length of the bar, denoted by , is:
$L=\frac{L_0}{2}$

2. Formula for True Strain:
True strain (denoted by ${\epsilon }_T$) is defined as the natural logarithm of the ratio of the final length to the initial length:
${\epsilon }_T=\ln \left(\frac{L}{L_0}\right)$

3. Calculate the True Strain:
Substituting the value of into the formula:
${\epsilon }_T=\ln \left(\frac{L_0/2}{L_0}\right)=\ln \left(\frac{1}{2}\right)$
Calculating the natural logarithm:
${\epsilon }_T=-\ln \left(2\right)\approx -0.693$

4. Magnitude of the True Strain:
The magnitude is the absolute value, representing the scale of deformation without the negative sign (which indicates compression):
$\left|{\epsilon }_T\right|\approx 0.693$
Rounding to two decimal places, we get 0.69.