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Solved: If the normal strain is defined in reference to
Chapter 2, Problem 2-34(choose chapter or problem)
If the normal strain is defined in reference to the final length \(\Delta s^{\prime}\), that is,
\(\epsilon^{\prime}=\lim _{\Delta s^{\prime} \rightarrow 0}\left(\frac{\Delta s^{\prime}-\Delta s}{\Delta s^{\prime}}\right)\)
instead of in reference to the original length, Eq. 2–2, show that the difference in these strains is represented as a second-order term, namely, \(\epsilon-\epsilon^{\prime}=\epsilon \epsilon^{\prime}\).
Questions & Answers
QUESTION:
If the normal strain is defined in reference to the final length \(\Delta s^{\prime}\), that is,
\(\epsilon^{\prime}=\lim _{\Delta s^{\prime} \rightarrow 0}\left(\frac{\Delta s^{\prime}-\Delta s}{\Delta s^{\prime}}\right)\)
instead of in reference to the original length, Eq. 2–2, show that the difference in these strains is represented as a second-order term, namely, \(\epsilon-\epsilon^{\prime}=\epsilon \epsilon^{\prime}\).
ANSWER:Step 1 of 3
The normal strain in the reference to the final length 
Here, 
The normal strain in the reference to the initial length 
