Keep in mind this is at the elastic limit of an exceptionally strong linearly elastic material, and so is a reasonably conservative estimate of the difference between true strain and engineering strain in the elastic regime. So the final equation of bending $(\frac$ times larger than engineering strain at the elastic limit, or about $1.003$ times, or about $0.3\%$ larger. is used in analysis of bending beams, twisting shafts and in buckling. We use engineering stress and engineering strain in this eq. Surprisingly this hasn't been asked before, so I must be missing something simple.
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