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Homework 1 Solution

# Homework 1 Solution - Problem 2.1 There was clearly a...

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Problem 2.1 There was clearly a typographical error in this question. Depending on what you read or what edition of the book you have you might have seen some slight differences. In the case that you read the second sentence as, “If the engineering displacements are - 1.5 cm and +1.5 cm, respectively, what will be the final lengths of the specimens.” You would have solved the problem as follows: The final lengths of the specimen are tension = 5 cm + 1.5 cm = 6.5 cm compression = 5 cm – 1.5 cm = 3.5 cm " e = # l l o e = 1.5 5 = 0.3 or 30% Knowing that t = ln 1 + e ( ) t = ln 1 + 0.3 ( ) = 0.262 or +26.2%, tension t = ln 1 # 0.3 ( ) = -0.357 or - 35.7%, compression The true strains are numerically different from engineering strains because in the former, the instantaneous gage length is used while in the latter; the original gage length is used.

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In the case that you read the second sentence as, “If the engineering strains are -1.5% and +1.5%, respectively, what will be the final lengths of the specimens.” You would have solved the problem as follows: " e = # l l o Thus, 0.015 = " l 5 cm , " l = 0.75 cm The final lengths of the specimen are tension = 5 cm + 0.75 cm = 5.75 cm compression = 5 cm – 0.75 cm = 4.25 cm Knowing that t = ln 1 + e ( ) t = ln 1 + 0.015 ( ) = 0.015 or +1.5%, tension t = ln 1 # 0.015 ( ) = -0.015 or -1.5%, compression

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Homework 1 Solution - Problem 2.1 There was clearly a...

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