$10$ analyze an element or material that is in a given state or normal and snear strain, aetermine the angles and values or in$-$plane principal strains, determine the angle and value of maximum in$-$plane shear strain, and determine the average normal strain.

As shown, a differential element of material is distorted after it is subjected to stresses resulting in a state of plane strain given by $lo{n}_x=-375\mathrm{.}0{10}^{-6}i\frac{n}{i}n,lo{n}_y=245\mathrm{.}0{10}^{-6}i\frac{n}{i}n,$ and ${}_{xy}=110\mathrm{.}0{10}^{-6}i\frac{n}{i}n.$

Part A $-$ In$-$plane principal strains and their orientation

Determine the in$-$plane principal strains $lo{n}_1$ and $lo{n}_2$ and their orientations that are associated with the differential element of material.

Express your answers to four significant figures separated by commas.

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$\sqrt[]{}A,$darrvec

$lo{n}_1,lo{n}_2,{}_p=,i\frac{n}{i}n,i\frac{n}{i}n,$rad

Part B $-$ Maximum in$-$plane shear strain and its orientation

Determine the magnitude of the maximum in$-$plane shear strain, ${}_{in\text{p}\text{l}\text{a}\text{n}\text{e}}^{\text{m}\text{a}\text{x}},$ and its orientation relative to the differential element of material.

Express your answers to four significant figures separated by a comma.

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${}_{in\text{p}\text{l}\text{a}\text{n}\text{e}}^{\text{m}\text{a}\text{x}},{}_s=$ in$/$in$,$ rad

Part C $-$ Average normal strain in the differential element of material

Determine the average normal strain in the differential element of material.

Express your answer to four significant figures.

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