Learning Goal:

To be able to use the general equations of plane$-$strain transformation to determine key characteristics of a differential element, including the equivalent strain on an oriented element, the in$-$plane principal strains on that element, the maximum in$-$plane shear strain, and the average normal stress.

The state of plane strain on a differential element of material is shown below. The strains are $lo{n}_x=0,lo{n}_y=-290({10}^{-6}),$ and ${}_{xy}=150({10}^{-6}).$

Part A $-$ Equivalent Strains on an Oriented Element

Determine the equivalent strains on an element oriented $45\mathrm{.}0$ counterclockwise from the differential element shown.

Express your answers, separated by commas, to three significant figures.

View Available Hint$($s$)$

$lo{n}_{x^{\text{'}}}=,lo{n}_{y^{\text{'}}}=,{}_{x^{\text{'}}{y}^{\text{'}}}=$Part B $-$ Principal Strains on the Oriented Element

Determine the in$-$plane principal strains on the oriented element.

Express your answers, separated by a comma, to three significant figures.

View Available Hint$($s$)$

$lo{n}_1=,lo{n}_2=$

Part C $-$ Maximum In$-$Plane Shear Strain and Associated Average Normal Strain

Determine the maximum in$-$plane shear strain and the associated average normal strain on the oriented element.

Express your answers, separated by a comma, to three significant figures.

View Available Hint$($s$)$

${}_{in\text{p}\text{l}\text{a}\text{n}\text{e}}^{\text{m}\text{a}\text{x}}=,lo{n}_{\text{a}\text{v}\text{g}}=$

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