Problem $7\mathrm{.}4-18$

An element in plane stress is subject to stresses ${}_x=22900$kPa,${}_y=9100$kPa, and ${}_{xy}=-3750$kPa

Draw Mohr's circles, identify the locations of the $x$ and $y$ planes on Mohr's circle. Solve for stresses on rotated elements specified in the problem and draw those stresses on an oriented element. Also, solve the principal stresses, ${}_1,{}_2,$ and ${}_3.$ Find the orientation of the plane with the maximum in$-$plane principal stress, ${}_p.$ Draw the properly oriented in$-$plane principal element. Find the maximum shear stresses, ${}_{\text{m}\text{a}\text{x}in-\text{p}\text{l}\text{a}\text{n}\text{e}}$ and ${}_{\text{m}\text{a}\text{x}\text{a}\text{l}\text{l}-\text{p}\text{l}\text{a}\text{n}\text{e}}.$ Find the orientation of the plane with the maximum in$-$plane shear stress, ${}_s.$ Draw the properly oriented in$-$plane maximum shear element. In total, you should have three element sketches: $(1)$ given oriented element, $(2)$ principal element, and $(3)$ shear element.

results?