At a point of a steel hydraulic piston that is subjected to a state of plane stress, the strains…

At a point of a steel hydraulic piston that is subjected to
a state of plane stress, the strains measured by the strain gauge rosette are _a
= -0.00150, _b = 0.00140, and _c
= 0.00086. The modulus of elasticity and Poisson’s ratio of the material are E
= 200 GPa and v = 0.33. What are the principal stresses and the absolute
maximum shear stress at the point? (See the figure for Problems 8.64–8.66.)