Complex Stresses · Strength of Materials · GATE PI

For a two dimensional state-of-stress defined as $${\sigma _{xx}} = {\sigma _{yy}} = {\tau _{xy}} = S,$$ the Mohr's circle of stress has

If the principal stress values are $$120$$ MPa, $$-50$$ MPa and $$10$$ MPa in a given state of stress, then maximum shear stress in the material, in MPa, is _______.

A bar of rectangular cross-sectional area of $$50$$ mm² is pulled from both the sides by equal forces of $$100$$ N as shown in the figure below. The shear stress (in MPa) along the plane making an angle $$45$$⁰ with the axis, shown as a dashed line in the figure, is _______.