Max Shear Stress Homework: Find Max Stress

[Air]

Homework Statement

Find the maximum shear stress for $$\sigma _{xx} = 120 MN/m^2, \sigma _{yy} = 50 MN/m^2, \tau _{xy} = 40 MN/m^2$$

Homework Equations

$$\sigma _{min} = 0.5(\sigma _{xx}+\sigma _{yy})-0.5((\sigma _{xx}-\sigma _{yy})^2+4\tau _{xy} ^2 )^{0.5} = 31.8$$
$$\sigma _{max} = 0.5(\sigma _{xx}+\sigma _{yy})+0.5((\sigma _{xx}-\sigma _{yy})^2+4\tau _{xy} ^2 )^{0.5} = 138.2$$

The Attempt at a Solution

$$0.5(\sigma _{max} - \sigma _{min}) = 53.1$$ 4. Problem
However, the correct answer states $$0.5(\sigma _{max} - 0) = 69.1$$. Why is $$0$$ taken as the minimum shear stress?

 

[Mapes]

Hint: the real world has a z axis as well.