The maximum shearing stress when σz=0 is 70 MPa. Hence the correct option is c.
In a two-dimensional state of stress, characterized by normal stresses σx and σy and a shear stress τxy, the principal stresses (σ1 and σ2) can be determined by solving the characteristic equation for the stress system:
σ^2 −(σx+σy)σ+(σxσy−τxy^2)=0
For the given state of stress, assuming σz=0, the minor principal stress (σ2) is zero. Solving for the major principal stress (σ1), we find its value. The maximum shearing stress (τmax) is then calculated using the formula:
σmax= σ1-σ2/2
Substituting the obtained values, the maximum shearing stress in the given state of stress is determined. In the presented scenario, the closest option among the provided choices is selected, yielding the maximum shearing stress as 70 MPa. The choice represents the highest intensity of shear stress in the material under the given stress conditions. Hence the correct option is c.