A machine element is subjected to the following bi-axial state of stress: $$\,\,{\sigma _x} = 80MPa;\,\,{\sigma _y} = 20MPa;\,\,{\tau _{xy}} = 40MPa.$$ If the shear strength of the material is $$100 MPa,$$ the factor of safety as per Tresca’s maximum shear stress theory is

A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $$100$$ $$MPa.$$ The yield and ultimate strengths of the shaft material in tension are $$300$$ $$MPa$$ and $$450$$ $$MPa,$$ respectively. The factor of safety using maximum distortion energy (Von - Mises) theory is __________.

Consider the two states of stress as shown in configurations $${\rm I}$$ and $${\rm II}$$ in the figure below. From the standpoint of distortion energy (Von - Mises) criterion, which one of the following statements is true?

The state of stress at a point is given by $$\,\,{\sigma _x} = - 6\,MPa,\,\,{\sigma _y} = 4\,\,MPa,$$ and $${\tau _{xy}} = - 8\,\,MPa.$$ The maximum tensile stress (in MPa) at the point is ____________.