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 homogeneous state of stress for a metal part undergoing plastic deformation is $$$T = \left( {\matrix{ {10} & 5 & 0 \cr 5 & {20} & 0 \cr 0 & 0 & { - 10} \cr } } \right)$$$

Where the stress component values are in $$MPa.$$ Using von Mises yield criterion, the value of estimated shear yield stress, in $$MPa$$ is

A solid circular shaft needs to be designed to transmit a torque of $$50$$ $$N.m.$$ If the allowable shear stress of the material is $$140$$ $$MPa,$$ assuming a factor of safety of $$2,$$ the minimum allowable design diameter in $$mm$$ is