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

A small element at the critical section of a component in bi-axial state of stress with the two principal stresses being $$360$$ $$MPa$$ and $$140$$ $$MPa.$$ The maximum working stress according to distortion energy theory is