List of top Applied Mechanics and Design Questions on Failure theories

Which one of the following failure theories in the most conservative design approach against fatigue failure
A structural member under loading has a uniform state of plane stress which in usual notations is given by $\sigma_x = 3P$, $\sigma_y = -2P$ and $\tau_{xy} = \sqrt{2}\,P$, where $P>0$. The yield strength of the material is 350 MPa. If the member is designed using the maximum distortion energy theory, then the value of $P$ at which yielding starts (according to the maximum distortion energy theory) is
The von Mises stress at a point in a body subjected to forces is proportional to the square root of the
A solid massless cylindrical member of 50 mm diameter is rigidly attached at one end, and is subjected to an axial force, P = 100 kN and torque T = 600 Nm at the other end as shown. Assume that the axis of the cylinder is normal to the support. considering distortion energy theory with allowable yield stress as 300 MPa. The factor of safety in the design is _____ (Round of one decimal place)