Problem $1$:

A solid circular steel shaft with the yield shear strength of $9000$ psi is

subjected to a pure torque of $T=650lb-$in in the positive axial direction.

a$.$ Determine the minimum allowable diameter of the shaft.

b$.$ Assuming that you are looking straight down the z axis at the side of the shaft, draw a stress element, showing the maximum shear stress in the shaft at this minimum diameter. Include coordinate axes and label the stresses, showing proper direction and magnitude. At what radial location in the shaft does this stress act $($i$.$e$.$ the central axis, the outside surface of the shaft, or somewhere in between$)?$