A static load is applied with Fy $=300$ IbF as drawn and with $Fx=0$ ibf and $Fz=0$ lbf$.$ Focus solely on shaft AB$.$ Assume section AB is made of AISI $1030$ hot$-$rolled steel; properties can be found in Table A$-20,$ page $1048$ of the text. $(30$ pts $)$

a$.$ As unambiguously as possible, identify the candidate trouble$-$spot in shaft AB $.$

b$.$ Find the principal stresses at the candidate trouble spot.

c$.$ Find the safety factor for yielding at the candidate trouble spot by the maximum shear stress theory.

d$.$ Find the safety factor for yielding at the candidate trouble spot by the distortion energy theory.

e$.$ Are the two values found above consistent with our views about the conservative$/$daring nature of each theory?

f$.$ Determine the required diameter of AB so that the safety factor would be $3,$ using the distortion energy theory.