A static load is applied with $Fy=300lbf$ as drawn and with $Fx=0lbf$ and $Fz=0lbf.$

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.