The Figure shows a $\backslash (30-\backslash$mathrm$\{$mm$\}\backslash )$ solid round shaft supported by self$-$aligning bearings at A and B $.$ Attached to the shaft are two chain sprockets that are loaded as shown. Treat this as a static loading problem.

a$.$ Identify the specific shaft location subjected to the most severe state of stress, draw the state of stress at that point, and make a Mohr circle representation of this stress state.

b$.$ What is the material strength required for a brittle material in order to provide a safety factor of $4?$ Use the modified Mohr theory and assume the material's strength in compression $3\mathrm{.}5$ that in tension. Show a sketch depicting the failure surface, the state of stress, and the margin of safety.