Problem $7-4,$ Shigley $1986$

The figure below shows a rotating round shaft supported in self aligning ball bearings at A and $D$ and loaded by a non$-$rotating force $F=9\mathrm{.}8kN.$ The shaft is made of BS$080$M$40$ carbon steel, harden and tempered to $HB=200$ units. The shaft is having a machine finish. Take all fillet radii $3$ mm and estimate:

a$)$ Support reactions and bending moment diagram.

b$)$ Bending stresses at sections B$,$ E$,$ and C$.$ Which point is critically stressed? State three reasons for that.

c$)$ The shaft endurance limit at the critically stressed point.

d$)$ The shaft life in number of cycles of the load applications.