Shown in the figure is a uniform-diameter shaft with bearing shoulders at the ends; the shaft is

Question:

Shown in the figure is a uniform-diameter shaft with bearing shoulders at the ends; the shaft is subjected to a concentrated moment M = 1200 lbf ?in. The shaft is of carbon steel and has a = 5 in and l = 9 in. The slope at the ends must be limited to 0.002 rad. Find a suitable diameter d.