A cantilever beam AB of circular cross section and length L = 450mm supports a load P

Question:

A cantilever beam AB of circular cross section and length L = 450mm supports a load P = 400N acting at the free end (see figure).
The beam is made of steel with an allowable bending stress of 60MPa.
Determine the required diameter dmin of the beam, considering the effect of the beam's own weight.