Consider a simply supported static beam of circular cross section of diameter d, so proportioned by varying the diameter such that the maximum stress σx at the surface due to bending is constant, when subjected to a steady load F located at a distance a from the left support and a distance b from the right support. Show that the diameter d at a location x is given by
d = (32Fbx/πlσmax)1/3 0 ≤ x ≤ a