Consider a simply supported beam of rectangular cross section of constant width b and variable depth h, so proportioned that the maximum stress x at the outer surface due to bending is constant, when subjected to a load F at a distance a from the left support and a distance c from the right support...

Consider a simply supported beam of rectangular cross section of constant width b and variable depth h,

Question:

Consider a simply supported beam of rectangular cross section of constant width b and variable depth h, so proportioned that the maximum stress σx at the outer surface due to bending is constant, when subjected to a load F at a distance a from the left support and a distance c from the right support. Show that the depth h at location x is given by
h = √6Fcx/lbσmax 0 ≤ x ≤ a