A beam of uniform rectangular cross.section is to be cut from a log having a circular cross section of diameter 2a. The beam has to be used as a cantilever beam (the length is fixed) to carry a concentrated load at the free end. Find the dimensions of the beam that correspond to the maximum tensile (bending) stress carrying capacity. Using Direct and Lagrange Multiplier methods a Ans: x = and y = 2 2 (Neutral axis)