A cantilever beam of length \(L\) and Young's modulus \(E\) is subjected to a bending force at its free end. Compare the spring constants of beams with cross sections in the form of a solid circle (of diameter \(d\) ), square (of side \(d\) ), and hollow circle (of mean diameter \(d\) and wall thickness \(t=0.1 d\) ). Determine which of these cross sections leads to an economical design for a specified value of bending stiffness of the beam.