Derive the material index for a torsion bar with a solid circular section. The length L and the stiffness S* are specified, and the torsion bar is to be as light as possible. Follow the steps used in the text for the beam, but replace the bending stiffness S F? * = by the torsional stiffness S T / ? * = (equation 5.8), using the expression for K given in Figure 5.2.