This is shown in Figure 2. Using the weight equation above and solving for the free variables, the solution arrived at is w = 6 M b L 2 ( ρ / σ ) {\displaystyle w={\sqrt {6MbL^{2}}}(\rho /{\sqrt {\sigma }})} , where L {\displaystyle L} is the length and b {\displaystyle b} is the height of the beam. Assuming that b {\displaystyle b} , L {\displaystyle L} , and M {\displaystyle M} are fixed design variables, the performance index for bending becomes P C R = σ / ρ {\displaystyle P_{CR}={\sqrt {\sigma }}/\rho } .