A cylindrical cantilever beam is subjected to a force F, as indicated in the accompanying figure. Derive strength and stiffness performance index expressions analogous to Equations CS1.9 and CS1.11 for this beam. The stress imposed on the unfixed end e is a= (CS1.12) L. r, and I are, respectively, the length, radius, and moment of inertia of the beam. Furthermore, the beam-end deflection & is FLr T FL 3EI (CS1.13) where E is the modulus of elasticity of the beam. 6= (b) From the properties database presented in Appendix B of the print textbook, select the metal alloys with stiffness performance indices greater than 3.0 (for E and in units of GPa and g/cm'. respectively). (c) Also, using the cost database, Appendix C conduct a cost analysis in the same manner as in this case study. Relative to this analysis and that in part (b), which alloy would you select on a stiffness-per-mass basis? (d) Now select the metal alloys with strength per- formance indices greater than 14.0 (for a, and p in units of MPa and g/cm', respectively), and rank them from highest to lowest P (e) Using the cost database, rank the materials in part (d) from least to most costly. Relative to this analysis and that in part (d), which alloy would you select on a strength-per-mass basis? Ict (f) Which material would you select if both stiff- ness and strength are to be considered relative to this application? Justify your choice.