A spherical pressure vessel that must hold compressed air is to be designed with a given inner radius r, and the wall thickness t may vary with material choice. The vessel must resist a pressure p such that there is a factor of safety X against the material exceeding its failure strength. a) Considering weight and cost, and any other factors that you believe to be important, make a preliminary materials selection from Table I for this application b) Calculate the vessel thickness required for each material. Assume a vessel inner radius of r = 2 m, a pressure p = 0.7 MPa, and a factor of safety on the material strength of X= 3. Comment on the values obtained. Why are some values much larger than others? Elastic Modulus Strength E. GPa Density Relative Material Type Example AISI 1020 steel AISI 4340 steel a.. MPa p. g/em' 260 1103 Cost. C. Structural (mild) steel 203 7.9 Low alloy steel 207 7.9 7075-T6 AI 469 High strength aluminum alloy 71 2.7 6. - inium alloy Ti-6AI-4V 117 1185 4.5 45 Engineering polymer Polycarbonate (PC) 2.4 1.2 Wood Loblolly pine 12.3 88 0.51 1.5 Economical composite 21 380 2.0 10 Glass cloth in epoxy (GFRP) 76 930 1.6 200 High-performance composite Graphite fiber in epoxy laminate (CFRP)