Fig. E8.4 shows a material chart with the two indices of Exercise E8.2 as axes. Identify and plot coupling lines for selecting materials for a column with \(F=10^{6} \mathrm{~N}\) and \(H=3 \mathrm{~m}\) (the same conditions as above), and for a second column with \(F=10^{3} \mathrm{~N}\) and \(H=20 \mathrm{~m}\).

Data From Fig, E8.4

Data From E8.2

The best choice of material for a light strong column depends on its aspect ratio: the ratio of its height H to its diameter D. This is because short, fat columns fail by crushing; tall slender columns buckle instead. Derive two performance equations for the material cost of a column of solid circular section and specified height H, designed to support a load F large compared to its selfload, the first using the constraints that the column must not crush, the second that it must not buckle. The table summarizes the needs.

M2 Density* Price / ( Modulus^0.5), ($/m)/(MPa^0.5) 04 Technical ceramics Zirconia Aluminium Silicon carbide Soda-lime glass 10- Cast iron Carbon steel 0.1 Polymers Composites GFRP Ti alloys CFRP PTFE PP Phenolics Granite Al alloys Pb alloys Cu alloys- PE Metals and alloys Brick Bamboo Softwood Natural materials.. Hardwood Concrete Cement Nontechnical ceramics 10 102 103 MFA 16 104 105 M = Density *Price/ Compressive strength, ($/m)/(MPa) FIGURE E8.4