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.

Transcribed Image Text:

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