A concept for a lightweight display stand. The stalk must support a mass \(m\) of \(100 \mathrm{~kg}\), to be placed on its upper surface at a height \(h\), without failing by elastic buckling. It is to be made of stock tubing and must be as light as possible. Use the methods of this chapter to derive a material index for the tubular material of the stalk of the stand that includes the shape of the section, described by the shape factor

\[\phi_{B}^{e}=\frac{12 I}{A^{2}}\]

where \(I\) is the second moment of area and \(A\) is the section area of the stalk. The table summarizes the requirements.

Function Constraints Objective Free variables Light weight column Specified buckling load F Height h specified Minimize mass m Choice of material Section shape and scale