Cost: structural materials for buildings $($floor beam$)$

Constraints: length, L$,$ square section, maximum deflection $,$ stiffness of $S^{**}$

Objective: minimize cost

Free variables: material, area of cross section

Material index already derived for a light stiff beam; adding cost: $C=m{C}_m=AL{C}_m$

Leading to material index $M=E^{\frac{1}{2}\frac{?}{}}{C}_m$

Figure $5\mathrm{.}15$ The materials of a building are chosen to perform three different roles. Those for the structure are chosen to carry loads. Those for the cladding provide protection from the environment. Those for the interior control heat, light and sound. Here we explore structural materials.