Show that the index for selecting materials for a strong panel with the dimensions shown here, loaded in bending, with minimum embodied energy content is where Hm is the embodied energy of the...

Show that the index for selecting materials for a strong panel with the dimensions shown here, loaded in bending, with minimum embodied energy content is

where Hm is the embodied energy of the material, ρ is its density, and σy is its yield strength. To do so, rework the panel derivation in Section 9.11 by replacing the stiffness constraint with a constraint on failure load F requiring that it exceed a chosen value F where

where C₂
is a constant and I is the second moment of area of the panel: I 5 b h3/ 12 .