For the cantilever beam shown in the diagram, L and d are the design parameters for the specified load F. For the beam loaded in this way, the deflection is given by:
d = 4FL³ / Et⁴, and M = rLt².

Eliminating t between these two equations and collecting design and material parameters gives:

(F / M² ) = {d/ 4L⁵ }(E/ r²)

The material selection criterion for a minimum weight structure chooses the material with the maximum value of ( E / r² ).

From: Ashby and Jones, "Engineering Materials 1," Pergamon (1986)

If the yield stress is the controlling parameter (s_y = 6 F L / t³ ) the corresponding selection criterion maximizes (s_y^2/3/ r )