Using the Euler–Bernoulli beam-bending differential equation we analyse the solution for a shelf deformed under gravity in two situations: (a) simple supports positioned at x = β and x = L – β and (b) Cantilever at one end with a simple support at x = β. We ask where the best position for the supports should be. A number of alternative positions are suggested though the eventual choice of support position is chosen to be that which minimizes the shelf's strain energy.
