At the Morris Library of University of Delaware, heavy books are stored on metal shelves. The shelves contain a beam of square cross-section in the middle that carries almost all the books weight (the mesh rack adds a trivial amount in terms of carrying the bending load due to the weight of the books). The width of the shelf is fixed (length of the beam) and is simply supported at the edges. The books can be modeled as a uniformly distributed load across the beam (book mass/ft). To make it easy to remove and replace books on the shelf, it is desirable for the beam to have minimum mass. a) Translate this design (create a free-body diagram and identify the function, constraints, objective, and free variables). b) Using proper translation, derive a material performance index for the support beam that does not yield under an assumed book load. c) Create a bubble chart using the performance index and the edupack Level 2 database excluding ceramics and glasses. Provide a rationale for excluding these materials. d) Identify 5 potential materials for the beam from the bubble chart. Include edupack output and clearly mark these materials on the graph.