For finite element software, you might take a look here.http://www.freebyte.com/cad/fea.htm#fea
I have used Lisa and a couple others. But the basic problem with the freeware stuff is that the interface is difficult or essentially missing. The expensive packages (Ansys, NASTRAN, CATIA, etc) will help you generate a mesh, configure loadings and constraints, solve for deflection (or stress, etc), and visualize the results.
This stuff is fascinating to use, but one definitely needs a degree in mechanical engineering just to start.
If you are just interested in deflection, you might use formulas in the Machinist Handbook or Roark's Formulas for Stress and Strain. They built bridges with this stuff in the days before modern computing.