What are cheap ways to build strong shelves with a large span?
I'd use plywood with a thicker piece of hardwood glued onto the front edge. This gives you very good strength. Here is an online calculator I use to find what kind of materials you can use and the amount of sag you will have. Here's a good quote from the author of the site. 


  “The eye will notice a deflection of 1/32″ per running foot.”


The sagulator