I need to build a shelf spanning 11'6" x 30". It is in front of a window so I can only attach it to the walls at either end. It will need to hold about 100lbs of speakers and audio/video gear, with a 65lb tv hanging from the center of it. How could I build a shelf strong enough to not bow and how to attach it to the walls?
I think your two choices are
- make the shelf stiffer by making it thicker
- support the shelf more inventively.
An example of the former would be to make the shelf into a T-beam (or use keshlam's suggestion of a torsion box)
An example of the latter might be support wires up to the top of the wall or to the ceiling, or a glass-brick pillar, or a wooden arch support.
I would think about the myriad of ways bridge builders have tackled the same structural problem over hundreds of years.
Your shelf is going to need to be pretty beefy -- in fact with those specs you're probably better off treating this as a flooring system rather than a shelf, design-wise. Using the calculator here as a guide I'd estimate you're going to need to create your shelf using 2x4s spaced every 4" or so as your "joists" to support this load. I'd make an 11'6" box out of 2x4s, then fill in the middle with the joists on 4" centers. Skinning the top and bottom with 1/2" plywood glued and screwed to these joists will turn it into a proper torsion box that should be nice and rigid.
With all this load (plus the weight of this shelf, which won't be trivial!) you're going to need to make sure it's securely fastened to at least two studs on each end. Drive two 3/8x4" lag screws with washers through the end of your box into each stud, before attaching the plywood skins to the top and bottom. You'll want to predrill for each screw: 3/8" holes in the box ends, and 1/4" holes into the studs.