I would like to build a 36 in deep desk into a 14ft wide space that has floor to ceiling windows along the back. My initial idea is put cleat plates on the side walls, then run a 2x6 joist at 12 in from the back, and another 2x4 joist along the front edge. The cleat plate will be anchored with 1/2x4 in lag bolts into existing wall studs. I plan on 3/4 in plywood for the surface. I would like to finish with a laminate sheet on top, and a bullnose trim piece along the front edge.
The load is basic office stuff, laptops, monitors etc. Visually I want to avoid legs or brackets if at all possible, and the 2x6 joist location is limited by some rolling file cabinets.
Will this be rigid enough to prevent the laminate from coming unglued? Is this enough framing to support the load if I choose a paint/stain finish instead of laminate?