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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?

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My 2 cents; upgrade you file cabinets, use them as your legs, and make sure you have 1-2 not just on the outside (middle somewhere). A 14' span with a 2x6 and 2x4 will most likely get by with the weight you mention with minimal sagging but is unsound and dangerous. If you want to test it out set up some saw horses, pickup trucks, whatever with 2 16' 2x4's close to max span (~14') and have a few people sit on it, you'll feel it bow. –  Jason Jun 26 '13 at 5:52
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This may be ridged enough, however I would recommend going with a torsion box design. This is how a professional furniture maker would attempt this. You can use 2x4 for the "core" and two skins of 3/4 inch ply. I would put a perimeter of 2x4 around the core (not shown in the picture) then lag bold the perimeter into your studs. You may have to cut a hole in the bottom skin to make this work. The key to making this work is to glue (subfloor adhesive) and screw (2") the skins to the core. Woodworkers have been using torsion boxes for years to create large desktops.

If you are using standard 8' plywood for the skins you will probably want to stagger the seams between the bottom and the top tortion box. For instance in the top use 2 7' pieces of ply. In the bottom skin use a 3' a 8' and a 3' piece of ply.

This will probably be your safest best. After you build it and before you install it you can test it out with two saw horses. I would be very surprised if it did not hold 200 lbs or more.

if you are still worried about flexing move up from a 2x4 to a 2x6 for the core and you should be able to support several people standing on it.

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