How can I support a desk without legs or brackets

Question

I plan to build a floating desk with the following dimensions: 75"-79" long and 22"-24" deep. I plan to mount it to concrete wall(see Image). My Preferred material is MDF.

The desk intended for use as computer desk and writing-reading desk. The load on the desk will be mainly consists of: monitor screen, books, laptop and so on.

My goal is to create a strong and stable desk that can support not only the load described above, but also beyond that(specifically: adult leaning on the desk with his arms).

My question is: How can I support the desk without any legs or bracket?

EDIT: There is a similar question to my question on the site(HERE) but I think the solution proposed does not fit my question. Since to my opinion the proposed support in solution is too weak for my purposes. I'm pretty sure that if I will lean down on the edge of the desk with time not only it will created a 'belly' but it will damage the Alum angle stability (maximum torque). I think the proposed solution is better suited for shelf that functions as a desk, and I want a strong desk that can support for example a person sitting over it.

Note: I do not care if the most of the entire thickness of the desk(based on the design offered) would be a hollow, as long as it's does not exceed 5''.

Answer 1

This is a pretty standard construction for floating shelves/counter top.

1. mount a cleat to the walls (the third wall is omitted for clarity sake). In this example it's a 1x4 but that will depend on how much weight it needs to bear.
2. Create a torsion box leaving a socket around the edges to accept the cleat.
3. mount the unit and apply a backsplash to cover the gap where the back and sides meet the wall. It's not impossible to scribe in a three sided surface but it's a tremendous pain in the neck.

I would recommend MDO over MDF as it has the strength to weight ratio of plywood but the surface of mdf. As for the thickness w.r.t the strength of the front edge... this is really pushing the limit of what you can support without a leg or integral steal beam and not experience serious deflection or failure.

Answer 2

You are essentially asking for a floating shelf--albeit a really large one.

This means all the support has to be hidden in a wall. Since you have a concrete wall, you're going to have to build out a new wall in front.

A technique to borrow is how floating stairs are built. A steel support structure is embedded inside the stud wall. The treads then attach to the steel support structure.

You'd have to do the same. One option would be to stud out a wall in front of the concrete then attach large steel T-brackets to the studs (so that the stem of the T sticks out). You'd then build the desk around the exposed stems of the brackets.