I have worked in a natural stone distribution center and we are good friends with the granite fabricators. Speaking only to natural stone, most would recommend for the stone support to add a corbel or hidden metal brace every 24” to be located under the stone countertop where it meets the base cabinet.. Hope this makes sense!

Hmmm... yes, that is what I'm afraid of. I may have to order the hidden metal braces from the US.

I also should make a pretty important correction: The granite will have 38 cm (15 inches) of overhang over a span of 210 cm (82 1/2 inches). That's over six feet!

The pictured legs and stretchers will adequately support a 3cm 15" natural stone cantilever.

I would totally defer to Joseph who is a professional in the industry. You may also wish to speak to your local fabricator whom you will be using! Good luck!

That would go to 18" with no trouble.

The cabinet maker just told me that the posts will be constructed using MDF board to create a solid block. I imagine that is probably Ok, since they bear the load vertically, but if he suggests using MDF for the apron stretchers, that would be a definite no, am I right?

I will definitely talk to the cabinet maker about adding cross pieces. Also, suppose that instead of 2 x 3 1/8 inch for the stretcher boards, I asked him to use square "beams" of 3 1/8 inch. Would that add more strength and combat warping? I'm not sure I can get a custom made steel frame. That is highly custom work here and would add several thousand euros to the cost. The legs and apron alone is probably going to set me back 3K.

If he is building a decorative box post out of MDF, it should be around a structural wood or steel post. No stretchers should be MDF. MDF is fine as a cabinet box material when joined correctly. But the spans are short, and the joins shouldn't use pin nails as anything but as fixing agents until adhesive sets.

edanz:

There is nothing wrong with MDF legs, hollow even, loaded vertically. I'd have him rip a piece of Laminated Veneer Lumber (structural plywood) for the stretcher with the LVL let into the top of the leg to transfer the load to the floor. Make this stretcher as deep as your decorative eye can stand, please, but 3 1/8" of LVL will span 51" without sagging. Two legs, two small stretchers on each end, and the 51" stretcher between the legs is plenty. These details will save you the cost of a custom metal frame, but are critically important.