will it stay up?

I'm going to start working on a makup table for my wife. It will be rather like a return for a desk...sticks out at a right angle from her vanity.
It will have a poplar frame covered by 3/4" ply on top of which there will be a couple of 3/4" soapstone tiles, each 1.5 ft. sq. It will have a 3" mahogany rail around it to hide the poplar, ply and tile edges. Basically, it is a torsion box without a bottom.
It is about 37" long, 18" wide and will weigh around 50-60 pounds (soapstone is heavy).
One long side abuts a wall and will be screwed to studs. One short side will be supported by the vanity. To support the other short side, I'm planning on a 1 1/2" thick mahogany knee, 12+" horizontally and about 10" vertically.
The knee will be firmly screwed to the structure of the table; I'm planning to attach it to the wall via a sliding dovetail the 3/4" oak pin of which will be screwed to a stud.
I'm thinking it will be fine attached as I have outlined; not sittable but satisfactory for its purpose. What do you think?
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On 12/17/2015 2:20 PM, dadiOH wrote:

Then it's not a torsion box, the TB gains its strength by the top and bottom along with the webbing in between.

I think the 3/4 ply will take the weight, but I think it will sag over time, even with the mahoganny edging. Are you planning on putting any thing under the 3/4 ply, a longeron, to help support the 37 Inches. basically from end to end, not across. I think that would help the mahogany take the load. Think 2x4 on edge under the ply going the length.
--
Jeff

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On 12/17/2015 3:54 PM, woodchucker wrote:

Scrap what I just said, I had the orientation wrong.
--
Jeff

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<...> >> The knee will be firmly screwed to the structure of the table; I'm

LOL.

I'd think so too. The 3" rail should be ample to stop the ply from sagging, and the knee sounds more than stout enough to hold up the end (you'd use a much smaller knee in a sailing dinghy to support the mast, and that's dynamic load with a lot of leverage).
I'm not sure you need to attach the knee to the wall - just bearing against it might suffice since the top of the knee is effectively connected thru the table. But the sliding dovetail will be a technically elegant piece of work :-)
John
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