Dark,
I built a desk like you are planning about 15 years ago for my father, a full time author/writer. Posted pictures long ago but have lost them. I should be at their house next month and will try and remember to take new photo's then.
A couple of items:
My tops were all 1" thick white oak. The longer side was frame and panel, with QS white oak panels inset into the solid wood frame with walnut borders. It was based on a design in Woodsmith #79. The shorter side was just a glued up panel of 1" thick oak.
To join the two sides together I used
these from Lee Valley.. One in front one in back. They butt the two tops together tightly and also align the horizontal surfaces perfectly.
My dad has had a PC monitor on the short L side with a slide out key board tray underneath the entire 15 years. I thought about the kind of stiffening support you have drawn but decided against it. There are no aprons ont he front like you've added There has been zero sagging of the top, none at all. Of course, he isn't sitting on the desk at the inside corner of the L.
Difference between mine and yours is there are drawer pedestals at each end of the L. These shorten the unsupported length, but it is still pretty roomy under there. I used Thomas Mosers Executive Desk in his Building Shaker Furniture book for a lot of inspiration for the one I built.
I also made this desk for my wife about ten years ago:
It also has a large opening for her feet under her tablet monitor, which has only gotten heavier since she upgraded and put a support arm under it. This top is a torsion box, I think it is 1/2" plywood top and bottom sandwiching 1" frame members. The top is four separate torsion boxes.
The right hand pedestal is the 30" full depth, as is the printer pedestal on the left the 24" depth. There isn't a rear apron, however past the chair you can see a bookcase underneath that supports the corner- and right-hand tops. I used a large angle bracket mounted to the wall at the joint underneath the corner- and left-hand top. Without a back apron there was nothing to support the tops. To join all the sections together I used
these countertop joiners from Lee Valley. They worked really well. All the case construction here is plywood joined with biscuits. The cabinets are mostly my design but based on designs in
this book.. This desk has had no sagging at all, either.
Not sure if any of this helps, but personally speaking a torsion box would work fine for that span. I also think with a 1" thick solid top you could manage that span without additional support if it is under 4 feet or so for the long leg and probably 3 feet for the short leg, that is roughly the unsupported part of my dads desk. His doesn't have that apron and it is fine. If your sons decides to store a collection of antique barbells on the inside corner it will eventually sag, but it is up to you if you want to design for that kind of intended use.
Mike
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