OK, you wanted a nerd's answer, so here it is! I reckon that a 5" square box made of the poplar and luan should equal in strength the 2"x2"x1/8" square steel tube that is often used for teardrop frames.
There is a wide varition in the strength of poplar - I have assumed strucutral grade No 2, but if you can get grade No 1, then a 4" box is probably enough. If your poplar is not structurally graded, don't use it. I have some doubt over the luan ply, as that is not really a structural material.
In order to join the corners, I've gone to a stitch-and-glue boatbuilding handbook. Three layers of 2.5oz cloth each 3" wide and staggered 1.5"/1"/2" along each side should do. This is required on both sides of the ply, which leaves you a problem to close the box - I think a 1" poplar square or triangular fillet, bonded with epoxy glue can replace the glass on two internal corners. The diagram below shows the overall layout and the staggering pattern for the cloth - I'm assume in practice you would put at least one layer all round the box to seal it.
According to my calcs, this should produce a beam with a maximum bending strength of 22,000 lb-in - this is about 1.5 times the strength of the steel tube, but that's intentional - wood materials are much more variable than steel, so you need a much bigger material safety factor.
All of this is just a rough estimate based on limited test data for poplar. The
only way to safely use this type of construction is to build a test beam and load it up. 22,000 lb-in is a 200 lb person standing in the centre of a 220" (18' 4") beam supported only at its ends - you can alter the ratios to suit, so the same result is obtained by a 400 lb load over a 110" long beam.
I stress - to use this construction without testing a sample beam would be intentionally dangerous.
Sorry for all these warnings but I don't want anyone thinking that any pieces of ply made into a 5" box and held together with a penny nail every 4" is suitable!
Andrew