any woodworking experts?

[hrt4me]

what is the best/proper/strongest way to join two pieces of plywood at a right angle to one another? _|_

the horizontal bottom piece is ¾" (so actually 23/32") thick, and the upright vertical piece is ½" (15/32" actual) thick, so I was planning to use a router to cut a notch in the horizontal bottom piece, then glue in it place and use brackets (not sure which type) on each side of the vertical piece...

 

[dtc81]

Depending on the access to tools you have, you could use a dado blade on a table saw to cut the notch in the horizontal piece. If you had a biscuit jointer that would be a good route too

 

[curtperry]

If you don't have a dado blade for your table saw then multiple passes with a normal blade will work fine, be careful to make it a tight fit.

 

[TheDurk]

Good advice above. As far as the brackets, either of these should do the job, depending on what the job is. I like the second set for looks and rigidity. You can bolt them on opposite sides with the same bolt going through both. That makes for a solid base despite the short horizontal because the two act together.

If the vertical is free standing, tall, and will get a lot of stress, then you would need something that has a brace:

 

[hrt4me]

the vertical piece(s) are 10" tall and will be used to support the horizontal platform on which we will sleep in the rear cargo area of the 4Runner; the brace would be a good idea for added strength and support, but unfortunately the diagonal piece would interfere with the storage space beneath the platform...

 

[1engineer]

the vertical piece(s) are 10" tall and will be used to support the horizontal platform on which we will sleep in the rear cargo area of the 4Runner; the brace would be a good idea for added strength and support, but unfortunately the diagonal piece would interfere with the storage space beneath the platform...

I'm not normally over in this area but I will give you something from an engineering prospective for the strongest joint:

Cut a slot in the horizontal piece maybe 1/4" deep
Attach your vertical pieces by screwing and gluing (screw from the back side and pre drill first!) and countersink the heads. Glue is important!
Use unequal length "L" brackets with the long side on the horizontal piece, say three or four screws on the horizontal piece and two screws on the vertical piece per bracket. Brackets must be attached to each side of each vertical piece and space them 18" apart or so directly across from each other. Don't stagger them unless you only offset them an inch or so to keep the screws from hitting each other.

This will give you the strongest joint for what you have. On the brackets, the diagonal gusset (the part you said will mess up your storage) will not be needed if you do it correctly. Gorilla glue would be a good choice for this. Make sure you use plenty of it too and as you screw from the back side just wipe the excess glue away. Hope this helps.

 

[tee-bone]

Assuming this is plywood, and guessing you don't have an easy way to make a dado (although a straightedge and a circular saw can do it, one kerf width at a time) I would glue and screw the 10" board (making sure to look up what size pilot hole to drill and use good hardware. Pick an end that isn't as critical to get full access (probably the front) and attach plywood that runs side to side, vertically oriented (if that makes sense) screwed into both the deck and the support.

At the back, run either plywood (laid plat) or angle iron or something that will secure the bottom of the support and prevent it from moving side to side.

There is no way (IMHO) that fasteners in plywood attached along the spine will stand up for a long time to very much weight on them. You need the reinforcement to prevent racking.

 

[TheDurk]

There is no way (IMHO) that fasteners in plywood attached along the spine will stand up for a long time to very much weight on them. You need the reinforcement to prevent racking.

This. Nothing short of a braced bracket will prevent a vertical from folding over if the structure permits it to do so when supporting a human body 10" high, let alone two. I don't have a clear vision of how you want to put this together, but you really should design it so you barely need any fasteners at all on this intersection. The structure should brace itself and not need the brackets. There ought to be a way to do this fairly easily.

 

[1engineer]

Assuming this is plywood, and guessing you don't have an easy way to make a dado (although a straightedge and a circular saw can do it, one kerf width at a time) I would glue and screw the 10" board (making sure to look up what size pilot hole to drill and use good hardware. Pick an end that isn't as critical to get full access (probably the front) and attach plywood that runs side to side, vertically oriented (if that makes sense) screwed into both the deck and the support.

At the back, run either plywood (laid plat) or angle iron or something that will secure the bottom of the support and prevent it from moving side to side.

There is no way (IMHO) that fasteners in plywood attached along the spine will stand up for a long time to very much weight on them. You need the reinforcement to prevent racking.

In my suggestion the screws in the spine are nothing more than to act as a clamp for gluing.