My brother and I have been discussing joinery and gluing for the shelves I’ve been making. He has suggested some design changes to maximize mechanical strength of the tabs and slots and less dependence on glue. So one of the things is to carry the back wall plate up higher than the shelve so that the shelf is cantilevered in a full slot rather than just resting on open joints. It does make the design different but takes care of a big question on strength. With the angle bracket, it holds very well as is, but does require adhesive.
Yes, in terms of the shelf platform in relation to the back mounting plate, the tabs that go into the wall plate that are fully enclosed into slots are what I am thinking of as you have done in this build. That extra hook on either side does make a difference for the sides too. Missed that detail of your post.
For this one you need a hanging cleat like used in cabinetry because of the space behind the backing plate.
Basically everything else is supported by the backing plate in this design. If you hold it by any other part, the whole thing falls apart if there is no adhesive. The side panels slip over and then drop into the tabs extending from the backing plate, this way the bottom portion of the side panel is positively locked to the backing and won’t tend to pivot out sideways. Everything else is just straight tabs as gravity does the job.
I like this type of design! Though, I’d be concerned about stress concentrations on the yellow tabs, and you’d want to make sure your wood grain was going the right direction.
IF this were my project I would simply glue it together. No mechanical fastening is going to be stronger than a proper fully glued and clamped joint for the very reason you bring up, stress concentration.
However, if the requirement is no adhesive, there is only so much you can do, or only so much load the structure will be able to handle.
On this particular tab you highlighted, the dead load isn’t the big issue, there’s plenty of meat in that direction to resist load (maybe it could be moved lower so there is more material in the red side panel to dissipate that compressive load above the yellow tab, but the lower tab is sharing that load too).
The main issue with the yellow tabs is the shear load imposed upon them because of the torque of the shelf (load pressing/pulling them perpendicular to the wall). These tabs could be made longer to dissipate more load (minimally effective), or the backing panel could be made of thicker material, or if the backer panel is made taller so the tabs can be spaced further apart, there is less torque load on them.
Or just keep it to light duty use and not worry about it.
