You are trying to do something that's next to impossible to do. Imagine joining two sheets of plywood together edge-to-edge.
Glue bonds things together much better in shear than it does in tension. That's Ed's first suggestion.
In the real world, you would weld the two pieces together if they were metal, and grind the bead. Ed's second suggestion is in that vein.
Maybe if the two pieces are flat, they could be keyed together. That might take the form of a piece of styrene the same thickness, an inch or so long and fairly narrow in width; being glued into a slot in each hal