'Glueing' a lap

There is a gap filling adhesive available, I forget the name, look around your local shed. Cheers Don

I'd use polyurethane glue, it expands and foams when you apply it to gap fill, but make sure the joints are clamped up as tightly as possible to prevent it forcing them apart:

Nether of those will add any strength to the joint (though "joint" seems a bit of an overstatement:-) If it's mechanically stable use nails or screws. If it isn't (though I can't see why it should want to go anywhere unless you've REALLY botched the joint) I think you'll just have to buy new wood and do it again properly.

If you want to make it look pretty with filler, that's up to you.

Glues will only work with lots of contact area, and that area needs to be in the sheer plane, not effectively a butt joint.

Polyurethane glues once foamed up have much reduced strength - it's only in the areas tightly clamped up that they offer strength.

Epoxies will gap fill *and* be strong - but it still doesn't sound like the contact area is sufficient.

Fillers have no significant adhesive properties.

External steel angle brackets might be a viable solution.

Otherwise slice off the mess and either replace the whole thing or properly joint on new timber.

I intended to strengthen the joint with 3 or 4 screws as well as 'glueing'. The filler option seems right in order to gap fill to prevent water getting inside the joint to undermine it.

Arthur

OK, so you're asking about filling, not gluing.

The general rule is that it's better to provide drainage than attempt sealing.