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Old School
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I disagree, a half lap has only half board thickness in 2 places, and makes a weaker member for side load. we'll just agree to disagree.
I would agree in the first case that there is only a half board thickness to resist the load, but in the second case, there is sufficient long rain surface to be as strong as the board itself. Agreed? :blink:
I don't know who to agree or disagree with. IMO, a true half lap is not half a board thickness in two places, constituting its integrity. When the two halves are glued and clamped, that joint is more robust than a single piece of wood. It's the same principle as glued up laminations. The glue joint makes those two parts stronger than if it was just one.

The joint could be further fortified by installing dowels.





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