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Half-lap joints typically feature one board "lapping" over another, as you know. My question is this: does the board on top--the one that "laps over" the one on bottom--necessarily have to "lap over" the full width of the bottom board? That is, would there be a significant disadvantage if the top board only "lapped over" part of the width of the bottom board, so that its end grain didn't show through on the finished joint?

I've attached a screenshot of a simple drawing that I did on Microsoft Publisher (I don't know how to use SketchUp yet). The image at the top shows a traditional half-lap joint, with the top board lapping over the full width of the bottom board. The image below that shows the theoretical joint that I'm asking about, with the top board only lapping over part of the width of the bottom board.

Hopefully this makes some kind of sense. :)
 

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The glued joint will be stronger than the rest of the piece. The width of the workpiece will matter somewhat. I think you just want to only have endgrain showing on one edge of the joint, not both. Personally, I think the L shaped endgrain is not as attractive as a conventional lap. But if the piece is wide enough you could turn the overlapping piece into a tennon so the entire end is endgrain. Cut a mortise to fit the tennon. The glue will help reinforce and hold the end piece in place.
 

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Half-lap joints typically feature one board "lapping" over another, as you know. My question is this: does the board on top--the one that "laps over" the one on bottom--necessarily have to "lap over" the full width of the bottom board?
no...
not at all...
 

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Another option would be cutting mitered ends and putting in a hidden spline, similar to cutting and gluing in a biscuit.. Or use dowels. Or double biscuits if you have the space. All of which will make a no-endgrain joint. Or, lightly glue up the miter corners, then cut a spline across the corners and use a matching or contrasting spline on the outside. Kind of depends on what part of the corner you want to be endgrain (or spline) free, the inside corner or the outside.
 
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