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I'm planning to make a desk with adjustable height. I want the legs to be two pieces: a lower, thicker leg from which a thinner upper leg can telescope. This means that the lower legs will essentially be a very tall open-top boxes which must support a fair amount of weight on their rims.

I know how to use a miter spline or a locked rabbet joint but I worry that those won't be able to support lots of longitudinal force. Do I need to worry about this?

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    You might look at the "Stickley leg joint" (perhaps a shade thinner board than usual since you want it to receive another leg in a telescoping manner.) "Lock-miter" is another name for it. – Ecnerwal Apr 23 '17 at 0:47
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If you can do a splined mitre joint long enough and accurate enough for this then I think you're good to go.

A lock-rabbet joint might be stronger under normal circumstances but here you'd be doing it along the long grain, not across it as this joint is used normally. It's not a suitable joint along the grain of solid wood.

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Do I need to worry? Nope. If you want to spline those mitres for alignment you can. Properly applied, splines or biscuits are fine, but the value added is limited to help with alignment. Your 3/4 inch material is going to give you an inch of gluing surface. Plenty. Glue both sides, clamp em up, and move on.

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