Complex joint technique

Does anyone here know how to create what I can only describe as a 3-way thru-mitre? The best analogy of what this would look like are the I-beam 'hedgehogs' on war-time beaches to stop the likes of tanks and other military vehicles. Now that I type this, I guess the other comparison would be a kids' game of jacks.
I want to build a pair of these as a table base for glass-topped table.
TIA,
Joe
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-- http://members.tripod.com/mikehide2

would
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The 'simple' version: Take three pieces of square stock, stack two of them up together, and drill a hole through the middle of both pieces. place a bolt through the hole, with a nut on the other end. tighten just enough to remove excess slack. rotate the two pieces so they are at 90 degrees to each other. tighten bolt. lay the 3rd pieces across the join of the first two. adjust for 90 degree angle to each piece. drill and then bolt through the middle of each of those pairs of pieces.
caveat -- made this way, they look 'squat and wide'.
For a taller, 'cleaner' look, you have to play with the angle of the 'inside' faces (the ones that butt against the other legs) on each piece.
For things to 'work', you have to keep the piece symmetric about the diagonal. Easiest way is to rip on a table-saw, with a 'bit' of an angle to the blade. Two passes (to trim two adjacent faces), with the _same_ corner of the stock at the fence/table join.
It assembles the same way, but the pieces meet at less than a 90 degree angle. Bolt the first pair of pieces together _loosely_, set the third in place, and tweak til you get a 'solid' fit.
IMPORTANT NOTE: the bolt-hole needs to be perpendicular to the _tapered_ (inside) faces. *NOT* square to the outside face.
The math for figuring out precisely what angle for what ratio of 'tall' to 'wide' is _messy_. "Cut and try" with some scrap stock is a _whole_ lot simpler. And doing 'test fitting' by holding things in place with a couple of rubber-bands. <grin>
With the faces at 90 degrees, you get the 'classical' hedgehog look. With a 30 degree 'taper' on each face, the three pieces stand absolutely upright, as if they were a single vertical -- *not* what you want. Wild-assed guess -- _without_ having done any experimentation -- is that something around 10-12 degrees of 'taper' will "look good". So, I'd start the experimenting at well under that.
Comment: for esthetics, once the appropriate 'inside' angle has been established, some people cut the -outer- faces parallel to the inside ones -- giving a parallelogram cross-section. Makes the bolt-up easier, too -- now the bolt hole _is_ perpendicular to both the inside and outside surfaces.
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wrote:

Do you simply mean how to joint three pieces of wood at an angle to each other, usually 90 degrees? You won't mean three coming to a point to support anything, but to come together at a level frame of some sort. So, can you be a bit more descriptive?
For three at 90. you just mortise one on two sides and attach the other two by tenons to that one.
Or do you mean some variation on the compound miters that have been discussed already at length? If that, you can readily do a search through this newsgroup.
Bill.
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My guess is that you're looking for a design that alows the thre axes of the beams to intersect a common point in the center.
The cleanest way I can think to do this leaves two beams strong and the third one a little weaker:
Half-lap two of the beams together at 90 degrees at their centers. This will leave you with a symmetrical cross, with the beams in the same plane.
Then cut a mortice all the way through the center of the cross. You'll have to decide for yourself how much material can be removed safely, but I'd probably use a square about half the size of the center (measured on a side, so 1/4 the area).
Your third beam will then be made up of a male (tenon) and female (mortise) piece. The tenon on the male piece must be long enough to pass through the center of the cross, and deep into the mortise on the female piece. The mortice on the female piece is cut into its end, and shares its axis with the beam.
Then you glue the tenon into the cross, and then into the mortise on the female piece of the beam.
If everything was cut to tight tolerances, the resulting form should be quite strong. It will be twice as strong across the half-lap joint as across the mortise and tenon joint. This is because the cross-section of the tenon (in my example) is 1/4 the area of the cross center, where the cross-section of the cut portion of the half-lap is 1/2 the area of teh cross center.
So figure out where you need the strength the most, and orient the hedgehog accordingly.
Good luck, and let us know what you decide.
-Mike
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Mike,
Thank you for taking my incredible lack of detail and turning it into something coherent.
You're right, I want the three axis to have a common intersection. I came up with one change to the design that requires an overhaul to the design. Picture the first two pieces half-lapped together. My original idea meant that if you laid that down on a table, a full face of each piece would be flat against the table. I think as an additional design feature, I'm going to rotate each piece 45deg so that the corner of each piece is all that's resting on the table (again, this example is only after the first two pieces have been joined). The drawback to this is that now only one 'leg' is going to remain whole. The other two will need to be cut in half. To combat the weakness that this is going to cause, I'm considering running threaded rod through the joint and epoxy it into the end grain of each piece.
I cut some test pieces to try to demonstrate this and posted the pics on abpw.
Thanks for your help and direction.
Joe ------

I-beam
would
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Joe,
I guess I would tend towards using a tenon rather than a threaded rod. Unless you require continuous grain through the piece, it will be stronger. Just cut a tenon into the end of a piece, then chisel out your V-shaped void. In the other piece, cut the mortise, then work the V into it. The advantage of this is that you only have glue in one side of the joint, while the other side is a continuation of the wood and will have no give.
If you use the threaded rod, stress may eventually work the rod loose, and having to epoxy both sides of the joint doubles that likelihood.
Anyway, if you offset the tenon so that one face of it is along the piece's axis, then you can run two of them perpendicular to each other through the one continuous piece. With this arrangement, the tenons from two pieces will be touching on one face. This will also make it easier to cut your V in the tenoned pieces because half of the V goes all the way through the piece, while the other half stops at the tenon.
Make any sense?
-Mike

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