You need gaps between the slats to both allow for expansion across the slats given the timber is going to be permanently outdoors and so subject to changes in humidity, and to allow water to more easily run off; thus preventing a puddle of water settling on the surface of the table in wet weather.
Big gaps between the slats are a "design" feature of most DIY wooden outdoor furniture. For those very reasons.
And any design will need to accommodate this requirement.
Make the underframe hexagonal with a leg on alternate vertices. Only one screw across the width of each slat with at least 10% interslat gap for expansion.
Saturate with preservative as generally the type of low cost wood selected for commercial indoor use will not have much rot resistance when used outside.
On approach would be to make a "ring" to go round the edge...
I would get some thicker and wider timber, and cut a rebate out of one side (table saw or router), say 3/4" across the width, and to the depth of the thickness of the slats you have.
Then chop into 8 equal length bits and mitre the "corners" at 22.5 degrees. Join the bits into an octagon[1]. You can now fix each of your slats into the rebate, with a small gap between each. Just fix once in the centre at each end of the slat.
Now if you want to get posh, trace a circle round the outside edge, and cut off the straight edges. You should then have a rigid circular table top that is self supporting and can be fixed to you base.
[1] Depending on ho complicated you want; pocket screws, glue and biscuits, dowels, floating tenons etc.
However, I could make a table top with three rails running at right angles to the slats. Then I could screw the legs to the rails. I think that would exhaust my carpentry skills. :)
It might be a good idea to paint it, rather than using wood preservative?
He needs to go the whole hog and laminate a circular ring.
Or do what I did and find a cheap metal circular table and use the ring it has to fix the slats and the legs. I was lucky to find one in aluminium so its rot proof too.
I think the table top will hold together okay, but I am not convinced that it would give a firm anchorage for the legs. It obviously depends how chunky the rails are.
That's another way of doing the ring that would work. Make two rings, one from wider timber than the other. Then sandwich the narrower one on top of the other, with a rotation such that the joins of one are mid board on the other - that way the whole thing can be glued up and each ring re-enforces the joints of the other (while more complicated to glue up it makes the joinery simpler since you don't need anything other than a butt joint at the board ends.
It also saves cutting the rebates since the top ring can be made with the required inner radius, and the bottom one with an inner radius a couple of inches smaller, to create the lip the slats sit on.
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