Rigidity of aluminium profiles and rectangular tube sections....

[Voicecoil]

So, I'd worked out roughly what sort of machine I need to build and had done some basic sums using both the excellent spreadsheet @routercnc provided and some other calculations and was just about to order in some great big lumps of profile. It seemed clear that for the gantry, torsion (twisting moment) was going to be the dominant source of cutting tool movement, kind of obvious when the tool tip is down near the bed as the length of the Z axis acts a a lever. I'd assumed that the performance of a piece of rectangular box section and a profile of roughly the same dimensions would be fairly similar as the moments of area (Ix, Iy) for normal flexing do seem to roughly match up weight for weight, so had happily gone ahead assuming I could plug values into the spreadsheet and get meaningful tool deflection figures for profiles.

THEN, I happened to come across the Item24 website, those guys are possibly the Nirvana of aluminium profiles, they have something to solve pretty well every problem ina very efficient german way. And, uniquely they state the torsion constant (J) for most of their profiles (basically how hard it is to twist it). AND the figures are very different (i.e. a LOT smaller) than the equivalent sized rectangular tube. Thinking about it now, it kind of makes sense, as playing around with anti-roll bars taught me that to get a stiff tube, you need to get as much thick, continuous metal as far away from the centre of rotation as possible. Whilst all the slots might add or certainly won't detract much from flexural stiffness, profiles only have a continuous "tube" at the bottom of the slots, a fair way in from the outer periphery, and the bits at each corner (where the stress is concentrated in a rectangular tube) do practically nothing to add torsional strength.
Anyway, here's a little comparative table of profiles and rectangular tubes: the profiles are all Item/KJN/Motedis patterns (they all are the same sort of shape and have similar Ix,Iy within a few %), stated prices are from whoever was cheapest when I looked. Prices for box are from my local stockholder, there's obviously money to be saved as well as gaining torsional stiffness

Profile	Moment of Area x	Moment of area y	Torsion constant	weight	cost per metre
Item 80 x 120 lite	201	422	165	8Kg	£55
Item 80 x 120	273	575	261	11Kg	£81
Item 80 x 160 Lite	270	919	250	11Kg	£77
Item 80 x 160	362	1232	397	13.5Kg	£101
Item 120 x 120	799	799	578	12.4Kg	£158
80x120x6.75 tube	251	482	498	6.9Kg	£48
2"x6"x1/4" tube	104	642	287	6.7Kg	£43
3"x6"x3/8" tube	352	1152	853	10.9Kg	£58
70x80x4.4 tube	191	860	493	5.9Kg	£39
80x200x6mm tube	360	1570	922	8.8Kg	£56
100x200x5mm tube	515	1522	1183	7.8Kg	£56

You can probably guess what I'm going to be using for my gantry