It's shaped like an "H" but imagine the bridge being box section with the sides sticking above and below about 30mm. Cant show pics because I'm not at home and my pics are on external drive.
The void the top and bottom sticking up bits create have had 60x30mm profile inserted and bolted to gantry which the profiled linear rails fasten onto.
The boxsection void is filled with sand to dampen resonance.! This was done afterwards because I wasn't happy with the tune it was Singing.!!
I wouldn't recommend anyone copy it because it's a rubbish why to do it and I only did it because I had the profile for free. It took me along time "Shimming" to get it working to an acceptable level of accuracy and I'm still far from happy with it regards strength and vibration so while It's strong there's easier and better ways to do it.
The secret to cutting aluminium successfully on a "Router" type machine is to limit tool and Z extension to the minimum possible and reduce resonance/vibration to minimum thru using dense gantry/machine materials.
That's why box section is not ideal for gantry's cutting aluminium unless filled (Made denser) but for woods then it's not really a problem if a decent wall thickness is used and like I say the rail alignment/parallelism etc has to be dealt with thru shimming or surface adjustment regardless if rail mounting surfaces are on individual pieces of profile/B-section or one big boxsection/profile.!!
If I was in the position lots are where they have to use off the shelf materials that can only be worked with hand tools then for a "Gantry" I'd choose Profile over box section every time.!
My machine came about by watching A U-tube vid and thinking "I can do that.!!" then looking at this piece of profile and pile of spare box section and hey presto 6hrs later the frame was roughed together.!!
The materials for whole main frame including gantry of my machine (1500mm,sq) cost £77 and that includes Ali for sides and profile on gantry, Z axis Ali cost £25. The complete thing including Z axis but excluding Ali bed cost less than £102. The profiled linear rails cost another £175 second hand of ebay. The ballscrews from chai/ebay and for roughly £500-600 I'd got a working machine that after plenty of tweaking cut's Ali fine and doesn't even know it's cutting wood.
Sorry bit off topic but JAZZ trying to get hold of you but pm's just bouncing back as your hoarding you must be collecting them lol
Bit late to the topic and most of it has already been discussed but here's my take on it
Forces on a gantry are difficult to judge because they can change direction and magnitude and are mainly dynamic. To get an ideaof the problem of dynamic forces look in to why Marching Armys have to break step when going over bridges! At a basic level most beams only have to deal with a force in one direction and as such have a larger dimension in that axis, hence rectangular beams. however gantry's are also subjected to twisting so need to be able to resist torsion. circular sections are best for this and square the next best. In comparison rectangular beams are not so good especially if the are slender. Therefore a square beam would be the best option.
To get an ideaof the problem of dynamic forces look in to why armys have to break step when going over bridges
Box vs Profile
A made up beam using tee slot extrusions will have an new 2nd moment of area but the calculation would assume that all the faces are bonded together to make one solid section. any movement in the bolted joints will reduce its torsional stability.
Box sections are deemed the most efficient as they have all their mass at the extreme edges but can be affected by resonance. this can be damped or designed out.
Extruded sections can have the same parallelism issues as box and I have seen builds that have milled the top of the extrusion to get the accuracy they need.
So as Jazz and so many others have said its horses for courses but it does seem easy to get carried away and dismiss simple solutions. Just using linear rails an ballscrews wont result in a precision machine, they have to be correctly mounted and tweaked so they work correctly. so why not use an easy option and extend this tweaking to the mounting structure as well.
I had a go at designing a composite beam a few years ago but not had time to progress it any further. Planned to use extruded Ali box and channel to made a sort of closed I beam that had a recess for the ball screw. Top and bottom sections filled with epoxy granite to provide damping and compressive strength.
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