Hi Ross,

Yes, I'm assuming the hinge can resist torsion. I'm trying to ignore the rest of the machine and just compare the sections themselves to show the differences.
For bending the load case is simply supported (i.e hinges), with load in the centre.
For torsion the ends are constrained, and the load is applied in the centre of the span, hence the x4 factor.

You might have made the same mistake I did initially (or may be I am wrong !), which is to find out the stiffness of a beam with just one end restrained and the other far end twisted. This is not the case with a gantry, where both ends are restrained and the torsion is applied in the centre. I think these two factors will give a x4 stiffness increase. Your FEA may be for a simple beam with one end constrained and the other far end twisted. Let me know if you follow this argument! I guess they are both 'right' in their own way.

Nice to have a double check on the torsion anyway. I think the x4 is just the end condition and twisting point difference.

It would be good for Lee to collect this sort of information together and post it somewhere appropriate on the site. I'm very happy for you (or others) to modify this sheet, but as it works well at the moment would prefer to see any mods as a seperate posting (rather than overwritten).

I use Roark's Formulas for Stress and Strains, which is a weighty book and takes a long time to wade through and get what you want, but it is all in there. Turning it into Excel versions with graphs helps me visualise the effects of different parameters.

I've been working on another spreadsheet which analyses the principles involved in cnc router (or mill) design, and the effects of geometry and inertia. When I feel ready I'll post this as well . . .

Barry