Chassis tube calculations

[chapmanite]

Does anyone know the formula for calculating the bending stiffness of a rectangular tube? I have round and square, but no idea for rectangular. While I have you, does anyone know the formula for sheet as well?

Thanks

[Greg Locock]

Bending stiffness of rectangular tube of external dimensions B and D, with D as the depth, and internal b and d is 1/12(B*D^3-b*d^3)

Plate is much more difficult as it depends how you load it.

[chapmanite]

Thanks Greg.

Do you happen to know if you can ballpark it by assuming a rectangle of extremely wide, short dimensions?

[Greg Locock]

Yes, that is a reasonable first approximation. The main assumption you are breaking is that the beam equation assumes that the beam does not warp at all - in crossection the rectangle remains rectangular, and in one plane.

If you are doing much of this I recommend Costin and Phipp's book, tho I suspect one of Carroll Smith's books probably covers it.

However if you are going to do much with plates then you'll either need some heavy weight books, or FEA.

[boyracer]

Little late to the party, but at least in Aust. design rules, a rectangular tube is considered as being 4 'corners' with leg lengths of 12t (it may be 16t ? I forget).
So if we choose a totally random tube size of 90mm x 40mm x 3mm (t)
As the 40mm width is less than twice the 12t, but the 90mm depth is more than twice 12t, the beam is analysed as 2 off c-channels offset from the neutral axis of bending by 0.5xdepth, in this case 45mm. If we chose a 90x90x3 section, then it's considered as 4 corners and it all starts to get a bit complicated.

The idea being that material so far away from a corner is not structurally 'stiff' and thus doesn't contribute to the section strength as it may buckle.
Roark's formulas for stress and strain are your best bet for the plate calculations.