"Ted Edwards" wrote in message
...
Ed Huntress wrote:

Correct me if I'm wrong, Ted (and this is stuff I'm 'way rusty about),
but
the larger diameter tube made possible by lower density of aluminum will
have a higher value for the radius of gyration than will a steel tube of
the
same weight, and of smaller diameter.

Correct?

Correct but misleading. Of course the radius of gyration increases with
increasing diameter but the increase in diameter is not simply "made
possible by lower density of aluminum". One could instead choose to
make the wall thinner for steel but keep the same diameter. You might
want to take a look at "Design of Weldments", Blodgett, Sec. 2.5. I'd
be surprised if you didn't have *that* book.

I don't, but I still have a couple of Mechanics and Statics-and-Dynamics
books from college, as old as I am. The formulas for moment of inertia and
radius of gyration are the same but the Earth rotated the opposite way in
those days, which makes it confusing. g

About those tubes, Euler's formula and much of the rest are long lost in my
memory, but my non-mathematical recollection of the situation is this.
Increasing resistance to buckling for a given *weight* of of a given tubular
material, by increasing tube diameter and thinning the walls, is
self-limiting. You reach a degree of wall thinness at which the diameter
(and the curvature) of the tube becomes a lesser factor and the thin walls
begin to behave more like a plate loaded in compression, on edge. In other
words, plate stiffness in compression-induced bending begins to cross curves
with the sectional stiffness of the large-diameter tube.

Aluminum in the form of a tube, having 1/3 the density of steel and also 1/3
the stiffness (roughly), can be made larger in diameter (for the same
material weight and length) because the relative wall thickness remains
greater, even when the tube is somewhat larger in diameter. In other words,
you can take advantage of aluminum's far greater plate stiffness, per pound
of material, and, in doing so, you can increase the diameter of the tube
somewhat. You can increase diameter and still have considerably thicker
walls than you'd have with steel tubes of the same weight. The total effect
is an increase in the radius of gyration for the aluminum tubes over the
steel tubes, because of the greater diameter, before you start to cross
curves with the plate stiffness of the walls.

To get back to the space frames for cars, and what I originally said about
there being no theoretical advantage in performance for an aluminum-tube
space frame, the things I've just said above don't change that. The
performance of a space-frame car chassis is limited by stiffness, not by
strength, and the actual resistance to buckling should never come into play
at all, in a properly designed, fully triangulated space-frame chassis --
until you crash. g

Ed Huntress