Pretty good discussion; I'm not sure I have much to add.

Indeed, it turns out that theoretical ultimate compression strength is
greater than tensile strength; it's the opposite in the real world.

Mark wrote:

Fused silica glass is about 20x stronger in compression than in

tension

Glass is a special case. Glass fails in tension due to surface
irregulaties; glass fails by cracking from the surface inward. This
is, in fact, the secret behind the strength of "Tempered glass;" the
thermal treatment puts the surface in compression and the interior in
tension, so surface irregularities won't cause failure, because they're
in tension.

In a different post, Mark wrote:

The force in a typical atomic bond gets ever stronger as the atoms
are compressed together.

But if the atoms are pulled apart, the force will eventually get

weaker

(after initially getting stronger for small tensile displacement of

the

atoms). Unless there is something unusual about the bonding, that
would mean tensile strength is weaker than compressive strength in

most

materials.

True, but not actually relevant to real materials.

In tension, the radial component of the interatomic force is pretty
much the main thing of interest. You're pulling the bonds between
atoms apart. In compression, though, both the radial and the
directional part of the force is relevant. Real world materials squish
when compressed, and that counts as failure even if the atoms don't
actually get closer together.

(An analogue in tensile failure is necking, actually-- once one part
stretches more than another part, the cross section decreases, the
force per unit area increases, and the failure goes exponentially.
Thus, structures fail catastrophically in tension, while they fail
softly in compression. Except for buckling, of course. qv.)


jbuch wrote:

Long compression members have to contend with buckling as a failure
mode. That is one of the reasons there is less attention paid to
compressive strength of structural materials, as a practical matter.

Buckling is ignored in the Landis paper you cite.

Yep. Buckling is a killer failure mode for structures with the
fineness ratio I considered. But for structures this large, buckling
failure has quite long time scales-- it should, in principle, be very
easy to apply active control to prevent it.

(Of course, in the case of a power failure, the tower goes down.)

--a point nobody's made here is simple scale height of the atmosphere.
When I originally did that analysis, I ignored it on the assumption
that interior walls could make the gradient irrelevant, but a couple of
people arguing that point have made me decide I was handwaving a
serious objection. The pressure gradient in the tower makes
pressurized towers of the height I was looking at pretty much
unrealizable in practice-- there are workarounds, but they're not
terribly practical in the real world.

jbuch wrote:

Landis says:

Fewer references are available about the ultimate compressive

strengths of materials than tensile strength.

Long compression members have to contend with buckling as a failure
mode. That is one of the reasons there is less attention paid to
compressive strength of structural materials, as a practical matter.

Buckling is ignored in the Landis paper you cite.

You can do an experiment with a toy long balloon, and readily
demonstrate axial compressive buckling failure in a long length at
really low axial loads.......

I wouldn't ignore buckling as a failure mode in postulating these
structures.

Rather than admiring the nuances of a formula.... (and the predicted
wonders of a magic value of a materials pareameter such as Poisson

ratio

of +1) it might be really useful to think of the meaning of the

formula.

The formula is based on bending of a (uniform) beam/disk under self
loading and probably has the boundary condition of fixed edges. I

must

admit to laziness in not going to my bookcase and dragging out Roark,

or

not reading the original

You are encouraged to look at a different formula, one for the

boundary

condition of a controlled line bending moment.... which will tend to
counteract the gravity induced bending.

The goal is to reduce the bending to useful levels, not to find

perfection.

It is long been said that one of the problems with the Roark

compilation

of mechanics of materials equations is that too often the user does

not

understand the derivation and assumptions of the example, and

therefore

cannot appreciate the limitations.

Do you have a reference that might calculate the deflection for a
plate with a multi-component material? This is what would be needed for
pressurized mirror.


Bob Clark