Re: Telescope mirrors under tension.

From: Robert Clark (rgregoryclark_at_yahoo.com)
Date: 03/18/05 

Date: 18 Mar 2005 10:12:03 -0800

redbelly wrote:
> Robert Clark wrote:
> > In this article Geoffrey Landis proposes builing a space tower
using
> > pressurized structures:
> >
> > THE TSIOLKOVSKI TOWER RE-EXAMINED
> > Journal of The British Interplanetary Society, Vol 52, pp.
175-180,
> > 1999.
> >
>
http://www.aeiveos.com/~bradbury/Authors/Engineering/Landis-GA/TTTR.html
> >
> > He notes that typically materials have higher failure or ultimate
> > strength in tension than in compression ...
>
> Funny, I could have sworn it was the other way around.
>
> Fused silica glass is about 20x stronger in compression than in
tension
> (1100 MPa vs. 50 MPa). See
>
> http://www.sciner.com/Opticsland/FS.htm
>
> and look at "compressive" and "tensile" strength on that page.
>
> Mark

 Yes, for brittle materials such as concrete or glass the compressive
strength is usually greater than the tensile strength. This is the
reason why steel is used to reinforce concrete, to give it greater
tensile strength. Perhaps Landis is considering the materials that
might be used for a space cable such as steel or carbon fibers for
instance, where the tensile strength is larger, since he makes a
comparison to the lengths that could be achieved with current materials
for a space cable.
 BTW, I received an answer to my question of why Landis did not have to
consider the compressive strength of the sides of the pressurized
structure. The situation is analogous to for example a beachball. It
can support significant compression due to the tensile strength of the
material, but the material itself has little compressive strength.
 Here's another interesting question to ponder. The formula for
deflection of a mirror due to its self-weight is:

Deflection ~ Density *(1-Poisson's ratio^2)/Young's Modulus

 Usually for constructing large mirrors it has only been the Young's
modulus and density that has been considered since the Poisson is
usually about 1/3 for most materials.
 But I thought what if you could find a material with a Poisson of 1?
Then the deflection would be 0.
 Honeycombed structures in 2-dimensions can have Poisson equal to +1:

Properties of a chiral honeycomb with a Poisson's ratio -1.
D. Prall and Roderic Lakes (University of Wisconsin), Int. J. of
Mechanical Sciences, 39, 305-314, (1996).
"Two dimensional honeycombs with regular hexagonal cells (Fig. 1a)
exhibit a Poisson's ratio of +1 in the honeycomb plane; the
out-of-plane properties differ due to anisotropy. The cell walls have
120 deg. angles between walls and all walls must be of equal thickness
and composition. In contrast honeycombs with inverted cells (Fig. 1b)
give rise to negative Poisson's ratios in the honeycomb plane [2-5]."
http://silver.neep.wisc.edu/~lakes/PoissonChiral.html

 Is it believed the Poisson ratio can not be +1 in 3-dimensions or is
this still an open question? Note that this Poisson ratio might not
have to be isotropic. It might be sufficient for example if when the
applied stress is in one direction say the vertical the expansion in
the horizontal direction is 1.
 

    Bob Clark

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