C[omp]ute

From: "andrew cooke" <andrew@...>

Date: Mon, 9 Oct 2006 10:49:14 -0400 (CLT)

Although I no longer post on Mefi, I still read it from time to time. 
It's dperessing how ugly some of the behaviour is, and how
stupid/incorrect some of the AskMe answers are.

Today there's a bunch of people talking about paper structures -
http://ask.metafilter.com/mefi/48182 - and they are in a complete mess
about the basic principles.

If you are going to support weight (from below) then a structure must
handle compressive forces.  There's no avoiding it.  The weight of
whatever you are carrying is going to pass down through he structure,
compressing it.

For reasons I will explain below, it's much easier to make stable paper
objects that rely on tensile, rather than compressive forces (the replies
have this much right).  But given my previous statement on the logical
necessity of compressive forces, you are forced to one of the following:
1 - Suspend the load (from above) rather than support it (from below)
2 - Use some other material in compression to take the weight
3 - Find a way to handle the compressive forces with paper

Options 1 + 2 are not possible, so you have to go with 3.

And, despite what people are saying in that thread, paper can, and does,
handle compressive forces.  How else does a rolled tube work?  The idea
that "the compression force gets distributed and turned into tension" is
meaningless crap - and that was written by someone who teaches this!

The problem is not that paper does not withstand compression.  The problem
is that a flat sheet of paper bends easily - it folds.  More exactly,
paper does not handle torsion along an axis that lies within the paper.

Torsion is the problem.  When do we get torsion?  When the weight pressing
down and the support pushing up do not coincide.  And when does this
happen?  When the weight pressing down does not pass through the paper. 
And why does this make things so hard?  Because paper is thin, so there is
little room for error - the "line of force" that supports the weight must
remain inside the thin sheet of paper.

This is why a cylinder buckles when it is dented - because at the dent the
forces supporting the weight pass outside the sheet of paper.

So to build a paper structure that is strong under compression we must do
two things: make sure that the weight passes down through the paper;
ensure that this remains the case.

The second of these requirements makes the structure stable.  And the most
obvious way to achieve it is to make the structure rigid - a rigid
structure will not flex, and the weight will remain pressing down through
the paper.

Hence the need for corrugations and cylinders.

Andrew