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© 2006-2013 Andrew Cooke (site) / post authors (content).

Paper Structures

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

Paper in Compression

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

Date: Wed, 26 Nov 2008 13:04:20 -0300 (CLST)

I am not sure I explained very well above; one more attempt...

Weight "presses down" through a structure.  If you hold a heavy object
over your head, you can feel that weight pushing down through your arms,
body and legs to the floor.

But if you hold a weight out straight to one side you feel something else:
you feel the weight pulling your arm down.  The weight isn't pushing down
through your body, it's pulling your arm down.  Your shoulder starts to
ache - you want to let your arm fold down to your side.

Something very similar happens to paper.  When the weight passes exactly
down a vertical piece of paper there is no problem (believe me - it will
make more sense in a minute).

But when the weight doesn't press *exactly* down through the paper, the
paper bends or folds instead.  Just like your arm wants to fold down when
a weight is to one side.

You can see this by carefully rolling a sheet of paper into a tube (use
scotch tape so it doesn't unroll).  If you stand the tube on the floor, on
one end, you should be able to balance something on the other end.  The
weight passes down the walls of the tube.

But if you put a dent in the tube then it will collapse.

Why?

Because as soon as there is a dent the weight at that part isn't passing
exactly down through the paper.  Instead, the weight is making the paper
fold, so that the dent gets bigger.  And as the dent gets bigger the
weight makes it fold more.  And so it gets worse and worse (very quickly)
and collapses.

A dent is similar to holding your arm out - the weight is no longer
passing down in a straight line.

Andrew

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