Re: Why does measuring tape bend one way?
From: Nick Rouse (nick_at_rouse.123isp.co.uk)
Date: 02/05/05
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Date: 4 Feb 2005 18:15:46 -0800
"CWatters" <colin.watters@pandoraBOX.be> wrote in message news:<lKOMd.3324$7j5.286768@phobos.telenet-ops.be>...
> <lemo5@optonline.net> wrote in message
> news:1107533159.730098.166440@z14g2000cwz.googlegroups.com...
> > Why does metal measuring tape easily bend one way but not the other?
>
> and before anyone replies that it's due to the curve... _How_ does the curve
> give it these properties?
>
> I think it's because the curve makes it easier to _twist_
I think it is because the initial bend in the direction that it
normally coils up in tries to put the centre line of the tape
into tension and the edges into compression. Because the
tape is thin compared to the length over which the compressive
force is acting and the edge is unconstrained it very soon
becomes unstable and buckles. I suspect (but can't pin down
exactly why) an outward (flattening) buckle is energetically
more favourable than an inward curling buckle.
In the classical analysis of a column failing under compression
you compare the energy needed to deform the column into a
slight curve with the energy released by the compressive force
moving as the deformation allows the force to move. If the
deformation energy is less than energy released by the compressive
force the deformation continues. Different deformation modes have
different ratios of these two forces and the most energetically
favoured will dominate but nearly all modes tend to show a greater
ratio of released energy to deformation energy the greater the degree
of deformation and conversely the ratio falls to zero for the initial
infinitesimal deformation. This implies that once a column starts to
buckle it will collapse catastrophically but that the initiation of
deformation is dependant on imperfections to take it to the
point at which the deformation starts to grow . The greater the
compressive force the smaller the imperfection that will take the
system to the point where further deformation is energetically
favourable. Generally the simplest modes of deformation involving
the fewest changes in curvature will be the most energetically
favourable. Complex modes with many curve changes will require
a greater compressive force before imperfections bring such modes
to the critical point.
To return to the tape, It takes only a small bending force before imperfections
allow the tape to start flattening and once the tape has started to flatten it
becomes ever easier to flatten it more and easier to bend it in its coiling
direction.
If you try to bend the tape in the opposite direction you are trying to
put the edges in tension and the centre into compression. because the
centre part of the tape is constrained on both sides, the lowest energy mode
of deformation will still be a complex one, probably involving the formation
of a dimple with an S shaped curve in two directions. It will therefore take
a greater bending force before likely imperfections make such deformations
likely
Nick Rouse
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