Re: Why does measuring tape bend one way?

From: Edward Green (spamspamspam3_at_netzero.com)
Date: 02/11/05 

Date: 10 Feb 2005 16:55:50 -0800

Nick Rouse wrote:

> 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

I owe you a slight apology. I had previously said that Philip Holman's
reply was the only one which seemed plausible and about on the right
level. I don't know about "on the right level", but your discussion is
very nice, and suggests the tools to take the thing a step beyond
intuition!

Now, to add something, I notice in actual experiment that slowly
bending a length of measuring tape in the hard direction causes a
slight flattening in the area of subsequent buckling, followed by a
sharp snap to the buckled position; slowly releasing the bending moment
eventually causes a snap back to the unbuckled shaped. The system is
bistable (obviously), and exhibits hysterisis.

Relevant Pages

  • When Knuth and I were young - Part 3
    ... At the time, this was a revolutionary concept, and NCR felt pressured ... by an ex-navy electronics chief, and a young woman borrowed from the ... while he made the connections and turned on the power switch. ...
    (comp.lang.asm.x86)
  • Re: Why does measuring tape bend one way?
    ... >> Why does metal measuring tape easily bend one way but not the other? ... In the classical analysis of a column failing under compression ... slight curve with the energy released by the compressive force ... moving as the deformation allows the force to move. ...
    (sci.physics)
  • Re: [Clax86list] When Knuth and I were young - Part 1
    ... The CPU in the CDC 6600 had a 10 MHz clock. ... I/O was handled by 10 separate "peripheral processing units", or PPUs. ... Hydra 895, CDC's most advanced mainframe disk, only did 3 MB/s. ...
    (comp.lang.asm.x86)
  • Re: Question on Cobol Move statement - mixed move x to zzz9.
    ... Then MOVE 3 TO WS-FORMAT-4 instead.... ... nobody uses REDEFINES anymore. ... Aside from shared memory bits, ...
    (comp.lang.cobol)
  • Re: GO TO HELL.
    ... You could gain a few white hair... ... or you could go bald on that :-) ... Old timer Cobol coders do that. ... then 2nd grade, ...
    (comp.lang.cobol)