Re: arch versus cantilever

["John S. Denker" <jsd@MONMOUTH.COM>]

Karl Trappe wrote:
....
> Regarding the cantilever/arch issue.   Two such "cantilever-like"
> structures placed as mirror images of each other result in the classical
> architectural arch, or the bridge without pillars in the water.

I am astonished to read this.

Is there any evidence for this claim whatsoever?

Here are some classical architectural arches:
  http://207.228.125.45/France/reims_france_arch.htm

http://www.people.virginia.edu/~dhm1h/images/RomanRuins/orage-arch1-700_JPG.html
  http://www.goldenboughmusic.com/news/Roman_arch.jpg

http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_115833AA_Med.jpg

http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_121241AA_Lg.jpg

http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_122013AA_Lg.jpg

I assert each such arch doesn't _look_ anything like a pair of
one-sided cantilevers.  I further assert that physically,  it
doesn't _work_ anything like a pair of one-sided cantilevers.

Observable fact:  Look at the ratio of the span to blocksize
in this arch:

http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_115833AA_Med.jpg
then calculate the number of blocks it would take to do
this using the one-sided cantilever principle.  This is
not my opinion;  this is plain high-school physics.

I'm willing to listen if anybody has any real evidence
(i.e. something beyond mere opinion) to support the
"arch=cantilever" notion.  But so far I haven't seen any.

====


BTW a useful reference on cantilevers is:
  http://mathworld.wolfram.com/BookStackingProblem.html
including a closed-form expression for how far
you can reach using N blocks.