Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: arch versus cantilever



How easily astonished John seems to be. I thought I'd have to wait a
lifetime...The hyperbole about "plain high school physics" was especially
illucidating. But, "if anybody has any real evidence", please send it to
John ASAP.

Regarding the arches presented in the URL's, they do, indeed rely on
keystones rather than weight/mass distribution to create their structure.

My remark was that you can take two cantilever-like structures and create
an arch. That arch can support considerable weight, and can even be used
to make a bridge.

But, John, as an archictect, realizes that there is no room for symantics
in describing arches.

If you want to look at the physics as done in the classroom, which I
understood was what Paul sought, you might prefer the references for the
tower of Lire, rather than those for examples of architectural arches.
They are, of course, discussed in the section of physics related to center
of mass, rather than resolution of forces. Karl..smile, John..

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_11
5833AA_Med.jpg

http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_12
1241AA_Lg.jpg

http://nrich.maths.org/~smt32/album/10_morroco/3_mouley/Morocco2001_0310_12
2013AA_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_11
5833AA_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.

Dr. Karl I. Trappe Desk (512) 471-4152
Lecture Demonstration Office Office (512) 471-5411
Physics Department, Mail Stop C-1600 Home (512) 264-1616
The University of Texas at Austin
Austin, Texas 78712-1081