Re: Physics of an arch?

[brian whatcott <inet@INTELLISYS.NET>]

At 15:39 7/29/00 -0400, Peter Schoch wrote:
> One of my colleagues ... wants to better understand the
> mechanics/physics of a classical arch built out of stone.  How do they
> stay together, some of them without mortar?  What is the significance of
> the keystone, and how do the forces interact to make it important....

> Thanks,
> Peter Schoch
> SCCC
The arch has been used since antiquity. One of the earliest visible uses
was as a cover over drains. One could argue then, that the arch bridge
was the archetypal form (sorry  :-)

 A vestigial arch form is the trangular form. It illustrates a property
 of all arches. When two stones lean together at a peak, there is not only
 the down acting force due to the stones' weight, but a thrusting force
acting outwards which transmits the side force holding the stones' peak
in place.

 In this example, you will see there is no keystone. To generalize, there
is no special role played by the center stone of a multistone arch.
 Another lesson to be drawn by the triangular form is that the faying
(touching) surfaces need to have some resistance to sliding over each other,
which aids the stability of the arrangement.

  The mechanics aspect of the arch focusses on the force which opposes
the weight. Near the middle of the arch, the slope of the joint which is
usually arranged to be radial has to provide a force component in the
upwards direction. A triangle of forces easily shows that it is a
considerable horizontal force that together with a vertical force
comprising half the weight of the remaining arch section above, composes
the actual force acting on the sides of the stone.

 This illustrates another virtue of the arch with traditional materials
like stone: they are strong in compression, but weak in tension.
(Much the same is true of modern concrete beams). The arch needs no
tension members at all.
    The other material choice of antiquity was wood. This has a much
better ratio of tensile to compressive strength, so wooden rafters
were often chosen to handle the bending loads where loads of both types
appear.

 Unfortunately, life forms have long evolved to process wood into weaker
forms, so the classical ikons of monumental buildings are usually now
roofless. (This feature was not particularly helped by the practice of
piling a dirt cover over classical roof covers.) A more durable means
of preserving the roof cover was a covering of some durable metal like
copper or lead: but then and now, these materials are attractive to
thieves and portable.



brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!