## Thursday, September 6, 2012

### Corrugations and ribs in a masonry arch

In a masonry roman arch (or round arch) the arch may be viewed as a horizontal half-cylinder.   The arch is subject to stresses from gravity which are represented by a catenary thrust line, as discussed several times on this blog (here, here and here).   Various techniques may be employed to strengthen the round arch against the thrusting forces of its catenary load.

A cylinder may –in turn- be seen as a shell structure, as also discussed several times on this blog.  An arch as a shell structure is seen as a curved plate.  A plate may employ various techniques to provide it with greater flexural rigidity.

Flexural rigidity, or increased structural stiffness, may be achieved by providing corrugations in the plate.  Corrugations are defined as a series of parallel ridges or furrows.  One example of this which most people are familiar with is corrugated cardboard.

Corrugated  paper (also called pleated) was patented in England in 1856 and was used as a liner for tall hats; tall hats which are nothing more than cylinders.

Another example of cylinders being made stronger by corrugations are the tin cans which employ corrugations to give them greater rigidity.

As I discussed earlier in this blog, I have developed triangular block to make cylinders and arches.  There are two types of triangular blocks used to assemble into a cylinder, or section of cylinder, or arch.  I call these two types of blocks “flat” and par” because one has a flat top, and the other has abutting edges which are parallelograms.

Each of these blocks has a “tilt” to it which departs from the vertical.  If the triangle which describes these blocks is lower and wider (more obtuse of a triangle) then the amount of “tilt” or departure from vertical is increased.  If the triangle which describes these blocks is taller and skinnier (more acute of a triangle) then the amount of “tilt” is decreased.

The tilt or “leaning” of the triangular blocks used to assemble a cylinder have the effect of introducing corrugations, or ribs into the arch.  These corrugations or ribs have the much desired and beneficial effect of increasing the flexural rigidity and strength of the resulting arch.  The effect is the same as the corrugations in a tin can, as shown above.  The structure is made much stronger and more robust to any applied force; whether it is gravity, wind loads, hurricanes, tornadoes or impacts.

This feature is a simple artifact of the design of these block, it is something of a “happy accident.”  Thus masonry arches made with corrugations are much stronger, more robust and better than a simple, rounded arch.