Stone Strength and Failures

So - one of the ways in which la Torre Pendente is in danger of failing is not that that it will tip over (although it could perhaps have done that eventually) but that the stones on the downward, more highly stressed side, could fail. In particular, the marble blocks on the outer skin that takes much of the load are in danger of failing.

(Another good example is the piece of marble from which Michelangelo's David is constructed. Why was it so tricky to sculpt without producing failures?)

Structural dangers in Michelangelo's David: http://dsc.discovery.com/news/briefs/20040524/michelangelo.html

Structural analyses and modelling of the 17-foot (5.2metres) naked marble man established that cracks in the left ankle, discovered in the 19th century, arose through traction from a slight forward inclination of the statue while it stood in the Piazza Signoria. Most probably, the reason was subsidence beneath the base following a flood in 1844.

The conservation team concluded that the stresses on the ankles are "within the limits of safety" provided the statue, which weighs more than six tons, remains upright. Concern remains on how David would cope with an earthquake.

"The restorers gave David a cosmetic job, without treating his real problem: its stability. Given its tall, narrow shape, the weakness of the stone on the right leg, and the structure of the nineteenth-century high base, a minor earthquake or a terrorist attack could make the statue fall, and break into a thousand pieces.

"It has already happened to a statue at the Met four years ago. The marble Adam which was made around the same time as the David by Tullio Lombardo is still in the lab," Beck told Discovery News.

So how does stone fail? And why could these stones fail if they are loaded mostly in compression?

For Tuesday or Thursday I think we should fail some stone in class! In this way, people can see that even when loaded in compression or shear, stone tends to fail along the directions of maximum corresponding stress. (Need to explain why this is so.)

Of course, it will have to be a rather weak stone...

Bring some pieces of chalk and prepare stone crushers (pliers with soft materials on the jaws to avoid stress concentrations) to class. Let people try crushing in compression, shearing in torsion and pulling and bending.

Refer back to the notes on ArchDomeConstruction and MasonryStability regarding the negligible-tensile-strength assumption and what it means. This will become relevant when trying to clear up the mystery of Brunelleschi's "sandstone chain" (or was it limestone?) to contain the hoop stresses in the dome of the cathedral at Florence.

-- MarkCutkosky - 10 Jan 2005; updated 12 aprile a Firenze.

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