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Both solid spire tips and hollow spire bodies, regarded as circular cones, can be considered using simple statics (applied, as an example, to the spire at Hemingbrough). Solid spire tips are at risk from wind forces if they are too short (or too light), but they may be stabilised by hanging weights from them inside the spire. Hollow spire bodies are at risk if they are too thin-walled (or too light); they can also be analysed with membrane techniques, which show that tensile stresses start to develop in their bases at about half the wind force that would be needed to overturn them. Spires often have eight sides; however, circular cones are demonstrably good models for them that conform reasonably well with an empirical safety rule. This is so even for decorative spires like that of Freiburg, made from open stonework tracery. Because of their low centres of gravity, spires can lean at visually alarming angles before overturning; again this can be shown by simple statics or membrane techniques. This tilting (and indeed twisting) is more common in timber than in stone, because timber spires can suffer through differential shrinkage of their frameworks.
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