Static analysis of a Guastavino helical stair as a layered masonry shell

An analytical structural study of general helicoidal timbrel shells is presented. The study is concerned in particular with Guastavino staircases based on a circular planform. Such stairs are composite masonry structures formed by a two or three layers of tiles disposed in a herringbone-pattern. The analysis is based on the assumption that the material is unilateral, namely a No-Tension material in the sense of Heyman; in particular the safe theorem of Limit Analysis is employed. In the spirit of the safe theorem the structure is stable if a statically admissible stress field can be constructed; for the unilateral material here employed, singular stress fields, that is stress concentrated on surfaces (membranes) or lines (arches) are allowed. The statically admissible stress fields that are constructed, combining membrane stresses and 3d diffuse uniaxial stresses, are purely compressive and balance transverse loads either uniformly distributed or localized. A simple order-of-magnitude calculation confirm that bending and torsion resistance is small compared to the structural demand, and that a purely compressive membrane equilibrium stress field is required; the level of compressive stresses required to balance the load is below the limit compressive threshold.