The Equilibrium of Helical Stairs Made of Monolithic Steps

An analytical structural study of helicoidal masonry stairs made of monolithic steps, built in torsionally at their external boundary, and supported on an inner rib, is presented. The results of the analysis are applied in particular to the case study of the triple helical stair of San Domingos de Bonaval. The analysis is based on the assumption that the material of the rib 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 employed here, singular stress fields, that is stress concentrated on lines (arches) are allowed. The statically admissible stress fields here constructed, combining concentrated stresses and 2D diffuse uniaxial stresses, are purely compressive and balance the transverse loads.