Equilibrium formulation of masonry helical stairs

Abstract

In this paper the lower bound theorem of limit analysis for No-Tension materials is applied to study the equilibrium of spiral vaults, modeled as continuous unilateral membranes. The most efficient approach to the equilibrium of a thin shell is the covariant representation proposed by Pucher and adopted in the present study. Statically admissible singular stresses in the form of line or surface Dirac deltas and lying inside the masonry, are taken into account. The unilateral restrictions require that the Airy stress function representing the stress, be concave. The case study is a helical stair with a central pillar in Sanfelice Palace in Naples, whose structure is a tuff masonry spiral vault. The maps of the stress corresponding to two different stress functions and the safety factors in the two cases are provided.