A new equilibrium solution for masonry spiral stairs. (1st July 2021) - Angelillo, Maurizio; Olivieri, Carlo; DeJong, Matthew J.
Highlights: A regime of equilibrium in compression can be found both for monolithic and non-monolithic spiral stairs. The loads are carried, in equilibrium, by a number of compressed lines: linear arches. The equilibrium solution can take into account permanent and accidental loads distributed or concentrated. The stress level inside the stairs is estimated parametrically by changing their aspect ratio. The new equilibrium solution that allows a compression regime for a given vertical load over a given planar or non-planar curve shape, is called Linear Arch Static Analysis. Abstract: This paper considers stone or brick staircases that appear to cantilever from an exterior wall as they spiral upward. A new equilibrium solution is proposed that does not rely on cantilevering from the wall. Unlike previously proposed membrane solutions, the proposed new analytical solution, called Linear Arch Static Analysis (LASA), is based on a 1D no-tension filament, or a set of such 1D filaments (that -by following Rankine's definition- we call space linear arches), and is therefore particularly efficient. Each space linear arch represents a compressive element that spirals down the staircase, simulating a compressive force that is transferred through and between each stair. In addition, the equilibrium of each filament requires the contribution of horizontal uniaxial compressive forces which are provided by the exterior wall support and transmitted horizontally through each stair. The lines of action of such uniaxial compressive stresses are entirely contained inside the masonry. The new solution is applied to both circular and elliptical stairs to demonstrate the new equilibrium solutions, but also to quantify and highlight the magnitude of resulting forces and the efficiency of the solution. The effect of geometric variations on internal forces are also explored to evaluate the efficiency and feasibility of various potential stair geometries.